Det r oi t T ypeAut omat i on I nt h i schap t erwec on si dert hea ut omat ede qui pmentu sedi nt hepr oc es s i ngofdi s c r e t epar t si n l ar gev ol umes .Theequi pmenti sof t eni nt hec onfi gur at i onofmec hani c al l yi nt egr at edt i o wl i nes , c ons i s t i ngofanumberofwor k s t at i onst hatper f or mt hepr oc es si ngoper at i onsont hel i ne.Thes e fl owl i nesar ec al l edt r ans f ermac hi nesort r ans f erl i nes .Themet hodsus edt ot r ans por tpar t s be t weens t at i onsar ee xami nedi nt hi schapt eraswel l ast heot herf eat ur est hatc har ac t er i z et hes e p r o du c t i o ns y s t e ms ms .Wee mph mp as i z ema c hi n i n go pe r a t i o nsa st h et y pi c al p r o ce ssc ar r i e do uto nt h es e s y s t e ms ms ,al t houg ht h ea ut omat edfl owl i nec onc ep ti sus edi nav a r i e t yofi n dus t r i esandpr o ces s es .
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AUTOMATED FL FLOW LI LINES
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Anaut oma t edfl owl i nec on si s t sofs ev e r al mac hi ne sorwor k s t at i o nswh i c har el i nk edt oge t herb y wor khandl i ngde vi c est hatt r ans f erpar t sbet weent hes t at i ons .Thet r ans f erofwor kpar t soc c ur s aut omat i c al l yandt hewor k st at i onscar r youtt hei rs pec i al i z edf unc t i onsaut omat i c al l y .Thefl owl i ne c anbes y mb mb ol i z edass h owni nFi g ur e4. 1us i n gt h es y mb mb ol sp r e s en t e di nT ab l e4. 1 .Ar a w wo r kp ar t en t er soneendo ft hel i n ean dt hepr o ces s i ngs t epsar eper f o r meds eq uen t i al l yast h epar tmo v es f r om ones t at i ont ot hene xt .I ti spos si bl et oi nc or por at ebuffers t or agez onesi nt ot hefl owl i ne,ei t her atas i ngl el oc at i onorbe t weenev er ywor k s t at i on.
I ti sal s opos s i bl et oi nc l udei ns pec t i ons t at i onsi n t hel i net oaut omat i c al l yper f or mi nt er medi at ec hec k sont hequal i t yoft hewor kpar t s .
Ma nual s t a t i onsmi mi gh ta l s obel oc at e dal o ngt hefl owl i net o pe r f or mc er t ai no per at i onswh i c har edi ffic ul toru nec onomi c alt oa ut omat e .Th es ev a r i ousf eat ur e sof mec hani z edflo wl i n eswi l l bedi s c us s edi ns ubs eq uents ec t i o ns .Aut omat edflo wl i ne sar ege ne r al l y
t hemos tappr opr i at emeansofpr oduc t i oni nc as esofr el at i v el yst abl epr oduc tl i f e;hi ghpr oduc t de man ma d,whi c hr equi r e shi ghr at e sofp r oduc t i o n;an dwhe r et h eal t e r nat i v eme t hodofmanuf ac t ur e woul di n vol v eal ar gel aborc ont ent .Theobj ec t i v esoft heus eoffl owl i neaut omat i onar e,t her ef or e: T or edu cel ab orc os t s T oi nc r eas epr oduc t i onr at es T or edu cewo r k i npr o ces s T omi n i mi z ed i s t a nc e smo v e db et we enop er a t i o ns T oac hi ev es pec i al i z at i onofoper at i ons T oac hi ev ei nt egr at i onofoper at i ons Al t houghFi gur e4. 1s ho wst hefl owpat t er nofoper at i onsi nas t r ai ghtl i ne,t her ear eac t ual l yt wo ge ner al f o r mst h att hewor kflo wc ant a k e.Thes et woc on figur at i onsar ei nl i neandr o t ar y . I nl i net ype Thei nl i nec onfi gur at i onc ons i s t sofas equenc eofwor k st at i onsi namor eor l es sst r ai ght l i ne ar r angement .Theflowofwor kc ant ak e af ew90°t ur ns ,ei t herf orwor kpi ec er eor i ent at i on,f ac t or y l a youtl i mi t at i ons ,oro t herr eas ons ,a nds t i l l qual i f yasas t r ai ght l i nec onfi gur at i on.Ac ommon pa t t er nofwor kfl ow,f ore x ampl e,i sar ec t angul a rs h ape,wh i c hwoul da l l o wt hes ameo per at ort o l o adt hes t ar t i ngwor k pi e cesandunl oadt hefi ni s he dwor k pi e ces .Ane x amp l eo fa ni nl i net r an sf er mac hi neus edf ormet al c ut t i ngoper at i onsi si l l us t r at edi nFi gur e4. 2. Rot a r yt y pe I nt her o t ar yconfi gur at i on,t hewor kpar t sar ei nde x edar oundac i r c ul art abl eordi al .Thewor k s t at i onsar es t at i onar yandus ual l yl oc at edar oundt heout s i deper i pher yoft hedi al .Thepar t sr i deon t her ot at i ngt abl eandar er egi s t er edorpos i t i oned,i nt ur n,ateac hs t at i onf ori t spr oc es si ngor as s embl yoper at i on.Th i st y peo fe qui pmenti sof t enr ef e r r edt oasani nde xi ngmac hi n eordi al i n de x ma ch i nea ndt h ec o nfi gu r at i oni ss ho wni nFi g ur e4 . 3 . Sel e ct i on Th ec h oi c eb et we ent h et wot y p esde pe nd so nt h ea pp l i c a t i o n.Th er o t a r yt y pei sc ommo nl yl i mi t e d t os mal ma l erwor k pi ec esandt of ewers t at i ons .Ther ei sgener al l yno tasmu muc hfl ex i bi l i t yi nt hedes i gnof t her ot ar yconfi gur at i on.Forex ampl e,t hedi al t y pedes i gndoesnotl endi t s el ft opr ov i di ngf orbuffer s t or agec apac i t y .Ont heot herhand,t her o t ar yc onfi gur at i onus ual l yi n vol v esal ower c os tpi ec eof equi pmentandt y pi c al l yr equi r esl es sf ac t or yfloors pac e.
Thei nl i nedes i gni spr ef er abl ef orl ar ger wo r k p i e c esa ndc a na c c ommo da t eal a r g ern umb ero fwo r k s t a t i o ns .Th en umb ero fs t a t i o nso nt h e di ali nde xmac hi nei smor el i mi t edduet ot hes i z eoft hedi al .I nl i nemac hi nesc anbef abr i c at edwi t h
t hemos tappr opr i at emeansofpr oduc t i oni nc as esofr el at i v el yst abl epr oduc tl i f e;hi ghpr oduc t de man ma d,whi c hr equi r e shi ghr at e sofp r oduc t i o n;an dwhe r et h eal t e r nat i v eme t hodofmanuf ac t ur e woul di n vol v eal ar gel aborc ont ent .Theobj ec t i v esoft heus eoffl owl i neaut omat i onar e,t her ef or e: T or edu cel ab orc os t s T oi nc r eas epr oduc t i onr at es T or edu cewo r k i npr o ces s T omi n i mi z ed i s t a nc e smo v e db et we enop er a t i o ns T oac hi ev es pec i al i z at i onofoper at i ons T oac hi ev ei nt egr at i onofoper at i ons Al t houghFi gur e4. 1s ho wst hefl owpat t er nofoper at i onsi nas t r ai ghtl i ne,t her ear eac t ual l yt wo ge ner al f o r mst h att hewor kflo wc ant a k e.Thes et woc on figur at i onsar ei nl i neandr o t ar y . I nl i net ype Thei nl i nec onfi gur at i onc ons i s t sofas equenc eofwor k st at i onsi namor eor l es sst r ai ght l i ne ar r angement .Theflowofwor kc ant ak e af ew90°t ur ns ,ei t herf orwor kpi ec er eor i ent at i on,f ac t or y l a youtl i mi t at i ons ,oro t herr eas ons ,a nds t i l l qual i f yasas t r ai ght l i nec onfi gur at i on.Ac ommon pa t t er nofwor kfl ow,f ore x ampl e,i sar ec t angul a rs h ape,wh i c hwoul da l l o wt hes ameo per at ort o l o adt hes t ar t i ngwor k pi e cesandunl oadt hefi ni s he dwor k pi e ces .Ane x amp l eo fa ni nl i net r an sf er mac hi neus edf ormet al c ut t i ngoper at i onsi si l l us t r at edi nFi gur e4. 2. Rot a r yt y pe I nt her o t ar yconfi gur at i on,t hewor kpar t sar ei nde x edar oundac i r c ul art abl eordi al .Thewor k s t at i onsar es t at i onar yandus ual l yl oc at edar oundt heout s i deper i pher yoft hedi al .Thepar t sr i deon t her ot at i ngt abl eandar er egi s t er edorpos i t i oned,i nt ur n,ateac hs t at i onf ori t spr oc es si ngor as s embl yoper at i on.Th i st y peo fe qui pmenti sof t enr ef e r r edt oasani nde xi ngmac hi n eordi al i n de x ma ch i nea ndt h ec o nfi gu r at i oni ss ho wni nFi g ur e4 . 3 . Sel e ct i on Th ec h oi c eb et we ent h et wot y p esde pe nd so nt h ea pp l i c a t i o n.Th er o t a r yt y pei sc ommo nl yl i mi t e d t os mal ma l erwor k pi ec esandt of ewers t at i ons .Ther ei sgener al l yno tasmu muc hfl ex i bi l i t yi nt hedes i gnof t her ot ar yconfi gur at i on.Forex ampl e,t hedi al t y pedes i gndoesnotl endi t s el ft opr ov i di ngf orbuffer s t or agec apac i t y .Ont heot herhand,t her o t ar yc onfi gur at i onus ual l yi n vol v esal ower c os tpi ec eof equi pmentandt y pi c al l yr equi r esl es sf ac t or yfloors pac e.
Thei nl i nedes i gni spr ef er abl ef orl ar ger wo r k p i e c esa ndc a na c c ommo da t eal a r g ern umb ero fwo r k s t a t i o ns .Th en umb ero fs t a t i o nso nt h e di ali nde xmac hi nei smor el i mi t edduet ot hes i z eoft hedi al .I nl i nemac hi nesc anbef abr i c at edwi t h
abui l t i ns t or agec apabi l i t yt os moot mo houtt heeffec tofwor kst oppagesati ndi v i duals t at i onsand ot heri r r egul ar i t i es .
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METHODSOFWORKPARTTRANSPORT
Th et r a ns f e rme ch an i s mo ft h ea ut o ma ma t e dfl o wl i n emu s tn oto nl ymo mo v et h ep ar t i a l l yc omp l e t e dwo r k par t soras s embl i esbet weenadj ac ents t at i ons ,i tmus tal s oor i entandl oc at et hepar t si nt hec or r ec t po si t i onf o rp r o ces s i ngate ac hs t at i on.Thegen er al me t hodsoft r ans po r t i ngwor kpi ec esonfl ow l i nescanbec l as si fi edi nt ot hef ol l owi ngt hr eec at egor i es: 1. Cont i nuoust r ansf er 2. I nt er mi t t en to rs y nc hr onoust r ans f er 3 . As y n c hr o no uso rp owe r a nd f r e et r a ns f e r Thes et hr eec at egor i esar edi s t i ngui s hedb yt het y peofmot i ont hati si mpar t edt ot hewor kpi ec eb y t het r ans f ermec hani s m.Themo m. mos tappr opr i at et y peoft r ans por ts y st em f oragi v enappl i c at i on d ep en dso ns u c hf a c t o r sa s: •
Thet y peso fop er at i o nt obeper f or med
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Thenu mbe mb ro fs t a t i o nsont hel i ne
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Th ewe i g hta nds i z eo ft h ewo r kpa r t s
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Whe t hermanu al s t at i onsar ei nc l u dedont hel i ne
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Pr oduc t i onr at er equi r ement s
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Bal anc i ngt hev ar i ouspr oc es st i mesont hel i ne
Bef or edi s c us si ngt het hr eet y pesofwor kt r ans por ts y st em,wes houl dt r yt oc l ar i f yapos si bl es our c e ofc on f u si on.Thes et r a ns f ers y s t emsar eus edf o rb ot hp r oc es s i n gandas s embl yoper at i ons .I nt he c as eofa ut omat i cas s embl yma chi nes ,wear er e f er r i ngt ot hemec hani s mst hatt r ans po r tt he pa r t i al l yc omp l e t edas s emb l i esbe t weenst a t i o ns ,no tt hef eedmec hani s mst h atpr es entne w c omponent st ot heas sembl i esatapar t i c ul ars t at i on.Thede vi c est hatf eedandor i entt he c omponent sar en or mal l yani n t egr alpa r to ft hewor k s t a t i on .Wet a k eac l o serl ookatt hes ed ev i c es i nCh ap t e r7wh enwedi s c us sa ut o ma t i ca s se mbl yi nmo r ede t a i l . Wi t ht h e Cont i nuoust r a ns f e r c on t i n uo usme t h odoft r an sf er ,t hewor kpar t sar emo v edc ont i nu ou sl yatc on st an ts peed.Thi s r equi r est hewor kheadst omo vedur i ngpr oc es si ngi nor dert omai nt ai nc ont i nuousr egi s t r at i onwi t h t hewor kpar t .Fo rs omet y pe sofop er at i o ns ,t hi smo v emento ft h ewor khe adsdur i n gpr o ces s i ngi s notf eas i bl e.I twoul dbedi ffic ul t ,f orex ampl e,t ous et hi st y peofs ys t em onamac hi ni ngt r ans f erl i ne be caus eofi n er t i apr obl emsduet ot hes i z eandwei g htoft hewor khea ds .I no t herc as es ,c ont i nu ous t r ans f erwoul dbev er ypr ac t i c al .Ex ampl esofi t sus ear ei nbev er agebot t l i ngoper at i ons ,pac kagi ng, ma nu al a s s emb l yo pe r a t i o nswh er et h eh uma no pe r a t o rc a nmo v ewi t h‘ t h emo v i n gfl o wl i n e,a nd r el at i v el ysi mpl eaut omat i cas sembl yt as ks .I ns omebot t l i ngoper at i ons ,f ori ns t anc e,t hebot t l esar e t r ans por t eda r oundac ont i nuo us l yr o t a t i ngd r um.Be v er agei sdi s c ha r gedi nt ot h emo vi ngbo t t l e sb y s pout sl oc at edatt hedr um’ sper i pher y .Theadv ant ageoft hi sappl i c at i oni st hatt hel i qui dbe ver age i sk ep tmo v i ngatast e adys pe edandhenc et he r ear enoi ne r t i apr o bl e ms . Cont i nu oust r an sf er s y st emsar er el at i v el yeas yt odes i gnandf abr i c at eandc anac hi e veahi ghr at eof pr oduc t i on. Ast h en ames ug ge s t s ,i nt h i sme t h odt h ewor k pi e ce sar e I nt er mi t t entt r ansf er t r ans por t edwi t hani nt er mi t t entordi s cont i nuousmo t i on.Thewor k s t at i onsar efi x edi npos i t i onand t hepar t sar emo vedbe t weens t at i onsandt henr egi s t er edatt hepr operl oc at i onsf orpr oc es si ng.Al l wor kpar t sar et r ans por t edatt hes amet i meand,f ort hi sr eas on,t het er m“ s ync hr onoust r ans f er s y st em”i sal s ous edt odes cr i bet hi smet hodofwor kpar tt r ans por t .Ex ampl esofappl i c at i onsoft he i nt er mi t t entt r ans f erofwor kpar t scanbef oundi nmac hi ni ngoper at i ons ,pr es swor k i ngoper at i ons o rp r o gr e s si v ed i e s,a ndme ch an i z eda s se mbl y . Mo s to ft h et r a ns f e rme ch an i s msr e v i e we di n Sec t i on4. 3pr o vi det hei nt er mi t t entors ync hr onoust y peofwor kpar tt r ans por t . Asynchr onous Thi ss ys t em oft r ans f er ,al s or ef er r edt oas a“ p ower andf r ees y st em, ”al l o wseac hwor k t r a nsf er pa r tt omo v et ot h ene x ts t at i onwh enp r o ces s i ngatt hecur r ents t at i onhasbe enc ompl e t ed.Eac h pa r tmo v esi nde pen de nt l yo fo t herpar t s .Henc e,s omepar t sa r ebei ngpr oc es s ed ont hel i n eatt he s amet i met ha to t her sar ebe i ngt r a ns po r t edbe t weenst at i on s.As y nc hr on ou st r an sf ers y s t emsoff er t heoppor t uni t yf orgr eat erfl ex i bi l i t yt handot heot hert wos ys t ems ,andt hi sfl ex i bi l i t yc anbeagr eat adv ant agei ncer t ai nci r c ums t anc es .I npr oc es sst or ageofwor kpar t sc anbei nc or por at edi nt ot he a sy n ch r o nou ss y s t e mswi t hr e l a t i v ee as e .Po we r a nd f r e es y s t e msc ana l s oc omp en sa t ef o rl i n e
ba l an ci ngpr obl emswhe r et h er ea r es i gn i fi c antdi ff er en cesi npr o ces st i me sbe t weens t at i ons . Par al l els t at i onsors ev er al s er i esst at i onscanbeus edf ort hel ongeroper at i ons ,ands i ngl es t at i ons c anbeu sedf ort hes hor t ero per at i o ns .Ther ef or e,t hea v er agepr od uc t i onr at esca nbe a pp r o x i ma t e l yeq ua l i z ed .As y nc hr o no usl i n esar eo f t e nu se dwh er et h er ea r eo neo rmo r ema nu al l y op er a t eds t at i on sandc y c l et i mev ar i a t i onswoul dbeap r obl em onei t hert hec ont i nuousor s y nc hr o no ust r a ns po r t s y s t e ms .L ar g erwo r kp ar t sc a nb eh an dl edont h ea sy n ch r on ou ssy s t e ms .A di s adv ant ageoft hepo wer andf r ees y st emsi st hatt hec y cl er at esar egener al l ysl owert hanf ort he ot hert y pes . et r ansf ersyst em i ssomet i mesdesi gnedt oaccommodat esomesor tof Pa l l e tfixt ur esTh pal l etfi xt ur e.Wor kpar t sar eat t ac hedt ot hepal l etfi xt ur esandt hepal l et sar et r ans f er r edbet ween s t at i ons ,c ar r y i ngt hepar tt hr oughi t ssequenc eofoper at i ons .Thepal l etfi xt ur ei sdes i gneds ot hati t c anbec on v eni e nt l ymo v ed,l o cat ed ,a ndc l a mpedi np os i t i ona ts uc c es s i v es t a t i o ns .Si nc et hepar t i sac cur at el yl oc at edi nt hefi xt ur e,i ti st her ef or ec or r ec t l ypos i t i onedf ore ac hoper at i on.I naddi t i ont o t heobv i ousadv ant ageofc on veni entt r ans f erandl oc at i onofwor kpar t s ,ano t heradv ant ageofpal l et fi xt ur esi st hatt he yc anbedes i gnedt obeus edf orav ar i et yofs i mi l arpar t s . Theo t he rme t hodofwor kpar tl oc at i o nan dfi x t u r i ngdoe sn otu sepa l l e t s .Wi t ht hi sme t ho d,t he wor k par t st hems el v esar ei ndex edf r om s t at i ont os t at i on.Whenapar tar r i v esatas t at i on,i ti s aut omat i c al l ycl ampedi npos i t i onf ort heoper at i on. Theobv i ousbenefi toft hi st r ans f ermet hodi st hati ta voi dst hec os tofpal l etfi xt ur es 3
TRANSFERMECHANI SMS
Th er ea r ev a r i o ust y pe so ft r a ns f e rme c ha ni s msus edt omo v ep ar t sbe t wee ns t a t i o ns .Th es e mec hani s msca nbegr oupedi nt ot wot y pes :t ho seus edt op r o vi d el i n eart r a v el f ori nl i n emac hi ne s, an dt hos eu sedt opr o v i der o t a r ymo t i o nf o rd i a li nde x i n gmac hi nes . Li neart r ansf ermechani sms We will explain the operation of three of the typical mechanim! the wal"in# $eam tranfer $ar ytem,t hepower edr ol l erc on ve yors y st em,andt hec hai ndr i v ec on ve yors y st em.Thi si sno ta
c omp l e t el i s t i n go fa l lt y pe s,b uti ti sar e pr e se nt a t i v es amp l e . WAL KI NG BEAM SYSTEMS.Wi t ht h e wal k i ngbeam t r ans f ermec hani s m,t hewor kpar t sar el i f t edupf r om t hei rwor k s t at i onl oc at i onsbya t r ans f erbarandmo vedonepos i t i onahead.t ot hene xts t at i on.Thet r ans f erbart henl ower st he par t si nt ones t swhi c hpos i t i ont hem mor eac cur at el yf orpr oc es si ng.Thi st y peoft r ans f erde vi c ei s
i l l us t r at edi nFi gur e4. 4.
POWEREDROLLERCONVEYOR
SYSTEM.Th i st y p eo fs y s t e mi su se di nge ner a ls t o ckha ndl i ngsy s t e msaswe l l a si nau t o ma t e dfl o w l i n es .Thec on v ey o rc a nbeu sedt omo v epansorp al l e t spo ss es s i ngfl atr i d i ngs ur f ac esTher ol l er s c anbep ower edb yei t heroft womec ha ni s ms .Thefi r s ti sab el tdr i v e ,i nwhi c hafl atmo v i ngb el t beneat ht her ol l er spr ov i dest her ot at i onoft her ol l er sbyf r i c t i on.Ac hai ndr i v ei st hes ec ondc ommon mec hani s mu sedt opo wert her o l l er s .Po wer edr ol l erc on v ey or sar ev e r s at i l et r a ns f ers y s t ems bec aus et he yc anbeus edt odi v er twor kpal l et si nt owor k s t at i onsoral t er nat et r ac ks .Wedi s cus s r ol l erc on v ey ors y s t e msi nCha pt er1 4. CHAI NDRI VECONVEYORSYSTEM.Fi g ur e4 . 5i l l u s t r a t e st h i st y p eo ft r a ns f e rs y s t e m.Ei t h era c hai norafl ex i bl es t eel bel ti sus edt ot r ans por tt hewor kc ar r i er s .Thec hai ni sdr i v enbypul l ey si n ei t heran“ ov er andunder ”c onfi gur at i on,i nwhi c ht hepul l e yst ur naboutahor i z ont al ax i s ,oran “ ar oundt hec or ner ”c onfi gur at i on,i nwhi c ht hepul l ey sr ot at eaboutav er t i c alax i s . Thi sgener alt y peoft r ans f ers y st em c anbeus edf orc ont i nuous ,i nt er mi t t ent ,ornons y nc hr onous mo v ementofwo r kpa r t s .I nt henons y nc hr onousmo t i on ,t hewor kpar t sar epu l l edb yf r i c t i onorr i de onanoi lfi l m al ongat r ac kwi t ht hec hai norbel tpr o vi di ngt hemov ement .I ti snec es sar yt opr o vi de s omes or toffi nal l oc at i onf ort hewor kpar t swhent heyar r i v eatt hei rr es pec t i v es t at i ons .
Rot ar yt r ansf ermechani sms
Ther ear es ev er almet hodsus edt oi nde xac i r c ul art abl eordi al atv ar i ousequal angul arpos i t i ons c or r e spondi ngt owo r k s t at i onl oc at i ons .Thos edes c r i b edbel o w ar eme antt obear e pr es ent at i v e r at hert hanac ompl et el i s t i ng.
RACKANDPI NI ON.Thi smechani sm i ssi mpl ebut i sno tc ons i der edes pec i al l ys ui t edt ot hehi ghs peedoper at i onof t enas soc i at edwi t hi nde xi ng mac hi ne s.Thed ev i c ei spi c t ur edi nFi gur e4. 6an du sesap i s t ont odr i v et h er a ck ,whi c hc aus est h e pi ni ongearandat t ac hedi ndex i ngt abl et or ot at e.Ac l ut c horot herdev i c ei sus edt opr ov i der ot at i on i nt hedes i r eddi r ec t i on. RA TCHETANDPAWL .Th i sd r i v eme c ha ni s mi ss h owni nFi g ur e4 . 7 .I t so pe r a t i o ni ss i mp l ebu t s ome whatun r e l i abl e,o wi ngt owea ran ds t i c k i n gofs ev er a loft hecomponent s .
GENEVAMECHANI SM.Thet wopr ev i ous me c ha ni s msc on v e r tal i n ea rmo t i o ni n t oar o t a t i o na lmo t i o n.Th eGe ne v ame c ha ni s mu s esa c ont i nuous l yr o t at i ngdr i v ert oi nde xt het abl e,aspi c t ur edi nFi gur e4. 8.I ft hedr i v enmemberhassi x s l ot sf oras i x s t at i ondi al i nde xi ngmac hi ne,eac ht ur noft hedr i v erwi l l c aus et het abl et oadv anc e ones i x t hofat ur n.Thedr i v eronl yc aus esmo vementoft het abl et hr oughapor t i onofi t sr o t at i on. Foras i x s l ot t eddr i v enmember ,120°o fac ompl et er ot at i onoft hedr i v eri sus edt oi nde xt het abl e. Theot her240°i sdwel l .Foraf our s l o t t eddr i v enmember ,t her at i owoul dbe90°f ori nde xand270° f ordwel l .Theus ual numberofi ndex i ngsperr ev ol ut i onoft het abl ei sf our ,fi v e,s i x ,andei ght . EXAMPLE4. 1 Le tuse xami net heo per a t i onofas i x s l o t t e dGene v amec hani s m.Su ppos et hatt hedr i v e rr o t at esat 6r pm.De t er mi net hecy c l et i meoft hei nde x i ngmac hi n e,t hepr o ces st i me,an dt h et i mespe nte ac h c yc l ei ni ndex i ngt het abl et ot henex twor kpos i t i on. Sol ut i on: Asi ndi c at edabo ve,f oras i x s l o t t edGene vamec hani s m,t hedr i v ers pends120°o fi t sr o t at i ont o i nde xt het abl e,andt her emai ni ng240°o fr ot at i onc or r es pondt odwel loft het abl e.At6r ev / mi n,t he c y cl et i meoft hei nde xi ngmac hi nei s10s .Thepor t i onoft hi scy c l et i mede vo t edt opr oc es si ng( dwel l oft h ei n de xi ngt abl e)i s24 0/ 360 =0. 667 .Th i sc or r es pondst o6. 67s .Thei n de xi ngt i mei s12 0/ 36 0 =0. 333 × 10s =3. 33s.
CAM MECHANl SMS.Var i ousf or msofca m mec hani s m,a ne x ampl eofwhi c hi si l l us t r at edi nFi gur e4. 9,pr o v i dep r ob abl yt h emos tac c ur at ean d r el i abl emet hodofi nde xi ngt hedi al .The yar ei nwi des pr eadus ei ni ndus t r ydes pi t et hef ac tt hatt he c os ti sr el a t i v el yhi ghc ompar edt oal t e r nat i v emec ha ni s ms .Thecam c anbede si gnedt ogi v ea
v ar i et yofv el oc i t yanddwel l c har ac t er i s t i c s.
%
&UFFE' STO'A(E
Aut omat edflowl i nesar eof t enequi ppedwi t haddi t i onal f eat ur esbe y ondt hebas i ct r ans f er me ch ani s msa ndwor k s t a t i o ns .Fo re x amp l e ,t h ei d eaofu si n gabu ffe rs t o r a geca pa ci t ybe t we en s t at i onswasi nt r oduc edi nSec t i on4. 1.I ti sno tunc ommonf orpr oduc t i onfl owl i nest oi nc l ude s t or agez onesf orc ol l ec t i ngbank sofwor kpar t sal ongt hel i ne.Onee x ampl eo ft heus eofs t o r age z oneswoul dbet woi nt er mi t t entt r ans f ers y st ems ,eac hwi t houtan ys t or agec apac i t y ,l i nk edt oge t her wi t hawor kpar ti nv ent or yar ea.I ti spos si bl et oc onnec tt hr ee,f our ,orev enmor el i nesi nt hi s manner .Ano t here x amp l eofwo r kpar ts t or ageonfl o wl i n esi st hea sy nc hr on ou st r an sf erl i ne.Wi t h t hi ss ys t em,i ti spos si bl et opr o vi deabankofwor kpar t sf orev er ys t at i onont hel i ne. Ther ear et wopr i nc i pa lr eas onsf ort heu seofbu ffe rs t or agez ones .Thefi r s ti st or e duc et heeff ec tof i ndi v i dual s t at i onbr eak downsont hel i neoper at i on.Thec ont i nuousori nt er mi t t entt r ans f ers ys t em ac t s a sas i n gl ei nt egr at edma chi ne .Whenbr eak do wnso c curatt hei n di v i d ual s t at i onso rwhe n pr e v ent i v emai nt en anc ei sappl i edt ot hemac hi ne,p r oduc t i o nmus tbeha l t ed .I nman yc as es ,t h e pr o po r t i ono ft i met h el i n es pen dsou to fop er at i o nc anb es i gn i fi c ant ,per hapsr eac hi ng50 %o r mor e.Someoft hecommonr easonsf orl i nest oppagesar e:
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Tool f ai l ur esort ooladj us t ment sati ndi v i dualpr oc es si ngs t at i ons
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Sc h ed ul e dt o ol c h an ge s
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Def e ct i v ewor kpa r t sorc omponen t sata ss embl yst at i on s,whi c hr equi r et hatt h ef e ed mechani sm becl ear ed
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Fe edho ppe rn eed st ober e pl en i s he da ta na s se mb l ys t a t i o n
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Li mi ts wi t c horo t here l ec t r i c al mal f unc t i on
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Mec hani c alf ai l ur eoft r ans f ers ys t em orwor k st at i on
Wh enabr e ak d ownoc c u r so na na ut o ma t e dfl o wl i n e,t h ep ur p os eoft h eb uff ers t o r a gez o nei st o al l o w apor t i onoft hel i net oc ont i nueoper at i ngwhi l et her emai ni ngpor t i oni ss t oppedandunder r epai r .Fore xampl e,as s umet hata20s t at i onl i nei sdi v i dedi nt ot wos ec t i onsandconnec t edb ya par t ss t or agez onewhi c haut omat i c al l ycol l ec t spar t sf r om t hefi r s ts ec t i onandf eedst hem t ot he s ec onds ec t i on.I fas t at i onj am wer et oc aus et hefi r s ts ec t i onoft hel i net os t op,t hes ec onds ec t i on c oul dc ont i nuet ooper at easl ongast hes uppl yofpar t si nt hebufferz onel as t s .Si mi l ar l y ,i ft he s ec onds ec t i o nwer et os hutdo wn,t h efi r s ts ec t i o nc oul dc ont i nuet oope r at ea sl on gast her ei s r oom i nt hebuff erz onet os t or epar t s .Hopef ul l y ,t hea ver agepr oduc t i onr at eont hefi r s ts ec t i on woul dbeaboutequal t ot hatoft hes ec onds ec t i on.Bydi v i di ngt hel i neandus i ngt hes t or agear ea, t hea v er agepr oduc t i onr at ewoul dbei mpr o vedo vert heor i gi nal20s t at i onfl owl i ne.Aquant i t at i v e anal y s i soft heeff ec tofaddi ngbufferi n vent or yz oneswi l l bepr es ent edi nChapt er5.Fi gur e4. 10 i l l us t r at est hec as eoft wopr oc es si ngl i nessepar at edb yas t or agebuff er .
Th es e c on dr e as o nf o ru s i n gs t o r a geo nHo wl i n es i st os moot houtt heeff ec t sofv ar i at i onsi nc y cl et i mes .Thes ev ar i at i onsoc curc i t herbe t ween s t at i onsor ,i nt hec as eoffl owl i neswi t honeormor emanuals t at i ons ,t he yc anoc c urf r om c y cl et o c y cl eatt hes ames t at i on.T oi l l us t r at et hes ec ondc as e,s uppos et hatwear ec ons i der i ngan
as s embl yl i neonwhi c hal l t h es t at i onsar eme chani z ede x ce pto ne.Theman ua ls t a t i o nr equi r est he op er a t ort op er f or m anal i gn mento ft woco mponen t sandt h et i mer equi r edt e ndst ov ar yf r om c y c l e t ocy c l e.Fort het r an sf ers y s t em i nt hi sl i ne ,wemu stc hoo sebe t weenas y nc hr o nou ss y s t em wi t hno p ar t ss t o r a gec ap ac i t yan da na sy n ch r o no uss y s t e m wh i c ha l l o wsa“ fl oa t ”o fp ar t sah ea do fe ac h s t at i on.Toi l l us t r at et hi sdi ffer enc ei noper at i on,l etuscons i dert hef ol l owi ngex ampl e. EXAMPLE4. 2 As sumet hatweha vec ol l ec t eddat aont heoper at i onandf oundt hef ol l owi ngdi s t r i but i onof op er a t i ont i mesf o rat o t al of10 0c y c l e s:7s ;t wooc c ur r enc es ,or2 9;8s ;10%:9s ;18 %;10s ;3 8%; 1 1s ;2 0% a nd12s ;1 2%.Th i sgi v e sanav e r a geof1 0s .I ft h i sma nu al o pe r a t i o nwe r eus edont h e s y nc hr o no usmac hi ne.t h el i newo ul dha v et obes etupwi t hc y c l et i meof12st oal l o wt heo per a t or t i met ofi ni s hal l as sembl i es .Thi swoul dgi v eapr oduc t i onr at eof300uni t s / hf r om t hel i ne.I ft he c y cl et i me wer eadj us t edt o11s,t hecy c l er at ewoul di nc r eas et o327perhour .butt heoper at or wo ul db eu na bl et oc omp l e t e1 2% o ft h ea s se mb l i e s .Th us ,t h ea c t u al p r o du ct i o nr a t eo fc o mp l e t e d as s embl i e swou l dbeonl y288un i t s / h.I ft h ec y c l ét i mewer ed ec r ea sedt o10s ,t hec y c l er at ewoul d i n c r e as et o3 60p erh ou r .Ho we v er ,t h eo pe r at o rwo ul db eu na bl et oc omp l e t et h ea s se mb l i e s r eq ui r i ng11sand12s .Th eac t ual p r oduc t i onr a t ewoul ds uff eradec r eas et o245u ni t s / h . Wi t ht h eas y nc hr onoust r ans f e rs y s t e m.t hel i n ec oul dbear r anged t oc ol l ec taban ko fwor kpar t s i mme di a t el ybe f or eandaf t ert h eman ual s t at i on.Thus ,t heoper at o rwoul dbeal l o we dar a ngeof t i mest ocompl e t et h eal i gnmentpr oc es s .Asl o ngast h eo per a t or ’ sa v er a get i mewer ecompa t i bl e wi t ht hec y cl et i meoft het r ans f ers y st em,t hefl owl i newoul dr uns moot hl y .Thel i nec y cl et i mec oul d b es e ta t1 0sa ndt h ep r o du ct i o nr a t ewo ul dbe36 0g oo da ss e mb l i e spe rh our . Thed i s adv ant a ge so fb uff ers t or a geonfl owl i ne sa r ei nc r eas edf ac t o r yfl o ors pac e.hi gh eri n pr oc es si n vent or y ,mor emat er i alhandl i ngequi pment ,andgr eat erc ompl e xi t yoft heo v er al lfl owl i ne s y s t e m.Th eb en efi t so fb uff ers t o r ag ea r eof t e ng r e ate no ught omo r et h anc omp en sa t ef o rt h es e d i s ad v an t a ge s.
)
%*) +ONT'OL FUN+TIONS
Co nt r o l l i n ga na ut o ma t e dfl o wl i n ei sac omp l e xp r o bl e m,o wi n gt ot h es he ern umb ero fs e qu en t i al s t epst hatmus tbec ar r i edout .Ther ear et hr eemai nf unc t i onst hatar eut i l i z edt oc ont , l t heoper at i on
ofanaut omat i ct r ans f ers y st em.Thefi r s toft hes ei sanoper at i onal r equi r ement ,t hes ec ondi sa s af et yr equi r ement ,andt het hi r di sdedi c at edt oi mpr ov i ngqual i t y . 1. Sequencecont .Thepur pos eoft hi sf unc t i oni st oc oor di nat et hes equenc eofac t i onsof r ol t het r ans f ers y s t em andi t swor k s t at i ons .Thev ar i ousac t i v i t i esoft heaut omat edfl owl i ne mus tb ec ar r i edo utwi t hs pl i t s ec ondt i mi nga nda cc ur ac y .Oname t alma chi ni ngt r an sf er l i ne,f ore xampl e,t hewor kpar t smus tbet r ans por t ed,l oc at ed,andcl ampedi npl ac ebef or e t h ewo r khe adscanbegi nt of eed .Seq uen cec ont r o li sbas i ct ot heo per at i onoft hefl owl i n e. 2. Sa sf unc t i onens ur est hatt het r ans f ers y st em doesno toper at ei n an f e t ymoni t or i ng.Thi u ns a f eo rh az a r d ou sc on di t i o n.Se ns i n gd ev i c esma ybea dd edt oma k ec er t a i nt h att h e c ut t i ngt ool s t at usi ssat i s f ac t or yt oc ont i nuet opr oc es st hewor kpar ti nt hec as eofa mac hi ni ngt y pet r ans f erl i ne.Ot herc hec ksmi ghti nc l udemoni t or i ngc er t ai nc r i t i c als t epsi n t h es eq uenc ec on t r ol f u nc t i ont omak esur et hatt h es es t ep sha v ea l l bee npe r f or me da ndi n t hec or r ec tor der .Hy dr aul i corai rpr es sur esmi ghtal s obec hec kedi ft hes ear ec r uc i al t ot he ope r at i o nofau t omat edflo wl i nes . 3. Qua hi r dc ont r olf unc t i oni st omoni t orc er t ai nqual i t yat t r i but esoft he l i t ymoni t or i ng.Thet wor kpar t .I t spur pos ei st oi dent i f yandpos si bl yr ej ec tdef ec t i v ewor kpar t sandas sembl i es . Thei n spec t i onde vi c esr eq ui r edt oper f o r m qual i t ymon i t or i ngar es ome t i me si nc or por at e d i nt oex i s t i ngpr oc es si ngs t at i ons .I not herc as es ,s epar at es t at i onsar ei nc l udedi nt hel i nef or t hes ol epur pos eofi ns pec t i ngt hewor kpar t . I ti spos si bl et oex t endt henot i onofqual i t ymoni t or i ngandt oi nc or por at eac ont r ol l oopi nt ot hefl ow l i neasi l l us t r at edi nFi gur e4. 11.Ani ns pec t i ons t at i onwoul dbeus edt omoni t orc er t ai nqual i t y c har ac t er i s t i c soft hepar tandt of eedbac ki nf or mat i ont ot hepr ec edi ngwor k st at i onssot hat a dj u s t me nt si nt h ep r o c es sc o ul db ema de . Thet r adi t i on al meansofc on t r ol l i ngt hes equenc eofs t e psont het r an sf ers y s t em h asbeent ou se el ec t r omec hani c al r el a ys .Rel a ysar eempl o yedt omai nt ai nt hepr operor derofac t i v at i ngt hewor k heads ,t r ans f ermec hani s m,ando t herper i pher al dev i c esont hel i ne.Howev er ,o wi ngt ot hei r c ompar at i v el yl ar ges i z eandr el at i v eunr el i abi l i t y ,r el ay shav el os tgr oundt oot herc ont r oldev i c es , suchaspr ogr ammabl econt r ol l er sandcomput er s.Thesemor emoder ncomponent soffer oppor t uni t i esf orahi gherl ev elofc ont r olov ert hefl owl i ne,par t i c ul ar l yi nt hear easofs af et y moni t or i ngandqual i t ymoni t or i ng.
Conv ent i onal t hi nk i ngont hec ont r ol oft hel i nehas be ent os t opope r at i onwhenamal f un ct i onoc c ur r ed .Whi l et h er ear ec er t ai nma l f unc t i o ns r epr es ent i nguns af econdi t i onst hatdemandshut downoft hel i ne,t her ear eot hers i t uat i onswher e s t oppageoft hel i n ei sno tr equi r edandper hap sno te v end es i r ab l e.Fore x ampl e,t ak et hec as eofa f e edme c ha ni s mo na na ut oma t i ca ss e mb l yma ch i n et h atf a i l st of e edi t sc omp one nt .As s umi ngt h at
t hef a i l ur e sar er andom andi nf r equent ,i tma ybeb et t e rt oc ont i nu et oop er at et h emac hi nea ndl o ck ou tt heaff ec t edas s embl yf r om f ur t heroper at i on s.I ft heas s embl ymac hi n ewer es t oppe d, pr oduc t i onwoul dbel os tatal l ot hers t at i onswhi l et hemac hi nei sdown.Dec i di ngwhet heri ti sbet t er t os t a yi noper at i onors t opt hel i nemus tbebas edont hepr obabi l i t i esandec onomi c soft he par t i c ul arc as e.Thepoi nti st hatt her ear eal t er nat i v ec ont r ol s t r at egi est oc hoos ebet ween, i n s t a nt a ne ou sc o nt r o la ndme mo r yc o nt r o l . 1. I .Thi smodeofc ont r ol s t opst heoper at i onoft hefl owl i nei mmedi at el y ns t a nt a ne ousc ont r ol whenamal f unc t i oni sdet ec t ed.I ti sr el at i v el ysi mpl e,i nex pens i v e,andt r oubl ef r ee. Di agnos t i cf eat ur esar eof t enaddedt ot hes y st em t oai di ni dent i f y i ngt hel oc at i onandc aus e oft het r oubl et ot heoper at ors ot hatr epai r sc anbequi c kl ymade.Ho we ver ,s t oppi ngt he mac hi ner es ul t si nl os sofpr oduc t i onf r om t heent i r el i ne,andt hi si st hes ys t em’ sbi gges t dr awback. 2. Memor .I nc ont r as tt oi ns t ant aneousc ont r ol ,t hememor ys ys t em i sdes i gnedt o ycont r ol k eept hemac hi neoper at i ng.I twor k st oc ont r olqual i t yand/ orpr o t ec tt hemac hi neby pr e v ent i ngs ubs eque nts t at i on sf r o m pr oc es s i ngt hep ar t i c ul a rwor kpar tan db ys egr eg at i ng t h epa r ta sd ef ec t i v eatt heendoft hel i ne.Thep r emi s eu ponwhi c hmemo r y t y pec ont r oli s bas edi st hatt hef ai l ur eswhi c hoc curatt hes t at i onswi l l ber andom andi nf r equent .I f , ho we ver ,t hes t at i onf ai l ur esr es ul tf r om c aus e( awor kheadt hathasgoneoutofal i gnment , f ore x ampl e)a ndt e ndt or ep eat ,t h ememor ys y s t e m wi l l no ti mpr o v epr oduc t i onbut ,r at h er , degr adei t .Thefl owl i newi l l c ont i nuet ooper at e,wi t ht hec ons equenc et hatbadpar t swi l l c ont i nuet obepr oduc ed.Fort hi sr eas on,ac ount eri ss ome t i mesus eds ot hati faf ai l ur e oc cur satt hes ames t at i onf ort woort hr eec ons ec ut i v ec y cl es ,t hememor yl ogi cwi l l c aus e t hemac hi net os t opf orr epai r s .
DESI GNANDFABRI CATI ONCONSI DERATI ONS Wh enama nu f a c t u r i n gfi r md ec i d est h ats o mef o r mo fa ut o ma t e dfl o wl i n er e pr e s en t st h eb es t me t hodofpr oduc i ngapar t i c ul arwor kpar toras sembl y ,t her ear et henas er i esofs pec i fi c at i onst hat mus tbede ci ded.I nd es i gni ngandbui l di n ganaut o mat edfl o wl i n e,s omeoft hede t ai l st oc on si der ar et hef ol l owi ng: •
Whe t hert h efl owl i nei st obeen gi n eer e di n h ous eo rb yamac hi net oo lbu i l der
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Si z e,wei ght ,g eome t r y ,andmat er i ali fapr oc es s edwor kpa r t
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Si z e ,we i g ht s ,a ndn umb ero fc o mp on en t si fa na s s emb l y
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T ol er anc er eq ui r e ment s
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T y p ea nds e qu en c eo fo pe r a t i o ns
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Pr oduc t i onr at er equi r ement s
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T ypeoft r ans f ers ys t em
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Me t hodsoffi x t ur i ngan dl oc at i n gwor kpa r t s
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Me t h od so fo r i e nt i n ga ndf e ed i n gc o mp on en t si nt h ec a seofa s se mb l i e s
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Rel i abi l i t yofi ndi v i duals t at i onsandt r ans f ermec hani s ms ,a swel lasov er al l r el i abi l i t yoft he l i ne
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Buffers t or agecapabi l i t y
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Easeofmai nt enance
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Cont r ol f eat ur esdes i r ed
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Fl oors pac ea vai l abl e
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Fl ex i bi l i t yofl i nei nt er msofpos si bl ef ut ur ec hangesi npr oduc tdes i gn
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Fl e xi bi l i t yofl i net oac c ommodat emor et hanas i ngl ewor kpar t
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I ni t i alc os toft hel i ne
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Oper at i onal andt ool i ngc os tf ort hel i ne
I nd ev e l op i ngt h ec on ce ptf o rame ch an i z edfl o wl i n e,t h er ea r et wog en er a la pp r o ac he st h atc a nb e c on si der ed.Thefi r s ti st ous es t anda r dma chi net ool sando t h erp i ec esofpr oc es s i ngequi pme ntat t hewor k s t at i on sa ndt oc on nec tt he m wi t hs t andar dors pe ci al mat er i a lha ndl i nge qui pmen t .The mat er i al handl i nghar d war eser v e sast het r an sf ers y s t em an dmo v es ,f ee ds ,a ndej ec t st hewor k be t weent h es t anda r dma chi nes .Th el i neofma chi ne si ss ome t i me sr ef er r edt oasal i n kl i ne.The i n di v i d ual ma chi ne smus tei t he rb ec apabl eo fop er at i n go nana ut omat i cc y cl eort he ymu stbe manual l yoper at e d.Ther ema yal s obefix t ur i nga ndl oc at i onpr obl emsatt hes t a t i o nswhi c ha r e di ffic ul tt os ol v ewi t houts omef or m ofhumanas s i s t anc edur i ngt hec y cl e.Afi r m wi l l of t enpr ef ert he l i n kl i neb ec au sei tc anbemad eupf r o m mac hi net ool st h atar eal r e ad yi nt hepl a nt ,t hes ema chi ne t o ol sc anb er e us e dwh ent h ep r o du ct i o nr u ni sfi ni s he d,a ndt h er ei sl e s sd eb ug gi nga nd ma i n t e na nc e.Th es efl o wl i n esc ana l s ob ee ng i n ee r e db yp er s on ne lwi t h i nt h efi r m,p er h ap swi t ht h e ai dofmat er i al handl i ngex per t s .Thel i mi t at i onoft hes efl owl i nesi st hatt he yf av ors i mpl erwor k pi ec e s ha pesa ndsma l l ers i z ess i nc et hewor khand l i ngequi pmenti sl es ss oph i s t i c at edandmo r ege ner a l pur pos e.Gr eat erf ut ur eus eofi ndus t r i alr obot sasmat er i al handl i ngdev i c eswi l l i nc r eas et he at t r ac t i v enes soft hel i nkl i ne.Thi st y peoffl owl i nei sus edi ns uc hpr oc es sesaspl at i ngandfi ni s hi ng oper at i ons ,pr es swor k i ng,r ol l i ngmi l l oper at i ons ,gearmanuf ac t ur i ng,andav ar i et yofmac hi ni ng
oper at i ons . Thea l t er na t i v eappr oa cht ode v el opi nga naut oma t edl i nei st ot u r nt hep r obl em o v ert oamac hi ne t oolbui l ders pec i al i z i ngi nt hef abr i c at i onoft r ans f erl i nes ,as sembl ymac hi nes ,orot herfl owl i ne equi pment .Us i ngt hec us t omer ’ sbl uepr i nt sands pec i fi cat i ons ,t hebui l derwi l l s ubmi tapr opos al f or t hel i ne.T ypi c al l y ,s ev er al mac hi net oolbui l der swi l l beas k edt omak epr opos al s .Eac hpr opos ed de si gnwi l l beb as edo nt h emac hi nec ompon en t sc omp r i s i ngt hebu i l de r ’ spr o du ctl i n easwel last h e i n gen ui t yande xpe r i e nc eo ft h ee ngi neerpr ep ar i ngt hep r opo sal .
On ceap ar t i c ul arpr op os al i sac c ep t ed,t hema chi ne t oolbui l derwi l l pr oc eedwi t ht hefi nal det ai l eddes i gn.Ther es ul t i ngmac hi newi l l ut i l i z ea“ bui l di ngbl oc k”pr i nc i pl e.Thati s ,t hes pec i al i z edfl owl i ne,des i gnedt opr oduc et hec us t omer ’ spar t i c ul ar pr o du ct ,wi l l beco ns t r uc t edoutofs t a ndar dc omponent s .Thes es t and ar dcomponent sc ons i s toft h e ba se ort r ans f e rs y s t e m,a ndwor kh ead sf orp er f or mi ngt hev a r i ou spr oc es s i n gora ss embl y oper at i ons .Thes es t andar dc omponent swi l l bef abr i c at edi nt ot hes pec i alc onfi gur at i onr equi r edf or t hec us t o mer ’ spr oduc t .Se v er a le x amp l eso ft h es es t and ar dt r an sf er l i nec omponent sar epi c t ur edi n Fi gur es4. 16and4. 17.Forme t al c ut t i ngt r ans f erl i nes ,t hewor kheadsc ons i s toft hef eed me ch ani s m,s p i n dl e ,a ndp owe rs o ur c e .Th ewor khe ad smu s tt h enb efi t t e dwi t hs p ec i a lt o ol st o c ar r you tt hepar t i c ul arpr oc es s .The sewo r kheadsdono tha v eaf r ameorwor k t abl e.I n st ead ,t he y ar eat t ac hedt ot het r an sf ers y s t e mf r a me,whi c hh asbe ens pe ci al l yad apt edf o rt h ewor kpa r t .Whe n afl owl i nehasbeenf abr i c at edus i ngt hi sbui l di ngbl oc kpr i nc i pl e,i ti ssomet i mesr ef er r edt oasa un i t i z edfl owl i ne .Th es t a ndar dma chi net ool c omponent sal l got og et he ra nda ctasas i ngl e mec hani c alun i t .
Hi gherpr oduc t i onr at esar egener al l ypos si bl ewi t h uni t i z edc ons t r uc t i onc ompar edt ol i nkl i nes .Al s o,l es sfl oors pac ei sr equi r edbec aus et heuni t i z ed l i n esar et y pi c al l ymuc hmor ec ompac t .Th ehi g herc os tofuni t i z edeq ui pmentmak e si ts ui t a bl eo nl y f o rl on gp r o duc t i o nr u nsandonp r o duc t sno ts ubj e ctt of r e quentd es i gnc hanges .Equ i pment ob sol es c enc ebec ome sadan geri ft hes et wor equi r ement sar en otme t .Appl i c at i on soft hi st y peof fl owl i nec ons t r uc t i onar ef oundi nt r ans f erl i nesf ormac hi ni ngaut omot i v eengi nepar t sandi n as s embl yma chi n esf orpen s,s mal l h ar d wa r ei t e ms ,el e ct r i c alas s emb l i es ,ands oon.Fi gur e s4. 2, 4. 12,4. 13,4. 14,and4. 15i l l us t r at et hi st y peoffl owl i nec ons t r uc t i on.
AUTOMATI ONFORMACHI NI NG OPERATI ONS T r ans f e rs y s t e msh av ebeende si gnedt oper f or m agr eatv a r i e t yofdi ff er entme t al c ut t i ngpr oc es s es . I nf ac t ,i ti sdi ffic ul tt ot hi nkofmac hi ni ngoper at i onst hatmus tbeex cl udedf r om t hel i s t .T ypi c al appl i c at i onsi nc l udeoper at i onssuc hasmi l l i ng,bor i ng,dr i l l i ng,r eami ng,andt appi ng.Howev er ,i ti s al s of eas i bl et oc ar r youtoper at i onssuc hast ur ni ngandgr i ndi ngont r ans f er t y pes y st ems . Th er ea r ev ar i o ust y p eso fme c ha ni z e da ndau t o ma t e dma c hi n est h atp er f o r m as eq ue nc eo f oper at i onss i mul t aneous l yondi ff er entwor k par t s .Thes ei nc l udedi al i nde xi ngmac hi nes ,t r unni on mac hi nes ,andt r ans f erl i nes .T oc ons i dert hes emac hi nesi nappr o xi mat el yt heor derofi nc r eas i ng c ompl ex i t y ,webegi nwi t honet hatr eal l ydoesnotbel ongi nt hel i s tatal l ,t hes i ngl es t at i onmac hi ne.
Si ngl e s t a t i onma chi ne
Th es eme ch an i z edp r o du ct i o nma ch i n espe r f o r ms e v er a lo pe r a t i on so nasi n gl ewo r kpa r twh i c hi s fi x t ur edi nonepos i t i ont hr oughoutt hec y cl e.Theoper at i onsar eper f or medons ev er aldi ff er ent s ur f ac esbywor khea dsl oc at eda r oundt hepi ec e.Thea v ai l ab l es pa ces ur r o undi ngas t a t i o nar y wo r k pi e cel i mi t st h en umb ero fma ch i n i n gh ea dst h atc anb eu s ed .Th i sl i mi to nt h en umb ero f oper at i onsi st hepr i nc i pal di s adv ant ageoft hes i ngl es t at i onmac hi ne.Pr oduc t i onr at esar eus ual l y l owt omedi um. Rot ar yi ndexi ngmachi ne
T oa chi e v ehi g herr at esofpr odu ct i on,t h er o t ar yi nde x i ngmac hi nep er f or msas equenc e ofmac hi ni ngoper at i onsonse ver al wor k par t ss i mul t aneous l y .Par t sar efix t ur edonahor i z ont al c i r c ul art abl eordi al ,andi nde x edbe t weens uc c es si v es t at i ons .Ane xampl eofadi al i nde xi ng ma ch i nei ss ho wni nFi g ur e4. 1 2.
Tr unni onmachi ne
Thi smac hi ne,s ho wni nFi gu r e4. 13 .us esav er t i c ald r um mou nt edo nahor i z ont a lax i s ,s oi ti sa
v ar i at i onoft hedi al i nde xi ngmac hi ne.Thev er t i c al dr um i sc al l edat r unni on.Mount edoni tar e s ev er alfi x t ur eswhi c hh ol dt hewor k par t sdu r i ngpr oc es s i ng. T r unni onmac hi n es ar emos ts ui t abl ef ors ma l lwor k pi e ces .Thec on figur a t i onoft hemac hi ne,wi t ha v er t i c alr at hert hanahor i z ont ali ndex i ngdi al ,pr o vi dest heoppor t uni t yt oper f or m oper at i onson oppos i J es i desoft hewor k par t .Addi t i onal s t at i onscanbel oc at edont heout s i deper i pher yoft he t nmni oni ft hi si sr equi r ed.Thet r unni ont y pemac hi nei sappr opr i at ef orwor k par t si nt hemedi um pr o du ct i onr ange.
Cent ercol umnmachi ne
Ano t herv er s i onoft hedi ali nde xi ngar r angementi st hec ent erc ol umnt y pe,pi c t ur edi nFi gur e4. 14. I naddi t i ont ot her adi al mac hi ni ngheadsl oc at edar oundt heper i pher yoft hehor i z ont al t abl e,v er t i c al u ni t sa r emo un t e do nt h ec en t e rc ol u mnoft h ema ch i n e.Th i si n cr e as e st h en umb ero fma ch i n i n g op er a t i onst h atc anbepe r f or me dasc omp ar edt ot her egul a rdi ali nd ex i ngt y pe.Thece nt erc ol umn ma c hi n ei sc on s i d er e dt ob eah i g hp r o du c t i o nma c hi n ewh i c hma k e se ffic i e ntu s eo ffl o ors p ac e .
Tr ansf ermachi ne
Themos thi ghl yaut omat edandv er s at i l eoft hemac hi nesi st het r ans f erl i ne,i l l us t r at edi nFi gur es 4. 2and4. 15.Thewor k s t at i onsar ear r angedi nas t r ai ght l i nefl owpat t er nandpar t sar et r ans f er r ed aut omat i c al l yf r om s t a t i ont os t at i on.Th et r a ns f e rs y s t em c anbes y nc hr ono usora sy nc hr on ous , wor k par t scanbet r ans por t edwi t horwi t houtpal l e tfi x t ur es ,buff ers t or agec anbei nc or por at edi nt o t hel i neoper at i oni fdes i r ed,andav ar i et yofdi ffer entmoni t or i ngandc ont r olf eat ur escanbeus edt o managet hel i ne.Henc e,t het r ans f ermac hi neoff er st hegr eat es tfl ex i bi l i t yofan yoft hemac hi nes di s c us s ed.Thet r ans f erl i n ec ana cc ommodat el ar ge rwor k pi ec est h ant her o t a r y t y pei nde x i ng s y s t e ms .Al s o,t henumbe ro fs t a t i o ns ,a ndt he r e f or et h enu mbero fo per a t i ons ,whi c hc anbe i nc l udedont hel i nei sgr eat ert hanf ort hec i r c ul arar r angement .Thet r ans f erl i nehast r adi t i onal l y beenus edf ormac hi ni ngasi ngl epr oduc ti nhi ghquant i t i esov erl ongpr oduc t i onr uns .Mor er ec ent l y , t r ans f ermac hi nesha v ebe end es i gnedf oreas eo fc han geo v ert oal l o ws ev e r ald i ff er entbu ts i mi l a r wor k par t st obepr oduc edont hes amel i ne.Thes eat t empt st oi nt r oduc efl ex i bi l i t yi nt ot r ans f erl i ne
de si gnaddt ot h ea ppeal oft h es ehi ghpr oduc t i onsy s t ems .
PROBLEMS
4. 1.Fo rt heei g ht s l o t t eddr i v enme mberoft heGen ev amec hani s mi nFi gur e4. 8 ,de t er mi net he pr opor t i onofeac hc ompl et er e vol ut i onoft hedr i v ert hatmo t i oni sbei ngi mpar t edt ot hedr i v en me mb er .Ex pr e sst h i si nd eg r e es .Ho w ma nyde gr e esofr o t a t i o nr e pr e se ntd we l l? 4 . 2 .AGe ne v ame ch ani s m wi t has i x s l o t t e dd r i v e nme mb eri su se di nad i a l t y p ea ss e mb l yma ch i n e. Th el o ng es ta s se mbl yop er at i o nt a k ese x ac t l y1st oc o mp l e t e ,s ot h ed r i v e nme mb ermu s tb ei na s t opped( dwel l )pos i t i onf ort hi sl engt hoft i me. ( a)Atwhatr o t at i onal s peedmus tt hedr i v erbet ur nedt oac compl i s ht hi s1sdwel l? ( b)Ho w muc ht i mewi l l ber equi r edt oi nde xt hedi alt ot hene xtpos i t i on? ( c )De t e r mi net h ei d ealp r oduc t i o nr a t eoft heas s embl ymac hi nei fe ac hi nd exo ft h edi alpr o duc esa c omp l e t e dwo r kp ar t .
4. 3.Ac er t a i nt r a ns f e rl i neper f or msas eque nc eo fmac hi ni nga ndas s embl yoper at i ons .Oneoft h e as sembl yoper at i onsneart heendoft hel i nei sper f or medmanual l y .Thedi s t r i but i onofoper at i on t i mesf ort hemanual s t at i oni sgi v eni nt hef ol l owi ngt abl e. Op er a t i o nt i me( s )
Fr e qu en cyo fo c cu r r e nc e( %)
1 5
2 . 7
1 6
6 . 1
1 7
1 2. 1
1 8
2 5. 9
1 9
3 2. 1
2 0
1 0. 9
2 1
6 . 9
_
100. 0
Thes l o wes taut oma t i cs t at i onh asac y c l et i meof18s . ( a)I ft hel i ne us es asy nc hr onous( i nt er mi t t ent )t r ans f ers ys t em,det er mi net hecy cl er at eand ac t ualpr oduc t i onr at eperhouri ft het r ans f ers ys t em wer es ett oi ndexpar t sateac hoft hef ol l owi ng i nt er v al s:onc ee ver y22s .21 s ,20s,19s ,18s .Ti met ak ent omo v epar t si snegl i gi bl e. ( b )I fana sy nc hr on ou spar t st r a ns f ers y s t em wer eu sedo nt hi sl i net oac c umul at eafl oatofpar t s bef or et h eman ual s t at i on ,atwha tc y c l er at es houl dt hes y s t e mb eop er at ed? De t e r mi net h ec or r e spondi n gp r oduc t i o nr at e.
ANALYSI SOFAUTOMATEDFLOW LI NES
I na nal y z i n gt h ep er f o r ma nc eo fa ut o ma t e dfl o wl i n es ,t wog en er a lp r o bl e ma r e asmu s tb e di s t i ngui s hed.Thefi r s ti sr el at edt ot hepr oduc t i onpr oc es sesus edont hel i ne.Fore xampl e, c ons i derat r ans f erl i net hatper f or msas er i esofmac hi ni ngoper at i ons .Ther ei sane xt ens i v ebodyof k no wl edger el at edt ot het heor yan dpr ac t i c eo fme t almac hi ni n g.Thi st ec hnol ogyi nc l u de st he pr opers pec i fi cat i onandus eofc ut t i ngt ool s ,t hemet al l ur gyandmac hi nabi l i t yoft hewor kmat er i al , c hi pc ont r ol ,mac hi ni ngec onomi c s,mac hi net oolv i br at i ons ,andahos tofo t hert opi c s.Man yoft he pr obl emsenc ount er edi nt heoper at i onofamet al c ut t i ngt r ans f erl i near edi r ec t l yr el at edt oandc an besol v edb yt heappl i c at i onofgoodmac hi ni ngpr i nc i pl es .Thesamei st r uef oro t herpr oduc t i on pr o ces s es .I neac ha r e ao fpr oduc t i on,at ec hnol ogyha sde v el o pedaf t erma nyy ear so fr es ear c h an dp r ac t i c al e xp er i e nc ei nt hear ea .Bymak i n gt heb es tu seoft hegi v enpr oc es st e chnol ogy ,e ac h i n di v i d ual wor k s t at i onont hel i nec anbemad et ooper at eato rn ea ri t smax i mum pr o duc t i v e c apabi l i t y .Howev er ,ev eni fi twer epos si bl et ooper at eeac hs t at i oni nanopt i mal wa y ,t hi sdoesnot guar ant eet hatt heo ver al l fl owl i newi l l beopt i mi z ed. I ti swi t ht hi svi ewpoi ntoft heo ver al lfl owl i neoper at i ont hatwei dent i f yt hes ec ondgener alpr obl em a r e ao ffl o wl i n ep er f o r ma nc e.Th i ss ec on da r e ai sc on ce r n edwi t ht h es y s t e msas pe c t sofd es i g ni n g andr unni ngt hel i ne.Nor mal l yas s oc i at edwi t ht heoper at i onofanaut omat edfl owl i nei st hepr obl em ofr el i abi l i t y .Si nc et hel i neof t enoper at esasas i ngl emec hani s m.f ai l ur eofonec omponentoft he mec hani s m wi l l of t enr es ul ti ns t oppageoft heent i r el i ne.Ther ear eappr oac hest ot hi spr obl em t hat
t r ans c endt hema nuf ac t ur i ngp r oc es s esa ti nd i v i du al s t a t i ons .Wha ti st heeff ec toft henumberof wo r k s t a t i o nso nt h ep er f o r ma nc eoft h el i n eHo wmu c hi mp r o v e me ntc a nh eo bt a i n edb yus i n go ne o rmo r eb uff ers t o r a gez on es ?Wh ati st h ee ffe cto fc omp on en tq ua l i t yont h eo pe r a t i o no fa n a ut o ma t e da s s emb l yma c hi n e?Ho w wi l l t h eu s eo fma nu alwo r k s t a t i o nsaff ec tt h el i n e?Th es ea r e q ue s t i o nst h atc a nh ea na l y z e du s i n gas y s t e msap pr o ac h . I naddi t i ont ot her el i abi l i t ypr obl em,anot hers ys t emsdes i gnpr obl em i soneofpr oper l ybal anc i ngt he l i ne.l nl i nebal anc i ng.t heobj ec t i v ei st os pr eadt het ot alwor kl oadasev enl yaspos si bl eamongt he s t at i onsi nt hel i ne.Thepr obl em i snor mal l yas s oc i at edwi t ht hedes i gnofmanualas sembl yl i nes .l t i sal s oac ons i der at i oni naut omat edfl owl i nes ,butt her el i abi l i t ypr obl em us ual l ypr edomi nat esWe wi l l c ons i derl i nebal anc i ngi nChapt er6 .Ther el i abi l i t yoft hel i newi l l bet hepr i nc i pal c onc er noft he pr es entc hapt er .
GENERALTERMI NOLOGYANDANAL YSI S Fl o wl i n ep er f o r ma nc eca nb ea na l y z edb yme an so ft h r eeba si cme as u r e s:a v er a gepr o du ct i o nr a t e , pr opor t i onoft i met hel i nei soper at i ng( l i neeffic i enc y) .andc os tperi t em pr oduc edont hel i ne.We wi l l c onc er nour s el v esi ni t i al l ywi t hfl owl i nest hatpos ses snoi nt er nal buffers t or agec apac i t y . T obegi nt heanal y s i s .wemus tas s umec er t ai nbas i cchar ac t er i s t i c saboutt heoper at i onoft hel i ne. As y nc hr ono ust r ans f e rs y s t em i sas s umed.Pa nsar ei nt r odu cedi n t ot hefi r s twor k s t at i o nan dar e pr oc es sedandt r ans por t edatr egul ari nt er v al st os uc ceedi ngs t at i ons .Thi si nt er v al defi nest hei deal ort heor et i calc yc l et i meTcoft hefl owl i ne.7]i sequal t ot het i mer equi r edf orpar t st ot r ans f erpl us t hepr oc es si ngt i meatt hel onges twor k s t at i on.Thepr oc es si ngt i mesatdi ff er ents t at i onswi l l no tb e t hes ame.Longhol est ak emor et i met odr i l lt hans hor thol es .Ami l l i ngoper at i onma yt ak el onger t hanat appi ngoper at i on.Thes t at i onswhi c hr equi r el es st i met hant hel onges ts t at i onwi l l ha vea c er t ai namountofi dl et i me.Thec omponent sofT car ei l l us t r at edgr aphi c al l yi nFi gur e5. 1.
Bec au seofb r eak do wnsoft hel i ne ,t hea ct u al a v er agepr oduc t i ont i meTpwi l l bel o nge rt h ant hei d eal c y c l et i me.Whenabr eak do wnoc c ur sat an yon es t a t i o n,wea ss umet h att h een t i r el i nei ss hu td own.Le tT sr e pr es entt hea v er aged ownt i me t odi agnoset hepr obl em andmaker epai r swhenabr eakdownoccur s.Si ncet her emaybemor et han on er ea sonwh yal i nei sdo wn,i ti ss ome t i mesco nv e ni entt odi s t i n gu i s hbe t wee nt h edi ff er ent r eas onsbysubs cr i pt i ngt het er m asTdj ,Thes ubs cr i ptj i sus edt oi dent i f yt her eas onf ort he br eak down( e. g. ,t oolf ai l ur e,par tj am,f eedmec hani s m,e t c . ) .Thef r equenc ywi t hwhi c hl i nes t ops perc y cl eoc curf orr eas onji sdenot edb yFj .Mul t i pl y i ngt hef r equenc yFj byt hea ver agedo wnt i me pers t opTdj ,gi v est hemeant i meperc y cl et hemac hi newi l l bedownf orr eas onj .I ft her ei sonl yone r ea s onwh yt h et r a ns f e rma ch i n ema ybedo wn ,t h ea v er ag ep r o du ct i o nt i meTpi sg i v e nb y Theeff ec toft hi sappor t i o neddo wnt i meont hecy c l e t i mei si l l us t r at edi nFi gur e5. 2. I ft her ear es ev e r a lr eas onswh yt hel i nei sdo wnandwewi s ht od i s t i ngui s ha mongt h em,t he a v e r a gepr o du c t i o nt i mebe c ome s I ti spos si bl et hatt her ear ei nt er ac t i onsbet ween s omeo ft h ec au s esofl i n es t o ps .Fo re x a mpl e ,i fwewe r et oi n t r o du c eas c he du l e dma i n t e nan c eo r t oolc hang epr ogr am,t hi swo ul dp r es umet of a v or abl yi nfl ue nc et hef r eq uen cyofunpl anneds t at i on br eakdowns. Oneo ft hei mp or t an tme as ur esofpe r f or man cef orat r an sf erl i nei st hea v er agepr od uc t i onr at eRp. Wemus tdi ff er ent i at ebet weent hi spr oduc t i onr at e,whi c hr epr es ent st heac t ual out putoft he mac hi ne,andt het heor et i c alpr oduc t i onr at e.Theac t ual a ver agepr oduc t i onr at ei sbas edont he a v er a gep r o du ct i ont i meTp: I It hefl owl i nepr oduc esl es st hana100% y i el d,t hi s pr o du ct i onr at emus tbead j us t edf ort hey i el d.Fore x ampl e,i f2 % oft h ewo r kpa r t sar es c r a pped dur i ngpr oc es si ng,t hepr oduc t i onr at ewoul dbe98% oft hatc al c ul at edb yEq.( 5. 3) .Thet heor e t i c al pr oduc t i onr at eoft hefl owl i ne,r ar el yac hi ev edi npr ac t i c e,i scomput edas Themac hi net oolbui l derwi l l us et hi sv al uei n des cr i bi ngt hefl owl i ne,andwi l l s peakofi tast hepr oduc t i onr at eat100% effic i enc y .Unf or t unat el y , t h ema ch i n ewi l l n oto pe r a t i o na t1 00 %e ffic i e nc y .
Thel i neeffic i enc yEi ss i mpl yt hepr opor t i onoft i me t hel i n ei supa ndo per a t i ngWecanc omput ei tasf ol l o ws: Anal t e r nat i v emea sur eo fp er f or man cei st he pr o po r t i ono fd own t i meDont hel i ne: Ce r t a i nl y ,t hedo wnt i mepr op or t i onandt heup t i me p r o po r t i o nmu s ta ddt o1: Th et h i r dme as ur eo ffl o wl i n ep er f o r ma nc ei st h e c os tp eri t em pr oduc ed.Le tCm e qual t h ec os to fr a w mat e r i al sperp r oduc t ,whe r et hepr o duc tr ef er s t ot heuni tofout putf r om t hel i ne.LetCer epr es entt hec os tpermi nut et ooper at et hel i ne.Thi s woul di nc l udel abor ,o ver head,mai nt enanc e,andt heal l oc at i onoft hec api t al c os toft heequi pment ov eri t sex pec t eds er v i c el i f e.Thel as ti t em,c api t alc os t ,wi l l l i k el ybet hel ar ges tpor t i onofCL.The c os to fa nydi s po sa bl et o ol i ngs h ou l db ec o mp ut e do nap erwo r k pi e c eb as i san di ss y mb ol i z edb y C1 .Us i ngt he sec omponent s ,t heg ene r alf or mu l af o rc a l c ul a t i ngt hec os tpe rwo r k pi e ceC,i s Thi sequa t i ond oesno tac c ou ntf ors uc ht h i ngsas y i el dors cr apr at es ,i ns pec t i onc os tas soc i at edwi t hi dent i f y i ngdef ec t i v ei t emspr oduc ed,orr epai r c os tas soc i at edwi t hfi x i ngt hedef ec t i v ei t ems .Ho we ver ,t hes ef ac t or scanbei nc or por at edi nt oEq. ( 5. 8)i naf ai r l ys t r ai ghtf or war dmanner . Wewi l l l e tnr epr es entt henu mb ero fwor k s t at i onsont h efl owl i neandQ wi l l des i g na t et h eq uan t i t y o fwo r kpa r tp r o du c edo fft h el i n e.Q ma yr e pr e se ntaba t c hs i z eo ri tma yme ant h en umbe ro fp ar t s pr o du cedo v eracer t ai nt i meper i od.Wewi l l u sei ti nwhat e v erwa ywefi ndco nv eni ent .Ho we v er ,one no t eofc aut i oni st hi s :Q ma yi nc l udeac er t ai nnumberofdef ec t si ft hefl owl i nehasahabi tofnot pr oduci ng100% goodpr oduct . Lo tusc ons i derane xampl et oi l l us t r at et het er mi nol ogyoffl owl i neper f or manc e. EXAMPLE5. 1 Su pp os et h ata1 0s t a t i o nt r a ns f e rma ch i nei sun de rc o ns i d er a t i o nt op r o du ceac omp on en tu s edi na p ump .‘ Th ei t e mi sc ur r e nt l ypr o du c edb ymo r ec o nv e nt i o na lme an s,b utd ema ndf o rt h ei t em c a nn ot beme t .Thema nuf ac t ur i nge ngi nee r i n gde par t menthases t i mat e dt h att h ei deal c y c l et i mewi l l b eT c =1. 0mi n.Fr om s i mi l art r ans f erl i nes ,i ti ses t i mat edt hatbr eak downsofal l t y peswi l l oc curwi t ha f r equen cy ,F=0. 10b r e ak do wn/ c y c l e,an dt ha tt hea v er agedo wn t i mepe rl i nes t opwi l l b e6. 0mi n. Thes c r a pr at ef ort hecur r entc on v ent i onal pr oc es s i n gme t hodi s5% an dt h i si sc ons i de r e dagood es t i mat ef ort het r ans f erl i ne.Thes t ar t i ngc as t i ngf ort hec omponentc os t s$1. 50eac handi twi l l c os t
$60. 00/ hor$l . 00/ mi nt ooper at et het r ans f erl i ne.Cut t i ngt ool sar ees t i mat edt oc os t$0. 15/ wor kpar t . Us i ngt hef or egoi ngdat a,i ti sdes i r edt oc omput et hef ol l owi ngmeas ur esofl i neper f or manc e: ( a)Pr oduc t i onr at e. ( b )Nu mb ero fh ou r sr e qu i r e dt ome etade ma ndof1 50 0u ni t s / we ek . ( c )L i nee ffic i enc y . ( d )Cos tpe ru ni tp r odu ced. Sol ut i on: ( a )‘ Th ea v er agepr od uc t i ont i meperp i ec ec anbec al c ul at edf r om Eq.( 5. 1) . Thea v er agepr od uc t i onr at ef ort hel i n ewoul dbe de t er mi nedb yEq.( 5. 3) . Ho we ver ,c or r ec t i ngf ort hes c r apr at eof5%,t he ac t ualpr oduc t i onr at eofgoodpoduc t si s ( b )T oc o mp ut et h en umb ero fh ou r sr e qu i r e dt o p r o du c e1 50 0u ni t s / we ek( wea s s umet h att h i sme an s1 50 0g oo du ni t spl u ss c r a pr a t h ert h an1 50 0 wi t h5% s c r a pi nc l uded) ,wedi v i det hepr oduc t i onr at eof35. 625uni t s / hi nt ot he1500uni t r eq ui r e ment:
( c )Thel i neeffic i enc yi sf oundbyt ak i ngt her at i ooft hei dealc y cl e t i met ot hea ver agepr oduc t i v et i me,ac c or di ngt oEq.( 5. 5) .
Thepr opor t i ondo wnt i mei sd et er mi nedbyEq.( 5. 6) .
( d )T hec o stp erp r o du c tc a nb ec o mp ut e df r o m Eq .( 5 . 8 )e x c e ptt h at wemus tac c ountf o rt h es c rr at e .Thi si sac c omp l i s he db ydi v i di ngt hec os tde t e r mi nedb yEq .( 5 . 8 ) b yt hey i el dofgoodpar t .I noure xampl et hey i el di s0. 95.
Th e$ 3. 4 2r e pr e se nt st h ea v er a gec o s tp er a cc e pt a bl ep r o du ctu nd ert h ea s su mp t i ont h atwea r ed i s c ar d i ngt h e5 %b adu ni t satn os al v a ge v al ueandnodi s pos al c os t .Suppos et hatwec oul dr epai rt hes euni t satacos tof$5. 00/ uni t .Woul di t b ee co no mi c al t odos o?Toc omp ut et h ec o s tp erp i e ce ,t h er e pa i rc o stwo ul dh av et obead de dt o t heo t herc omponent sofEq.( 5. 8) .Al s o,s i nr epai roft hedef ec t smeanst hatoury i el dwi l l be100%, t h e0 . 9 5u se da bo v et oo bt a i nac os to f$ 3. 4 2c anb ei g no r e d.
Thel owerc os tperuni ti sas soc i at edwi t ht hepol i c y ofs c r appi ngt he5% def e ct sr at hert ha nr epai r i ngt hem.Unl e sst hee x t r aun i t sar enee dedt omee t d ema nd,t h es c r a pp ol i c ys ee mspr ms e f e r ab l e .
ANAL YSI SOFTRANSFER LI NESWI WI THOUTSTORAGE
In this section we consider the analysis of continuous and intermittent transfer machine without internal storage storag e capacity. capacity. e will supplement the results of Section !." # considering what happens at a wor$station when it #rea$s down. %here are two possi#ilities and we refer to their analyses as the upper&#ound approach and the lower& #ound approach In practical terms' the di(erence #etween the two approaches is simply this) ith the upper&#ound approach' we assume that the wor$part is not removed from the station when a #rea$down occurs at that station. ith the lower&#ound approach' the wor$ part is ta$en out of the station when the station #rea$s down. %he circumstances under which each approach is appropriate are discussed in the following su#sections.Upper-bound su#sections. Upper-bound approach %he upper&#ound upper&#ound approach provides an estimate of the upper limit on the fre*uency fre*uency on line stops per cycle. e assume here that a #rea$down at a station does not cause the part to #e removed from that station. In this case it is possi#le' perhaps li$ely' that there will #e more than one line stop associated with a particular wor kpar t .Ane x ampl eo ft h i s
s i t uat i oni st hatofah ydr aul i cf ai l ur eatawor k s t at i onwhi c hpr e vent st hef eedmec hani s mf r om wor k i ng.Anot herpos si bi l i t yi st hatt hec ut t i ngt oolhasnear l ywor noutandneedst obec hanged.Or , t hewor k par ti scl os et obei ngoutoft ol er anc eandat ool adj us t menti sr equi r edt oc or r ec tt he c on di t i on .Wi t heac ho ft h es ee x ampl e s,t her ei snor eas onf ort h epar tt ober emo v edf r om t h e t r ans f ermac hi ne. Letpi r epr es entt hepr obabi l i t yt hatapar t wi l l j am atapar t i c ul ars t at i oni ,wher ei =1,2, ...,n. Si nc et hepar t sar eno tr emo vedwhenas t at i onj am oc cur s ,i ti spos si bl e( al t houghno tpr obabl e)t hat t hepar twi l l j am ate ver yst at i on.Thee xpec t ednumberofl i nes t opsperpar tpas si ngt hr ought hel i ne c anbeo bt a i ne dmer e l ybys ummi ngupt hepr obabi l i t i esp,o v ert hens t at i ons .Si nc eea choft hen s t at i onsi spr oc es si ngapar teac hc y cl e,t hi sex pec t ednumberofl i nes t opsperpar tpas si ngt hr ough t hel i nei sequal t ot hef r equenc yofl i nes t opsperc yc l e.Thus , I ft hepr obabi l i t i espar eal lequal ,p1=p2 =...= p n =p ,t h en EXAMP MPLE5. 2
I na10s t at i ont r ans f erl i ne,t hepr obabi l i t yt hatas t at i onbr eak downwi l l oc curf oragi v enwor kpar ti s equalt o0. 01.Thi spr obabi l i t yi st hes amef oral l 10s t at i ons .Det er mi net hef r equenc yofl i nes t ops pe rc y c l eont h i sfl owl i neus i n gt heup per bou ndappr oac h. Sol ut i on: Thev al ueofFc anbecal c ul at edf r om Eq .( 5. 10) . Th i si st h ev a l u eo fFu se di nEx a mp mp l e5 . 1 . Lowe wer boundappr oach
Thel o we r b oun dap pr oa chgi v e sanes t i mat eoft hel o werl i mi to nt heex pe ct ednumb ero fl i nes t ops perc y cl e.I nt hi sappr oac hweas sumet hatt hes t at i onbr eak do wnr es ul t si nt hedes t r uc t i onor da mag ma eoft h ewor k pi e ce.Fore x ampl e ,adr i l l ort apbr eak soffi nt hepar tdu r i ngpr oc es s i ng.The br o kent ool mus tb er epl a cedatt hewor k s t at i onandt h ewor kpa r tmus tber emo v edf r om t h el i n ef or s ubs equentr e wor kors cr ap.Ac cor di ngl y ,t hepar tc anno tpr oc eedt ot hene xts t at i onsf orf ur t her pr o ces s i ng . Agai n,l etp1bet hepr obabi l i t yt hatapar twi l l j am atapar t i c ul ars t at i oni .Then,c ons i der i ngagi v en wor kpar tasi tpr oc eedst hr ought hel i ne,p1i st hepr obabi l i t yt hatt hepar twi l l j am ats t at i on1,and ( 1-p1)i st hepr obabi l i t yt hatt hepar twi l l notj am ats t at i oni andt husbeav ai l abl ef ors ubs equent pr oc es si ng.Thequant i t yp2( 1-p1)i st hepr obabi l i t yt hatt hi sgi v enpar twi l l j am ats t at i on2. Gener al i z i ng,t hequant i t y i st hepr obabi l i t yt hatt hegi v enpar twi l l j am atany s t at i oni .Summi ngal l t hes epr obabi l i t i esf r om i =1t hr oughnwoul dgi v et hepr obabi l i t yorwhathas pr e vi ous l ybeenc al l edt hef r equenc yofl i nes t opsperc y cl e.Ther ei saneas i erwa yt ode t er mi net hi s f r equen cy . Thepr obabi l i t yt hatagi v enpar twi l l pas st hr oughal l ns t at i onswi t houtal i nes t opas soc i at edwi t hi t s pr oc es si ngi sgi v enb y
Ther ef or e,t hef r equenc yofl i nes t opsperc y cl ei spr o vi dedb y i ft hepr obabi l i t i espi t hatapar twi l l j am ata par t i c ul ars t at i onar eal lequal ,p1=p2...=pn=p.t hen Wemi g htb et emp t e dt ov i e wt h i sf r e qu en cy , F ,a s t hepr obabi l i t yofal i nes t opperc yc l e,ex ceptt hati ti spos si bl e,i nt heupper boundappr oac h,f ort he f r equenc yofl i nes t opsperc y cl et oe xc eeduni t y .Apr obabi l i t ygr eat ert hanl c annotbei nt er pr et ed. Wi t ht h el o wer bou ndappr oac h,t hen umbe rofwor kpar t sc omi ngofft hel i newi l l bel e sst hant he n umb ers t a r t i n g.I ft h ep an sa r er e mo mo v edf r o mt h el i n ewh enab r e ak do wno c cu r s ,t h eyar en ot a vai l abl et obec ount edaspar toft heout putoft hel i ne.Ther ef or e,t hepr oduc t i onr at ef or mul agi v en
b yEq .( 5 . 3 )mus tb eamendedt or e flec tt hi sr edu ct i oni nout pu t .Us i ngt hel o we r b oun dap pr oa ch, t hepr oduc t i o nr at ef or mul abec omes
wher eFno tonl ys t andsf ort hef r equenc yofl i nes t opsbutal s ot hef r equenc yof par sr emo val .I fnor e wor ki sper f or med,Fi st hes cr apr at e.Ther ef or e,t het er m( 1–F)r epr es ent s t hey i el doft het r ans f ermac hi ne.Tpi si nt er pr et edt omeant hea v er agec y cl et i meoft hemac hi ne. EXAMP MPLE5. 3 Co mp mp ut et h ev a l ueofFu si n gt h el o we r b ou ndap pr o ac hf o rt h ed at aofEx a mp mp l e5. 2 .Al s oco mp mp ut e t hepr oduc t i onr at e. Sol ut i on: Fr om Eq.( 5.l 2)t hev al ueofFi s Al t hought hev al ueofFi ss mal ma l erasc al c ul at edb yt hel o wer b ou nda pp r o ac h,t h ed i ff er e nc ei ss ma ma l l .Th i sdi ff er e nc eg r o wsast h ev a l u eo fpa ndt h en umb ero f wor k s t at i onsi nc r eas e. T oc omput et hepr oduc t i onr at e,wemus tadj us tEq.( 5. 3) ,asi ndi c at edi nt hepr e vi ousdi s cus si on,b y t hev a l ueofF ,Pr od uc t i ont i meTpwasc al c ul at edi nEx ampl e5 . 1as1. 6mi n.Ther ef or e,t he pr oduc t i onr at e Th i si ss ome wh atb el o wt h e3 5. 6p i e ce s/ ho bt a i n ed i nEx a mp mp l e5 . 1 ,wh er et h es c r a pr a t ewa s0 . 0 5r a t h ert h ant h e0 . 0 95 6c o mp mp ut e dh er e .Wec a n r ea s ont h att h e5 %s c r a pr a t ep r o ba bl yr e pr e se nt sami x t u r eo ft h et woc a se sa s su me me db yt h eu pp er a ndl o we r b ou ndap pr o ac h es .Wh enb r e ak d own soc c u r ,t h ewo r kp a r t sa r es ome t i me sr e mo mo v e df r o m t hel i n ea ndot h ert i mest he yar eno t ,Theup per -andl o we r b oundapp r oa ches ,ast h ei rn amesi mpl y , p r o v i d eu pp era ndl o we rl i mi t sont h ef r e qu en c yo fd own t i meo cc u r r en c es .Ho we v er ,t h es et wo ap pr o ac he sal s og ener at euppe ra ndl o werl i mi t sont hepr od uc t i onr at e,a ss umi ngt hats t a t i o n b r e ak do wn sa r et h es o l eca us eofs c r a p.Ofc o ur s e,t h e5 %s c r a pfi g ur ema ma yal s oi n c l u deot h er c ondi t i ons ,s uc haspoorqual i t yoft hewor kpar t s . Some mecomm mment sandobser vat i ons
De t e r mi ni ngwhe t hert heuppe r -ort hel o wer bou ndappr oac hi smo mo r eappr opr i at ef o rapa r t i c ul ar t r ans f erl i ner equi r eskno wl edgeaboutt heoper at i onoft hel i ne.Theoper at orma yber equi r edt ous e j udgmenti neac hbr eak downt odet er mi newhet hert hewor kpar ts houl dber emov ed.l fpansar e s ome t i me sr e mo mo v edan ds ome t i me sno t ,t h ea ct u al f r eq ue nc yo fb r e ak do wn swi l l f a l l s ome wh er e b et we ent h eu pp era ndl o we rb ou nd s .Oft h et woap pr o ac h es ,t h eu pp er b ou nda pp r o ac hi s pr ef er r ed,c er t ai nl yf orc onv eni enc eofc al c ul at i onandpr obabl yf orac cur ac yal s o. Ther ear eot herr eas onswh yl i nes t opsoc curwhi c har enotdi r ec t l yr el at edt owor k s t at i ons( e. g. ,
t r ans f ermec hani s mf ai l ur e,s c hedul et ool c hangesf oral l s t at i ons ,pr ev ent i v emai nt enanc e,pr oduc t c hangeo ver ,e t c . ) .Thes eot herf ac t or smus tbet ak eni nt ocons i der at i onwhendet er mi ni ngl i ne p er f o r ma nc e . Thebi gges tdi ffic ul t yi nus i ngEqs .( 5. 9)t hr ough( 5. 12)l i esi ndet er mi ni ngt hev al uesofp1f ort he v ar i ousst at i ons .Per hapst hebes tappr oac hi st obas et hev al uesofp1onpr ev i oushi s t or i c aldat a ande xper i enc ewi t hs i mi l arwor k s t at i ons . Ther ear eanumberofgener al t r ut hsaboutt heoper at i onoft r ans f erl i neswhi c har er e veal edb yt he equat i onsofSec t i ons5. 1and5. 2.Fi r s t ,t hel i neeffic i enc ydec r eas es s ubs t ant i al l yast henumberofs t at i onsi nc r eas es .I ti snotunc ommonf orl ar get r ans f erl i nes c ons i s t i ngofupt o100s t at i onst obedo wnmor et han50% oft het i me.l ti sdoubt f ul t hats uc hl i nes ac hi e v et her e t ur noni n v es t mentwhi c ht hei ro wner sant i c i pat e df r om t h em.Thei n fluenc eoft he numberofs t at i onsonl i ne’ effic i enc yi sdr amat i c al l ydi s pl a yedi nFi gur e5. 3f ors ev er al as sumed v al uesofs t at i onbr eak downpr obabi l i t i es .
Th i sfi gu r ewa sc a l c ul a t e du s i n gt h eu pp er b ou nd a pp r o ac h .I nc o mp ar i n gt h eu pp er -a ndl o we r b ou nda pp r o ac h es ,wefi n dt h att h eu pp er b ou nd c al c ul at i onsl eadt oal owerv al ueofl i neeffic i enc ybutahi gherv al uef ort hepr oduc t i onr at e.The r eas onf ort hi sappar entanomal yi st hi s:Us i ngt hel ower boundappr oac hwi t hi t sas sumpt i onof par t sr emo val .t her emo vedpar t sar enota vai l abl eats ubs equentwor k s t at i onst ocaus el i ne s t oppages .Henc e,t hepr opor t i onofupt i meont hel i nei sgr eat er .Ho wev er ,i ft hepar t sar er emo ved f r om t hel i ne,t hepr oduc t i onr at eoft hel i nei sr educ ed.
PARTI ALAUTOMATI ON
Th er ea r ema nye x amp l e so fHo wl i n esi ni n du s t r yt h atc on t a i nb ot ha ut o ma t e da ndma nua l l y oper at edwor k s t at i ons .Thes ec as esofpar t i al l yaut omat edpr oduc t i onl i nesoc curf ort womai n r eas ons .Fi r s t ,mec hani z at i onofamanual l yoper at edHo wl i nei sof t eni nt r oduc edgr adual l y . Aut omat i onoft hes i mpl ermanualoper at i onsi scar r i edouti ni t i al l y ,andt het r ans i t i ont owar daf ul l y aut omat edl i nei sac c ompl i s hedpr ogr es si v el y .Al ong pe r i odoft i mema yel a ps eb ef or et h et r ans f or ma t i onhasbee nc omp l e t ed.Mean whi l e ,t hel i ne oper at esasapar t i al l yaut omat eds y st em.Thes ec ondr eas onf orpar t i al aut omat i oni sbas eds t r i c t l y o ne c on omi c s .So mema nu alo pe r a t i o nsa r edi ffic u l tt oau t o ma t ean di tma yb eu ne c on omi c a lt odo s o.Ther ef or e,whent hes equenc eofwor k s t at i onsi spl annedf ort hefl owl i ne,c er t ai ns t at i onsar e d es i g ne dt ob ema nu al l yop er a t e dwh i l et h er e s ta r ed es i g ne dt ob ea ut o ma t i c .Ex a mp l e so f op er a t i onst h atar eo f t e ndi ffic ul tt oaut omat ear epr o ces s esr equ i r i ngal i gnmentors pec i al human s ki l l st oc ar r yout .Manyas sembl yoper at i onsf al l i nt ot hi sc at egor y .Al s o,i ns pec t i onoper at i onsof t en c r eat ep r obl emswhenaut omat i oni sbei ngc ons i der edt os ub st i t ut ef orahumanope r at or .Def e ct si n awo r kpa r t t h atc a nb ee as i l ype r c e i v e db yah uma ni n sp ec t o ra r es ome t i me se x t r e me l ydi ffic ul tt o i dent i f ybyanaut omat i ci ns pec t i onde vi c e.Anot herpr obl em i st hatt heaut omat i cde vi c ec anonl y c he c kt h ed ef e c t sf o rwh i c hi twa sd es i g ne d,wh er e asah uma no pe r a t o ri sc ap ab l eo fs en s i n ga v ar i et yofunf or es eeni mper f ec t i onsi nt hepar t . T oan al y z et hepe r f or ma nc eofap ar t i al l yaut o mat e dHo wl i ne ,wewi l l b ui l dont hed ev el o pment sof t hepr e vi ouss ec t i ons .Ouranal y s i swi l l bec onfi nedt ot heoper at i onofas y st em wi t houtbuff er s t or age.Lat eri nt hi ssec t i onwewi l l s pec ul at eont hei mpr o vement st hatwoul dr es ul ti fi npr oc es s i n v ent or yban kswer eus edf o rt h eman ual wor k s t at i ons .Th ei deal c y c l et i meT cwi l l b ede t enni ne d b yt hes l owes ts t at i oni nt hel i ne,whi c hgener al l ywi l l beoneoft hemanual s t at i ons .Weas s umet hat br e ak do wn soc c uro nl yatt heaut omat i cs t a t i o nsandt h att her e as onsf orb r eak do wn sar easv ar i ed ast heyar ef orac ompl et el yaut omat eds ys t em ( e. g. ,t oolf ai l ur es ,def ec t i v ec omponent s ,el ec t r i c al a ndme ch an i c a lma l f un c t i o ns ,e t c . ) .Br e ak do wn sd ono to c cu ra tt h ema nua ls t a t i o nsbe ca us et h e hu manope r at or sar efle xi bl een ough,weas s ume,t oadap tt ot h ek i ndsofv ar i at i onsanddi s r up t i ons t hatc aus eanaut omat i cwor k headt os t op.Thi s ,ofc our s e,i snotal wa yst r ue,butouranal y s i swi l l be ba sedont h i sas s ump t i o n.Le tpequ al t hep r obabi l i t yofas t at i onb r e ak do wnf orana ut o mat i cwor k head.Theval uesofpmay bedi ffer entf ordi ffer ents t at i ons ,butwewi l l l eav et ot her eadert het as kofgener al i z i ngonour par t i c ul arc as eofequalpf ora l l s t at i ons . Si nc eni st het o t al numberofwor k s t at i onsont hel i ne,l e tnaequalt henumberofaut omat i cst at i ons a ndn oe qu al t h en umb ero fma nu alo pe r a t o rs t a t i o ns .Th es u mo fn aa ndnomu s tb en .l nou r pr e vi ousdi s cus si onofc os t si nSec t i on5. 1,CLwasus edt or epr es entt hec os tt ooper at et hel i ne,
i nc l udi ngl abor ,c api t al ,ando v er head.Forapar t i al l yaut omat eds y st em,wemus ts epar at et hi st er m i nt os ev er alc omponent s .LetCoequal t heoper at orc os tpermanual s t at i on.Thi si sal aborc os ti n $/ mi n ut ewhi c hap pl i e st oe ac hman ual l yo per at edwor k s t at i o n.Thec os tperaut omat i cwo r k s t at i o ni n $/ mi nut ewi l l bedenot edbyCasThi scos twi l l of t env ar yf ordi ff er ents t at i ons ,dependi ngont hel ev el ofs ophi s t i c at i onoft hemec hani s m.Wec anal l o wf ort hes edi ff er enc esi nCas ,wi t hl i t t l edi ffic ul t y ,as wi l l b es ho wni nas ub se qu ente x amp l e .Th el a s tc os tc o mp on en to fCLi st h ec os tp ermi nu t eo ft h e aut omat i ct r ans f ermec hani s m whi c hwi l l beus edf oral l s t at i ons ,manual andaut omat i c ,t ot r ans por t t hewor kpar t s .Lett hi scos tbes ymbol i z edbyCat .I ti snotac os tpers t at i on,butr at herac os tt hat i nc l udesal l ns t at i ons .Combi ni ngt hes ec os t s .t het ot al l i nec os tCLi sgi v enby T ofi gur et hea v er agepr o duc t i ont i me,t hei dea l c y c l et i mei sad dedt ot hea v er agedo wn t i mepe rc y c l easf ol l o ws: Byus i ngno( t h enu mberofa ut omat i cwor k s t at i ons ) , wear eco ns i s t en twi t houras s ump t i ont hatbr ea kdo wn sdono toc c uratma nual s t at i ons .Equ at i on ( 5 . 1 4)i sba s edo nt h eu pp er -b ou nda pp r o ac ho fSe c t i o n5 . 2 . Bys ubs t i t ut i ngEqs .( 5. 13)and( 5,14)i nt oEq.( 5. 8) ,weobt ai nt hec os tperuni tpr oduc ed: EXAMPLE5. 4 Ap r o po s alh asb ee nma det or e pl a ceon eo ft h ec u r r e ntma nua ls t a t i o nswi t hanau t o ma t i cwo r k h ea do na1 0s t a t i o nt r a ns f e rl i n e,Th ec ur r e nts y s t e mh ass i xaut o ma t i cwo r khe ad sa ndf o urma nu al s t at i ons .Thec ur r entc y cl et i mei s30s .Thebot t l enec ks t at i oni st hemanual s t at i ont hati st he c an di dat ef orr epl ac ement .Thep r opo sedaut o mat i cs t a t i onwoul dal l o wt hec y c l et i met ober edu ced t o24s .Thenews t at i oni scos t edat$0. 25/ mi n.Ot herc os tdat af ort hee xi s t i ngl i ne:
Br eak downsoc curateac hoft hesi xaut omat i cwor k s t at i onswi t hapr obabi l i t y p=0. 01 .Th ea v er ag ed ownt i mep erbr ea kdo wni s3mi n.l ti ses t i mat e dt h att hev al u eofpf ort he n ewa ut o ma t i cs t a t i o nwou l dbep=0 . 0 2.Th ea v er a gedo wn t i mef o rt h el i n ewo ul db eu na ffe c t e d. Mat er i al f ort hepr oduc tc os t s$0. 50/ uni t .T ool i ngc os t scanbenegl ec t ed( C1=0) .I ti sdes i r edt o c ompar et hec hal l e nge r( t hene w aut omat eds t at i on)wi t ht hedef ender( t hec ur r en tma nuals t a t i o n) ont hebas i sofc os tperuni t . Sol ut i on: Fort hec ur r entl i ne,t hepr oduc t i ont i mei s
Fo rt het r ans f e rl i ncwi t ht h en ewwor k head r epl ac i ngt hcc ur r entmanuals t at i on,s i mi l arc omput at i onsar easf ol l ows:
Theconc l u si oni st ha tt hei mpr o v edpe r f or manc eof t heaut omat i cwor kheaddoesno tj us t i f yi t sgr eat erc os t .I ts houl dbeno t edt hatt her educ ed r el i abi l i t yoft heaut omat i cwor k hc adsfigur es pr omi ne nt l yi nt h ec os tc al c ul at i ons .I ft hev al ueofpf ort hene w aut oma t i cwor kheadha dbeen equa lt o0. 0l i ns t eado f0 . 02 ,t hec onc l us i onwo ul dha v eb eenr e v er s ed. Bufferst or age
Th ep r e ce di n ga na l y s i sas s ume sn ob uff ers t o r a geb et we ens t a t i o nsont h el i n e.Th er e f o r e ,wh ent h e aut omat e dpo r t i onoft hel i n eb r e ak sdo wn,t h emanual s t at i onsmu stal s os t opwor k i n gf o rl ac kof wor kpar t s ,I twoul dbebenefi ci al t ot hel i neoper at i ont obui l dupani n vent or yofpar t sbef or eand af t ereac hmanual s t at i on.l nt hi smanner ,t hes es t at i ons ,whi c hus ual l yoper at eatas l owerpac e t hant heaut omat i c s,c oul dcont i nuet opr oduc ewhi l et heaut omat edpor t i onoft hel i nei sdo wn.Thi s woul dt endt ohel ps ol v et hel i nebal anc i ngpr obl em t hatof t enoc c ur sonpar t i al l yaut omat ed mac hi nes .T oi l l us t r at e,c ons i dert hepr e vi ousex ampl eoft hec ur r entt r ans f ers y st em whos ei deal c y c l et i mei s0. 50mi n.Un dert hec ur r en tme t hodofope r at i o n,bo t hmanu al an da ut o mat i cs t at i ons a r eou to fo pe r a t i o nwh enab r e ak do wnoc c ur s .Th e0 . 5 0mi ncy c l et i mei sc au se db yon eo ft h e manual s t at i ons .Suppos et hatt hei deal c y cl et i meont heaut omat i cpor t i onoft hel i nec oul dbes et at0. 32mi n.Th er es ul t i nga v er agepr oduc t i ont i meont hea ut oma t i cst at i on swoul dt henbe l fabankofwor kpar t scoul dbepr o vi dedf ort he h uma no pe r at o r st owo r kond ur i n gt h ed own t i meo c cu r r e nc e s,t h ea v er a gep r od uc t i ont i meo ft h e e nt i r ea s s emb l ys y s t e m wo ul dbe0 . 5 0mi nr a t h ert h an0 . 6 8mi na sc omp ut e di nEx a mp l e5 . 4 .Th e r es ul t i ngc os tperas sembl y ,i gnor i ngan yaddedc os tasar es ul toft hebuffers t or agec apac i t y ,woul d be whi c hi sas ubs t ant i al r educ t i onf r om t he$1. 384/ uni t pr ev i ous l yc al c ul at edf ort hec ur r entl i ne. Wet r eatt het opi cofbuff ers t or agei nmor ede t ai li nt hene xts ec t i on.
AUTOMATEDFL OW LI NESWI THSTORAGEBUFFERS On eo ft h eme t h od sbywh i c hfl owl i n esc a nb ema det oop er a t emo r eeffic i e nt l yi st oad do neor mor epar t ss t or agebuff er sbe t weenwor k s t a t i onsal ongt h el i ne .Th ebuff erz one sd i v i det hel i nei n t o s t ages .I fones t or agebufferi sus ed,t hel i nei sdi v i dedi nt ot wos t ages .I ft wos t or agebuffer sar e us edatt wodi ffer entl oc at i onsal ongt hel i ne,at hr ees t agel i ner es ul t s .Theupperl i mi tont he nu mbe ro fs t or agez onesi st oh av ei np r oc es si n v ent or ycapac i t ybe t weene v er ywor k s t at i on.‘ Di e numberofs t ageswi l l t henbeequal t ot henumberofs t at i ons .Foranns t agel i ne,t her ewi l l ben–l s t or agebuffer s .Thi s ,ofc our s e,doesno ti nc l udet hei n vent or yofr a w wor kpar t swhi c har ea vai l abl e f orf eedi ngont ot hef r ontoft hefl owl i ne.Nordoesi ti nc l udet hei nv ent or yoffi ni s hedpanst hat ac c umul at eatt h een doft hel i ne. I nafl owl i newi t houti nt er nalwor kpar ts t or age,t hewor k s t at i onsar ei nt er dependent .Whenone s t at i onsbr eak sdo wn,al l t heot hers t at i onswi l l beaff ec t ed,ei t heri mmedi at el yorb yt heendofaf e w c y cl esofoper at i on.Theo t herwor k s t at i onswi l l bef or c edt os t oppr oduc t i onf oroneoft wor eas ons: 1. St ar v i ngofs t at i on s.I fawo r k s t at i onc anno tc ont i nu et oope r at ebec aus ei thasnopanst o wo r kon ,t hes t a t i oni ss ai dt ob es t ar v e do fp ar t s .Whenab r e ak do wnoc c ur satag i v en s t at i oni nt hel i ne,t hes t at i onsf ol l owi ngt hebr ok endowns t at i onwi l l bec omes t ar v ed. 2. Bl o ck i ngo fs t at i ons .Thi soc c ur swh enas t at i oni spr e v ent edf r om p as s i ngi t swor kpa r ta l ong t ot hef ol l o wi ngs t at i on .Wh enas t at i onbr eak do wno cc ur s ,t hepr ec ed i ngorup st r eam s t at i onsar es ai dt obebl oc k ed,bec aus et he yar eunabl et ot r ans f erwor kpar t st ot hes t at i on t h ati sdo wn. Thet er ms“ s t ar v i n g”an d“ bl o ck i ng ”a r eo f t enus edi nr ef e r enc et oman ual ho wl i ne s.Ho we v er ,t he y a r eu se f u lf o re x p l ai n i n gh owb uff ers t o r a gez on esc anb eu se dt oi mp r o v et h ee ffic i e nc yof a ut o mat e dfl o wl i n es .Wh ena na ut o ma t e dfl o wl i n ei sdi v i d edi n t os t a ge sb ys t o r a geb uff er s ,t h e o v er al leffic i e nc yandpr oduc t i onr at eo ft hel i near ei mpr o v ed .Whenoneoft hes t age si nt hel i ne b r e ak sdo wn ,t h es t o r a geb uff er spr e v en tt h eo t h ers t a ge sf r o mb ei n gi mme di a t e l yaff ec t e d.Co ns i d er at wos t aget r ans f erl i newi t hones t or agebuff erbe t weent hes t ages .I ft hefi r s ts t agebr eak sdo wn, t hei n vent or yofwor kpar t st hathasac c umul at edi nt hes t or agebufferwi l l al l o wt hesec onds t aget o c ont i nueoper at i ngunt i lt hei nv ent or yhasbeene xhaus t ed.Si mi l ar l y ,i ft hes ec onds t agebr eak s do wn,t hes t or agez onewi l l ac ceptt heout putoft hefi r s ts t age.Thefi r s ts t agec anc ont i nuet o oper at eunt i l t hec apac i t yoft hes t or agebuff eri sr eac hed. Th ep ur po ses er v e db yt h es t o r ag eb uff erc anbeex t e nd edt ofl owl i n eswi t hmo r et h ant wos t a ge s. Thepr es en ceoft he sei npr o ces si n v ent or i esa l l o wse ac hst ag et oope r at es ome wha ti nde pen de nt l y . I ti sc l ea rt h att hee xt en toft hi si nd ependenc ebe t weenonest ag ean dt h ene x td epe ndsont h e
s t or agec apac i t yoft h ebuff erz on es epa r at i ngt hes t age s. Th et woex t r e mec as eso fs t o r a gebu ffe re ffe c t i v e ne s sca nb ei d en t i fi e da s 1 . Nobu ff ers t o r a gec ap ac i t ya ta l l 2 . St o r a geb uff er swi t hi n fin i t ec ap ac i t y NO BUFFERSTORAGECAPACI TY.I nt h i sc as e,t hefl owl i n ea ct sasonema chi ne.Whenas t at i on
br e ak do wnoc c ur s ,t h een t i r el i nei sf or c eddo wn.Thee ffic i enc yoft hel i newaspr e vi ous l ygi v enb y Eq.( 5. 5) .Wewi l l r ewr i t et hi sequat i onas Thes ubs c r i pt0i dent i fi est hi sast heeffic i enc yoft he l i newi t hnobuff ers t or agec apac i t y .I tr epr es ent sas t ar t i ngpoi ntf r om whi c ht hel i neeffic i enc yc anbe i mpr ov edbyaddi ngpr o vi s i onf ori npr oc es sst or age. eo pp os i t ee x t r e mei st h ec a s ewh er eb uff erz o ne s I NFI NI TECAPACI TYSTORAGEBUFFERS.Th ofi nfi ni t ec apac i t yar ei n st al l edbe t weene ac hs t a ge.I fweas s umet ha te ac ho ft he seb uff erz on esi s hal ff ul l ( i not herwor ds ,eac hbuff erz onehasani nfi ni t es uppl yofpar t saswel l ast hec apac i t yt o ac ceptani nfi ni t enumberofaddi t i onal par t s ) ,t heneac hs t agei si ndependentoft her es t .I nfi ni t e s t o r a geb uff er sme an st h atn os t a gewi l l e v erb eb l o ck e do rs t a r v e db ec au seo ft h eb r e ak d owno f someot herst age. Ofc our s e,afl owl i newi t hi nfi ni t ec apac i t ybuff er scanno tber eal i z edi npr ac t i c e.Howev er .i fs uc ha l i nec oul dbeappr o xi mat edi nr eal l i f e,t heo v er al l l i neeffic i enc ywoul dbede t er mi nedb yt he bo t t l enec ks t age.Wewoul dhav et ol i mi tt hepr oduc t i onont heo t hers t agest obec ons i s t entwi t ht hat oft hebot t l enec kst age.Ot her wi s e,t hei npr oc es si n vent or yups t r eam f r om t hebo t t l enec kwoul d gr owi ndefi ni t el y ,e vent ual l yr eac hi ngsomepr ac t i c almax i mum,andt hei npr oc es si n vent or yi nt he do wns t r eam buffer swoul ddec l i net oz er o.Asapr ac t i c al mat t er ,t her ef or e,t heupperl i mi tont he e ffic i e nc yofa nys uc hal i n ei sde fin edb yt h ee ffic i e nc yoft h ebo t t l e ne cks t a ge .I fwea ss umet h e c y cl et i meT ct obet hes amef oral ls t ages ,t heeffic i enc yofear l ys t agei sgi v enb y wher et hes ubs cr i ptki sus edt oi dent i f yt hes t age. Theov e r al l l i neeffic i enc ywoul dbegi v enby wher et hes ubs cr i ptooi sus edt oi ndi c at et hei nfi ni t e s t o r a geb uff er sbe t we ens t a ge s . r o v i d i n go neormo r eb uff erz o ne sona BUFFERSTOCKEFFECTI VENESSI NPRACTI CE.Byp fl o wl i n e,weex pe ctt oi mp r o v et h el i n ee ffic i e nc yab ov eEobu tweca nno te x pe ctt oac h i e v eEo o, s i mpl ybec aus ebuff erz onesofi nfi ni t ec apac i t yar eno tpos si bl e.Henc e,t heac t ual v al ueofEwi l l l i e
somewher ebet weent heseext r emes: Be f o r ee mb ar k i n go nt h ep r o bl e mo fe v al u at i n gEf o r r eal i s t i cl ev el sofbufferc apac i t y ,i ts eemsappr opr i at et oc ommentont hepr ac t i c ali mpl i c at i onsof Eqs .( 5. l 6)t hr ough( 51. 9): 1.Equat i on( 5. 19)i ndi c at est hati fE0andEooar enear l yequal i nv al ue,r el at i v el yl i t t l eadv ant age wi l l begai nedf r om t headdi t i onofs t or agebuffer st ot hel i ne.I fEooi ssi gni fi cant l yl ar gert hanEo, s t o r a geb uff er sc anp r o v i d eap r o no un ce di mp r o v eme nti nt h el i n e’ seffic i e nc y . 2.Thewor k s t at i on sal ongt h el i n es ho ul db edi v i dedi nt os t age ss oast omak et heeffic i e nc i esofal l s t a ge sa seq ua la spo s s i b l e .I nt h i swa yt h ema x i mu md i ff er e nc eb et we enEoan dEo owi l l b e ac hi ev ed,andnos i ngl es t agewi l l s t andoutasas i gni fi cantbot t l enec k. 3 .Th ee ffic i e nc yofa na ut o ma t e dHo wl i n ewi t hb uff ers t o r a gec a nb ema x i mi z e du nd ert h ef o l l o wi n g c ondi t i ons: a.Byse t t i ngt henumberofs t agesequalt ot henumberofwor k s t at i ons .Thati s ,al l adj ac ents t at i ons wi l l b es epa r at edb ys t or a geb uff er s . b.Bypr o vi di ngt hatal l wor k s t at i onsha v eanequal pr obabi l i t yofbr eak do wn. c .Bydes i gn i ngt h es t or agebu ffer st obeo fl ar gec ap ac i t y .Th eac t ual c apac i t ywo ul db ede t e r mi n ed b yt hea ver agedownt i me.I ft hea ver agedo wnt i me( i npar t i c ul ar ,t her at i oTd/ T c)i sl ar ge,mor ebuffer c ap ac i t ymus tbepr o vi dedt oe ns ur eadequat ei ns ul at i onbe t weenwo r k s t a t i ons . 4.Al t houghi ti snotobv i ousf r om Eqs .( 5. 16)t hr ough( 5. l 9) ,t he“ l awofdi mi ni s hi ngr et ur ns ”o per at es a st h en umbe ro fs t a ge si n cr ea s es .Th eb i g ge sti mpr o v emen ti nl i n ee ffic i e nc yc ome sf r o ma dd i n g t hefi r s ts t o r agebu ffe rt ot hel i ne.Asmor es t or agebu ffer sar eadd ed,t h ee ffic i e nc yi mpr o v es ,b utat anev er s l owerr at e.Thi swi l l bedemons t r at edi nEx ampl e5. 6l at eri nt hi ssec t i on. Ana l y si sofat wos t a gel i ne
Mu cho ft h ep r e ce di n gd i s c us s i o ni sba se do nt h ewo r kofBu z ac o t t[ 2 ] ,wh oh aspi o ne er e dt h e anal y t i c alr es ear c honfl owl i neswi t hbuffers t oc k s.Se ver alofhi spubl i c at i onsont hes ubj ec tar e l i s t edi nt her ef er enc esatt heendoft hi schapt er[ 2, 4, 5, 6, 7] .Ot herr es ear c her sha veal s os t udi edt he pr obl em offl owl i neswi t hs t or agebuff er s ,es pec i al l yt het wos t agel i ne,andt hei nt er es t edr eaderi s r ef er r edt ot hei rwor k[ 12, 15, 16] . Ourpr es ent at i onoft het wos t agefl owl i nepr obl em wi l l c l os el yf ol l owBuz ac ot t ’ sanal y s i sde vel oped i nr ef er enc e[ 2] .Thet wos t agel i nei ssepar at edb yas t or agebuff erofc apac i t yb.Thec apac i t yi s e x pr e ss edi nt e r msoft h en umb ero fwo r kpa r t st h es t or a gez on ec a nh ol d .L etF1a ndF2r e pr e se nt , r es pec t i v el y ,t hebr eak do wnr at esofs t ages1and2.Wewi l l us et het er m rt odefi net her at i oof b r e ak do wnr a t e sa sf o l l o ws:
Thei dea lc y c l et i me,T oi st h es amef orb ot hs t age s.
Weas s umet hatt hedo wn t i medi s t r i bu t i onso fal l s t at i on swi t hi nas t a gea r et hes ame,an dt ha tt he aver agedownt i mesofst agesIand2ar eTd1andTd2. Ov ert hel o ngr un,bo t hs t a gesmus tha v ee quale ffic i e nc i es .Fore x ampl e,i ft hee ffic i e nc yofs t ag eI woul dt en dt obegr e at e rt hant hes t age2effic i e nc y ,t hei n v ent or yi nt hes t or agebuff erwo ul dt e ndt o bui l dupunt i l i t scapac i t ybi sr eac hed.Ther eaf t er ,s t agel woul dev ent ual l ybebl oc kedwheni tt r i ed t oout pr oduc es t age2.Si mi l ar l y ,i ft heeffic i enc yofs t age2i sgr eat er ,t hebufferi nv ent or ywoul d be comed epl e t ed,t huss t ar v i ngs t ag e2.Ac c or di ngl y ,t h eeffic i e nc i esoft h et wos t ag eswo ul dt endt o equal i z eo vert i me. Th eo v er a l l l i n ee ffic i e nc yf o rt h et wos t a ge sc a nb ee x pr e ss e da s wh er eEoi st hel i nee ffic i enc ywi t h outb uff er s t or age.Thev al ueofEowasgi v enbyEq.( 5. l 6) ,butwewi l l wr i t ei tbel owt oe xpl i c i t l ydefi net het wost agesys t em effici encywhenb=0: Th et e r m D1 h( b )a p pe ar i ngi nEq .( 5 . 2 5r e pr e s en t s t hei mpr o v ementi neffic i e nc yt hatr es ul t sf r om a ddi ngb uff erc apac i t y( b>0) . D1i st hepr o por t i o no ft o t al t i met ha ts t age1i sdo wn.Ho we v er ,Buz ac ot tde finesD1as Not et hatt hef or m oft hi sequat i oni sdi ffer entf r om t h ec a segi v e nb yEq .( 5 . 6 )wh enwewe r ec o ns i d er i n gt h eHo wl i n et obeani n t e gr a lme ch an i s m, u nc omp l i c at e db yt h ep r e se nc eo fb uff ers t o ck s . Thet er mh ( b)i st h ei de alp r opor t i onoft hed own t i meD1( whenst ag e1i sdo wn)t hats t age2c oul d beupandoper at i ngwi t hi nt hel i mi t sofbuff erc apac i t yb.Buz ac ot t[ 2]pr es ent sequat i onsf or e v al ua t i ngh ( b)u si n gaMar k o vc hai nanal y s i s .Th eeq uat i onsc ov ers ev er ald i ff er entdo wn t i me di s t r i but i onsandar ebas edont heas sumpt i ont hatt hepr obabi l i t yofbot hs t agesbei ngdownatt he s amet i mei snegl i gi bl e.Fouroft hes eequat i onsar epr es ent edi nT abl e5. l . I ns ampl ec al c ul at i ons ,t heaut horhasf oundt hatEq.( 5. 21)t endst oo ver es t i mat el i neeffic i enc y .Thi s i sbec aus eoft heas sumpt i oni mpl i c i ti nt hec omput at i onofh( b)t hatbo t hs t ageswi l l notbebr ok en do wnatt hes amet i me.An ot he rwa yofs t at i ngt hi sas s umpt i oni st hi s :Dur i n gt h edo wn t i meofs t a ge l ,s t age2i sas sumedt oal way sbeoper at i ng.Howev er ,i ti smor er eal i s t i ct obel i ev et hatdur i ngt he do wnt i meo fs t a ge1 ,s t age2wi l l bed ownac er t ai npor t i o noft het i me ,t hi sdo wn t i mede t er mi nedb y t hee ffic i e nc yofs t ag e2.Hen ce,i ts eemsmor ea cc ur at et oe xpr es st heo v er al ll i n eeffic i e nc yofa t wo~s t agel i neasf ol l ows ,r at hert hanbyEq.( 5. 21): wh er eE2r e pr e s en t st h ee ffic i e nc yo fs t a ge2b yEq . ( 5 . l 7 ) .I nwor ks ubs eq ue ntt ot her es ear c hd oc ument e di nr ef er en ce[ 2] ,Buz ac ot tde v el o psamor e e xac ts ol ut i ont ot het wos t agepr obl em t hant hatpr o vi dedbyEq.( 5. 2l ) .Thi si sr epor t edi nr ef er enc e 5a nds eemst oagr eec l o sel ywi t ht her e sul t sgi v enb yEq.( 5. 29) .
EXAMPLE5. 5 Thi se xampl ewi l l i l l us t r at et heus eofEq.( 5. 29)a ndT abl e5. l t oc al c ul at el i neeffic i enc yf orat r ans f er l i newi t hones t or agebuff er .Thel i nehasI 0wor k s t at i ons ,eac hwi t hapr obabi l i t yofbr eak do wnof 0. 02.Thec y cl et i meoft hel i nei sImi n,andeac ht i meabr eak do wnoc cur s ,i tt ak esex ac t l y5mi nt o mak er epai r s .Thel i nei st obedi v i dedi nt ot wos t agesbyas t or agebanks ot hateac hs t agewi l l c on si s toffi v es t a t i o ns .Wewantt oc omp ut et h eeffic i e nc yoft het wos t agel i nef orv ar i o usbu ffe r c apac i t i es . Sol ut i on: Fi r s t ,l etuscomput et heeffic i enc yoft hel i newi t hnobuff erc apac i t y . ByEq.( 5. 16) ,
Ne xt ,di v i di ngt hel i nei nt ot woequal s t agesbyabuff er z on eofi nfi ni t ec ap ac i t y ,ea chs t a gewoul dha v eane ffic i e nc ygi v e nb yEq.( 5 . l 7 ) .
ByEq .( 5 . 1 8) ,Eo o=0 . 6 66 7r e pr e se nt st h e max i mum po ss i b l e:e ffic i en cyt hatc ou l dbeac hi e v edbyus i ngas t or ag eb uff erofi nfi ni t ec apac i t y . T ABL E5 . 1Fo r mu l a sf o rCo mp ut i n gh ( b )f o raT wo St a geFl o wl i n eu nd erSe v e r a lDo wn t i me Si t uat i ons Thef ol l o wi ngdefi ni t i onsan das s ump t i onsap pl yt oEqs .( 5. 25)t hr o ug h( 5 . 2 8)us edl oc omp ut eh( b ): As s umet h att het wos t agesha v eequal r e pai rl i mesan deq ual c y c l et i me s.Tha ti s , and l et whenBi st hel ar ges ti nt egers at i s f y i ngt her el at i on
a ndLr epr es en t smel e f t o v eru ni t s ,t hen umberb ywh i c hbe x c eed sBTd/ T c .Enal l y ,l e tr =F1 / F1 ,a sg i v e nb yEq _( 5 . 2 0) . Wi t ht hes edefi ni t i onsandas s umpt i ons ,wecane xpr es st her el at i ons hi psf ort wot heor e t i c al do wnt i med i s t r i b ut i on sasde v el ope db yBuz ac ot t[ 2] : 1.Cons t antr epai rdi s t r i but i on.Eac hdo wnt i meoc cur r enc ei sas s umedt or equi r eacons t antr equi r e t i meTd .
2. Geomet r i cr epai rdi s t r i but i on.Thi sdownt i medi s t r i but i onas sumest hatt hepr obabi l i t yt hatr epai r sar e c omp l e t e dd ur i n ga nycy c l ei si n de pe nde nto ft h et i mes i n cer ep ai r sbe ga n.De fin et h ep ar ame t e rK:
Th enf o rt h et woc a s es No w,wewi l l s eeho w Eq.( 5. 29)andt hef or mul asi nT abl e5. 1ar eus ed.Letusi n ves t i gat et hef ol l owi ng buff erc apac i t i es :b=1,10,100,and° ° . Wh enb=1 ,a c co r d i n gt oEq .( 5 . 2 4)i nT ab l e5 . 1 ,t h eb uff erc ap ac i t yi sc on v en edt oB=0 ,a ndL=1 . Wear ed eal i n gwi t hac on st antr epai r t i medi s t r i bu t i ona ndt heb r eak do wnr at e sar et hes amef or bo t hSt ages ,s or=1.Wewi l l t h er ef o r eus eEq.( 5 . 26 )t oc omput et he v al ueofh( 1): Us i ngEq.( 5. 23)t ogett hepr opor t i onoft ot alt i me t hats t a ge1i sdo wn
No wt h el i n ee ffic i e nc yc a nbec o mp ut e df r o m Eq .( 5 . 2 9) On l yav er ymo de s ti mp r o v eme ntr e su l t sf r o mt h e us eofast o r agebu ffe rwi t hc apa ci t yofonewo r kpar t . Wh enb=1 0,B=2an dL=0 .Th ev a l u eo fh ( 1 0)i sa ga i nc omp ut e df r o m Eq .( 5 . 2 6):
Ther es ul t i ngl i neeffic i enc yi s Weseea12% i ncr easei nl i neeffici encyoverEo f r om us i n gab uff erc ap ac i t yof10wor kuni t s Whenb=100,B=20,L=0,and
Ther e f or e , E=0 . 5 0+0 . 2 5(0 . 9 52)(0 . 6 667)=0 . 6 58 7 A3 2% i n cr e as ei nl i n ee ffic i e nc yr e su l t swh ent h eb uff erc a pa ci t yequ al s10 0.Co mp ar i n gt h i st ot h e c as ewh enb=1 0,wec a ns eet h el a wo fd i mi n i s hi n gr e t u r n so pe r a t i n g. Whent hes t or agec apac i t yi si nfi ni t e( b=° ° ) ,
E=0 . 5 0+0 . 2 5(1 . 0)(0 . 6 66 7)=0 . 6 66 7 ac cor di ngt oEq.( 5. 29) ,whi c hequal st her es ul tgi v enb yEq.( 5.18) . I ti sofi ns t r uc t i onalv al uet oc ompar et hi sr es ul tf orb=0° °g i v enbyEq.( 5. 29) ,wi t ht her es ul tgi v en b yEq.( 5. 21) ,whi c hnegl ec t st hepos si bi l i t yofo ver l appi ngs t agedo wnt i meoc c ur r enc es .Ac cor di ng t oEq.( 5. 2l ) ,t hel i neeffic i enc ywoul dbec al c ul at edas E=0 . 5 0+0 . 2 5(1 . 0)=0 . 7 5 wh i c h,o fc our s e,e x c eed st hema xi mum po ss i bl ev a l uegi v enb yEq.( 5.l 8) .Thec or r ec t edf or mul a , Eq.( 5. 29) ,pr ov i desbet t erc al c ul at edr es ul t s ,s i nc ei tac count sf ort heoc cur r enc eofo ver l appi ng b r e ak do wn sf o rt h et wos t a ge s. Fl ow l i neswi t hmor et hant wost ages
Wewi l l no tc ons i d ere x ac tf or mul a sf orc omput i n geffic i e nc i esf o rHo wl i ne sc ons i s t i n go fmor et han t wos t ages .l ti sl ef tt ot hei nt er es t edr eadert oc ons ul ts omeoft her ef er enc es ,i npar t i c ul ar[ 1] ,[ 2] , and[ 5] .Howe ver ,t hepr ev i ousdi s cus s i oni nt hi ssec t i ons houl dpr o vi deagener algui def ordec i di ng ont hec onfi gur at i onofmul t i s t agel i nes .Letusc ons i ders omeoft hes edec i s i onsi nt hec ont e xtofan exampl e. EXAMPLE5. 6 Suppo set hatt h efl owl i neunde rc o ns i der a t i onher eh asI 6st at i on swi t hc y c l et i meo f1 5s( as s ume t hatal l s t at i on sh av er oughl yeq ua lpr oc es st i mes ) .Whe ns t at i onb r e ak do wnsoc c ur ,t h ea v er a ge do wnt i mei s2mi n.Theb r eak do wnf r equenc i e sf oreac hs t at i onar epr es ent edi nt hef ol l o wi ngt a bl e. St at i on
pt
St at i on
pt
1
0 . 0 1
9
0 . 0 3
2
0 . 0 2
1 0
0 . 0 1
3
0 . 0 1
1 1
0 . 0 2
4
0 . 0 3
1 2
0 . 0 2
5
0 . 0 2
1 3
0 . 0 2
6
0 . 0 4
1 4
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7
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1 5
0 . 3 3
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1 6
0 . 3 1
Wewantt oc ons i dert her el at i v eper f or manc eswhent hel i nei ssepar at edi nt ot wo,t hr ee,orf our s t a ge s. Sol ut i on: Fi r s t ,t heper f or manc eoft hel i nec anbedet er mi nedf ort hes i ngl es t agec as e( nos t or agebuff er ) Fr om t het ab l e,t h ef r equenc yofdo wnt i meoc c ur r enc esi sgi v enb yEq .( 5 . 9 ):
Thel i n ee ffic i e nc yi s ,b yEq.( 5 . 16 )
T odi v i det hel i nei nt os t ages ,wemus tfi r s tdec i det he op t i mum l oc at i o nsf ort hest or ageb uff er s .Thest at i onss houl dbegr oupedi nt ost age ss oast omak e t heeffic i enc i esoft hes t agesasc l os easpos si bl e.Then,t oas ses sr el at i v eper f or manc esf ort he t wo,t hr ee,andf our s t agel i nes ,wewi l l bas et hec ompar i s onont heus eofs t or agebuffer swi t h i nfi ni t ec apac i t y . Fo rt h et wo s t a gel i n e,t h eb r e ak do wnf r e qu en cyofF=0 . 3 0s h ou l db es ha r e de v en l ybe t wee nt h e t wos t ag es .Fr o mt hef or egoi ngt ab l eofp,v al u esi tc anbede t er mi ne dt hatt hes t or a geb uff ers houl d bel oc at edbe t weens t at i ons8and9.Thi swi l l y i el dequal Fv al uesf ort het wos t ages .
Ther es ul t i ngs t ag eeffic i e nc i esan
Fr om Eq.( 5. 18) ,E. .=0. 454 5. Si mi l ar l y ,f ort het hr ees t agec onfi gur at i on,t hef r equenc yofbr eak downsshoul dbedi v i dedas equal l yaspos si bl eamongt het hr ees t ages .Ac cor di ngl y ,t hel i nes houl dbedi v i dedasf ol l ows; St a ge
St a t i o ns
Fk
Ek
1
1 5
0 . 0 9
0 . 5 81 4
2
6 1 0
0 . 1 0
0 . 5 55 6
3
1 11 6
0 . 1 1
0 . 5 31 9
Thet hi r ds t age,wi t ht hel owes teffic i enc y ,de t er mi nest heov er al l t hr ees t agel i neeffic i enc yEoo= 0 . 5 31 9. Fi nal l y ,f orf ours t agest hedi v i s i onwoul dbet hef ol l owi ng: St a ge
St a t i o ns
Fk
Ek
1
1 4
0 . 0 7
0 . 6 41 0
2
5 8
0 . 0 8
0 . 6 09 8
3
9 1 2
0 . 0 8
0 . 6 99 8
4
1 31 6
0 . 0 7
0 . 6 41 0
Ther es ul t i ngl i neeffic i en cyf o rt hef our s t agec onfi gur at i o nwoul dbeEoo=0. 60 98 Thee x ampl es ho wst hepr op era ppr oac hf o rd i v i di ngt hel i nei nt os t a ges .l ta l s os ho wsho wt h el i ne effic i enc yc ont i nuest oi nc r ea seast h enumberofs t or ag eba nk si si nc r e as ed.Ho we v er ,i tc anbe s ee nt h att h er a t eofi mp r o v eme nti neffic i e nc ydr o psoffasmo r es t a geb uff er sa r ead ded .I nt h e
f or egoi ngc al c ul at i onsweas sumedani nfi ni t ebuff erc apac i t y .Forr eal i s t i cc apac i t i es ,t heeffic i enc y woul dbel es saswasi l l us t r at edi nEx ampl e5. 5. Th ema x i mu mp os s i b l eeffic i e nc ywo ul dbeac h i e v e db yu s i n ga ni n fi ni t es t o r a geba nkb e t we ene v er y wor k s t at i on.St at i on6woul dbet hebot t l enec ks t age.Wel ea vei tf ort her eadert ofi gur eoutt hel i ne effic i enc yf ort heI 6 s t a gec as e.
COMPUTERSI MULATI ONOFAUTOMATEDFLOW LI NES
Anu mbe rofs t u di esha v ebeencon cer ne dwi t hsi mul at i ngt heo per at i onoffl owl i ne s,bo t h a ut o mat e da ndno na ut o ma t e d.So meoft h es est u di e sha v eb ee np er f or me db yl a r g ei n du s t r i al c on cer n sandt hemo del sde v el o peda swe l last h er es ul t sob t a i nedar eof t enc on si der edpr opr i e t ar y , Ref er enc es[ 8] ,[ 10] ,[ 11] ,[ 13] ,and[ 14]ar eas ampl i ngoft he r epor t soft hes es t udi es . Pr o duc t i o nmag az i ne[ 8 ]r epor t ss omeoft h er es ul t spr o v i d edb yac omput ers i mul at i o nmod el dev el opedbyI nger s ol lManuf ac t ur i ngc ons ul t ant s .Howev er ,v er yl i t t l ei nf or mat i oni sgi v enaboutt he det ai l soft hemodeli t s el f .Phi l l i psandSl ov i c k[ 13]r epor tonananal y si sofanac t ual c ont i nuous pr oduc t i onl i neatoneoft heWes t er nEl ec t r i cpl ant s .Thel i nei smanual l yoper at edwi t hs ev en wo r k s t a t i o ns .AGERTSt y pes i mu l a t i o nl a ng ua gewa su se dt od ev e l o pt h emo de lo ft h el i n e. Al t hought hes t udywasl i mi t edi ns copet ot hepar t i c ul aras sembl yandt es tl i ne,t hei nv es t i gat or s f oundt heGERTSs i mul at i onappr oac ht obequi t ev al uabl ef orpr oduc t i oncont r ol pur pos es .Phi l l i ps an dPr i t s k er[ 14]e x pl or et hep os s i bi l i t i esofus i ngGERTSo nanu mb erofp r oduc t i o ns y s t em s i t uat i ons . Oneo ft hemor ec ompr ehen si v ea ut omat edfl owl i nes i mul at i o ns t udi e sr e por t edi nt h el i t e r at ur ewas per f or medb yHani fi n[ 10, 11] .Hani fi nus edast heobj ec tofhi si n ves t i gat i ons ev er al ac t ual t r ans f er l i n esatt h eKo k omoWo r k sofCh r y s l e rCo r p or a t i o n.Hi sc omp ut e rmo de l ,u s i n gGPSSa st h e s i mu l a t i onl a ng ua ge ,wa sba se do nt h eo pe r a t i o no ft h es ema c hi n i n gfl o wl i n es .Th emo de lwa s de vel opedt odealwi t hs ev er als pec i fi cpr obl em ar easatChr y s l er .Yett her es ul t sofhi ss t udycanbe gener al i z edt os omee xt ent .Hi si nv es t i gat i onc ons i der edt heeff ec tofaddi ngupt ot hr ees t or age buff era r easoft hr ees pec i fi cl oc at i onsal ongt hel i ne.Heal s oi n ves t i gat edt heeff ec tofdi ffer ent a v er a get oo lc h an get i me s.
Si mu l at i o nh asbec omeamuc hmor ef ami l i art ool f ort hea nal y s tt ous et os t ud yt r ans f erl i nesan d o t h erp r o du ct i ons y s t e ms .Si mul a t i o ns o f t wa r ep ac k ag esha v eb ec omea v ai l ab l et h ata r emu c h ea si ert ous e,y e tpr o v i demor ec ap abi l i t i e st oi n v es t i g at es y s t em pe r f or manc e.Th es el a nguages i n cl udeSLAM l l ( Pr i t s k er&As s oc i at e s,I nc . ,We stLaf a y et t e,I ndi a na ) ,SI MAN( Sy s t emsMode l i ng Cor por at i on,St at eCol l ege,Penns y l v ani a) ,SEEWHY( I s t el l nc . ,Bur l i ngt on,Mas sac hus et t s ) ,and s e v e r a li mp r o v e dv e r s i o nso fGPSS.An i ma t e dg r a ph i c sc a pa bi l i t i e sar ebe c omi n gmo r ec ommo no n s i mul at i onl anguagess uc hast hes e,per mi t t i ngt heus ert ov i s ual i z emor ec l ear l yt heoper at i onoft he fl owl i ne( orot hers y st em) .Al t hought heequat i onspr es ent edi nt hi schapt erar eus ef ul asl ongast he a ss u mp t i on su nd er l y i n gt h em a r ev a l i d ,t h er ea r eman yflo wl i n es y s t e mswh os ec o mp l e x i t i e sa r e b ey o ndt h ea ss ume dc on di t i on so ft h es emo del s .As y nc hr o no ust r a ns f e rl i n esar eg oo de x amp l e so f pr oduc t i ons y st emsi nt hi sc at egor y .Robo tc el l s ,fl ex i bl emanuf ac t ur i ngs y st ems ,aut omat edmat er i al ha ndl i ngs y s t ems ,andot he rs y s t e mst hatwec ov e rl a t eri nt hi sbookar eal s os ome t i mest oo c omp l e xt os ub mi tt oanal y t i cmat he mat i c almo del s .Co mput ers i mul a t i on,es pec i al l ywi t han i mat ed g r a ph i c s ,c anbeus e dt oas s es st h ep er f o r ma nc eo ft h es eco mp l e xpr o du c t i o ns y s t e msa ndt o i dent i f yt hei rdes i gnfla wsandoper at i ngpr obl ems .
PROBLEMS 5. 1.Anei ght s t at i onr o t ar yi nde xi ngmac hi neoper at eswi t hani dealc y cl et i meof20s .The f r equen cyofl i nes t opo cc ur r enc esi s0. 06s t op/ c y c l eont h ea v er age.Whe nas t opoc c ur s ,i tt ak e san a v er ageof3mi nt oma k er ep ai r s .De t e r mi net h ef o l l o wi ng: ( a )Av e r agepr o duc t i ont i meTp ( b)Av er agepr oduc t i onr at eRp ( c )L i nee ffic i enc yE ( d )Pr op or t i onofdo wnt i meD 5 . 2 .As s umet h att h ef r eq ue nc yofl i n es t o po c cu r r en ce si nPr o bl em 5 . 1i sdu et or a nd om me ch an i c al andel ec t r i c al f ai l ur esont hel i ne.Suppos e,i naddi t i ont ot hef or egoi ngr eas onsf orl i nes t ops ,t hat t hewor k s t at i ont ool smus tber es etand/ orc hangedatr egul ari nt er v al s .I tt ak esana ver ageof4mi n t oi ns pec tandadj us torc hanget het ool satal l ei ghts t at i ons .Thi spr oc edur ei sper f or mede ver y200 c y c l e s .Re c omp ut eTp,Rp,E,a ndD wi t ht hes eaddi t i onal dat af ort hei nde xi ngmac hi ne.
5 . 3 .Co mp on en tc os t sas s oc i a t e dwi t ht h eo pe r a t i o no ft h ei n de x i n gma ch i n eo fPr o bl e m5 . 2a r ea s f ol l ows: c os to fr a w wor k par t=$0. 35 / wor k pi ec e c os tt ooper at et hel i ne =$0. 50( mi n c os tofdi s pos abl et ool i ng =$0. 02/ wor k pi ec e Co mp ut et h ea v e r a gec o s tp erwo r k p i e c ep r o du c edo fft h er o t a r yi n de x i n gma c hi n e. 5. 4.I nt heoper at i onofac er t ai n15s t at i ont r ans f erl i ne,t hei dealc y cl et i mei s0. 58mi n.Br eak downs o c c ura tar a t eo fo nc ee v e r y1 0c y c l e s ,a ndt h ea v e r a ged own t i mep erb r e ak d ownr a ng esbe t we en2 and9mi n,wi t hanav er ageof4. 2mi n.Thepl anti nwhi c ht het r ans f erl i nei sl oc at edwor k san8h d ay , 5da y spe rwe ek .Ho w ma nypa r t swi l l t h el i n eb ec ap ab l eo fp r o du c i n gd ur i n ga na v er ag e week? 5. 5.Thef ol l owi ngdat aappl yt oa12s t at i oni nl i net r ans f ermac hi ne: 01( al l s t at i onshav eanequal pr obabi l i t yoff ai l ur e) p =0. T c =0 . 3mi n
=3 . 0mi n Td Us i n gt heup per boundappr oac h,c omput et hef ol l o wi ngf ort het r an sf ermac hi ne: ( a)F,t hef r equenc yofl i nes t ops . ( b)Rp,t hea ver agepr oduc t i onr at e. ( c )E,t hel i neeffic i enc y . 5 . 6 .So l v ePr o bl e m5 . 5u s i n gt h el o wer b ou nda pp r o ac h.Wh atp r o po r t i o no fwo r k pa r t sar er e mo v ed f r om t het r ans f erl i ne? 5. 7.Ac i r c ul ari nd ex i ngma chi neper f o r ms10as s embl yop er at i o nsat10s epar at es t at i ons .Thet o t al c yc l et i me,i nc l udi ngt r ans f ert i mebet weens t at i ons ,i s10s .St at i o nsbr eakdo wnwi t ha pr obabi l i t y =0 . 0 07 ,wh i c hc anb ec on s i d er ede qu al f o ra l l 1 0s t a t i o ns .Wh ent h es ewo r ks t o pp ag es p oc cur ,i tt ak esana v er ageof2mi nt oc or r ec tt hef aul t .Par t sar eno tnor mal l yr emo vedf r om t he ma ch i newh ent h es es t op soc c ur .Co mp ut et h ep r o po r t i o no fd own t i me ,t h ee ffic i e nc y , a ndt h e pr oduc t i onr at eoft hi sci r c ul ari nde xi ngmac hi ne. 5. 8.At r ans f ermac hi nehass i xst at i onsasf ol l o ws : St at i o n
Oper at i o n
p i
Pr oc es st i me( mi n)
1
L oa dp ar t
0
0 . 7 8
2
Dr i l l t hr eehol es
0. 02
3
Ream t wohol es
0. 01
0. 90
4
T apt woh ol e s
0 . 0 4
1 . 4 2
5
Mi l lfl at s
0. 01
1. 42
6
Un l o adp ar t
0
0 . 4 5
1. 25
Thet i met ot r ans f erbet weens t at i ons=0. 28mi n.I ft hepar ts t opsduet oaj am i nt hel i ne,i ti s r emo v eda sd ef ec t i v e.I tt ak e sana v er ageof8mi nt ode t er mi net hef au l t . a ndc or r ec tt h ep r o bl e m an dr emo v et h epar t .Al s o,t h er ei sasc he dul edt ool c hang ee v er y40par t swhi c ht ak e s6mi nt o c omp l e t e.Th er ear e20, 000pa r t st obes t ar t e don t ot het r an sf ermac hi ne . ( a )Ho w man ydef e ct i v ep ar t swi l l b er emo v edf r om t hel i ne ? ( b )Ho w man yt o t a lh ou r swi l l b ec on su me di nt h ema nu f a ct u r i n gp r o ce ss ? ( c )Fi ndt hepr opor t i onofdo wnt i me. ( d)Fi ndt her at eofpr oduc t i onofac cept abl epar t s . 5. 9.I nPr obl em 5. 8,t hec os tofoper at i ngt het r ans f ermac hi nei s$60/ h,ases t i mat edbyt he ac c ount i ngdepar t me ntoft hec ompan y .I ti spr opos edt ha tacomput era nds ens or sbei ns t al l edt o a i di nd i a gn os i n gb r e ak do wn swh ent he yoc c ur .Th ea nt i c i pa t e ds a v i n gsar e2mi no fft h e8mi nt o i dent i f yandc or r ec tt hef aul twheni toc cur s .Thecomput erwi l l ha venoeff ec tont oolc hanges .The es t i mat edc os tofi ns t a l l i ngt h emoni t or i ngs y s t em i s$11 , 000 .Ho w ma nyun i t smus tt h es y s t em pr o du cei nor dert opa yf ort hec omput er ? 5. 10.A23s t at i ont r ans f erl i nehasbeenl oggedf or5day s( at ot al of2400mi n) .Dur i ngt hi st i me, t her ewer eat o t alo f1 58do wnt i meo cc ur r enc esont h el i ne.I heac c ompan yi ngt a bl ei dent i fi est he t y peofd own t i meoc c ur r e nc e,h owma nyoc c ur r en ce s ,a ndho w mu c ht o t a lt i mef o rt h et y peof o c c u r r e n c e . Nu mb ero f
T o t a lmi n ut e s
T y peo fo cc ur r e nc e
o c cu r r e nc e s
l o s t
As s oc i at edwi t hs t at i on s
1 32
793
T ool r el at edc aus esats t at i ons
104
520
Mec hani c alf ai l ur esats t at i ons
21
189
Ot hermi s c el l aneouss t at i onf ai l ur es
7
As s oc i a t e dwi t ht r a ns f e rme ch an i s m
2 6
84 7 8
Thet r an sf erl i nep er f or msas eq uenc eofmac hi n i ngope r at i ons ,t hel onge sto fwh i c ht ak e s0. 42mi n. Thet r an sf ermec han i s mt ak es0. 08mi nt oi nde xapa r tf r om on es t at i ont ot h ene x tpo si t i on. As sumi ngnopar t sr emo valwhent hel i nej ams ,det er mi net hef ol l owi ngc har ac t er i s t i c sf ort hi sl i ne f ort he5dayper i od: ( a)Howmanypar t sar epr oduced. ( b )Do wnt i mepr opor t i on. ( c )Pr oduc t i onr at eandpr oduc t i ont i me. ( d )Fr e qu en cyr a t epa s so c i a t e dwi t ht h et r a ns f e rme ch ani s mb r e ak do wn s. 5. 11.Anei ght s t at i ont r ans f erl i nehast hef ol l owi ngoper at i onsateac hs t at i on;al s ogi v enar et he pr oc es si ngt i meandt hef r equenc yofl i nes t opsf oreac hs t at i on.Dur i ngt heobs er v at i onper i odt her e we r e20 00pa r t sc o mp l e t e d. St a t i o n
Pr o c es s
Pr o c es st i me( mi n )
Br e ak d own s
1
L oa dp ar t
0 . 4 0
0
2
Mi l l t op
0. 85
22
3
Mi l l s i des
1. 10
31
4
Dr i l l t wohol es
0. 60
47
5
Ream t wohol es
0. 40
8
6
Dr i l l s i xhol es
0. 90
58
7
T aps i xh ol e s
0 . 7 5
8 4
8
Un l o adp ar t
0 . 5 0
0
Al s oi nfl ue nc i ngt h ec y c l et i mei st heope r at i o noft het r a ns f ermec ha ni s m,whi c ht ak e s0. 15mi n e ac hc y c l e .Wh enb r e ak do wn so c cu ri tt a k esana v er a geo f7 . 0 0mi nt oma k er e pa i r san dg ett h el i n e op er a t i nga gai n .As s umet h att heupper boundappr oac hi sop er a t i v ei ny oura nal y s i sf ort he f ol l owi ng: ( a)De t er mi net hea ver agepr oduc t i ont i meperpi ec eandt hehour l ypr oduc t i onr at ef ort hi st r ans f er l i ne. ( b )Whati st heup t i meeffic i enc yoft h el i n eandt hepr opor t i ondo wn t i me?
( c )Ho wma nyh ou r swe r er e qu i r e dt opr o du c et h e2 00 0p ar t s ? 5 . 1 2.I nPr o bl e m5 . 1 1,i ft h el o we r b ou nda pp r o ac hwer eu se di n s t e ado ft h eu pp er b ou nda pp r o ac h, an di ft hef r equenc yofbr ea kdo wn si nt hel o wer b oun da ppr oac hF=0. 10,de t e r mi net h ef ol l o wi n g ( a s su mi n gt h att h ep r o ce sst i me s,t r a ns f e rt i me ,a nda v er a ged ownt i mep ero c cu r r en c ea r et h es ame i nPr obl em 5. 11 ): ( a )Ho w man yr a w wo r k pa r t swo ul dh av es t a r t e do nt h el i n ei nor d ert oc o mp l e t et h e2 00 0p ar t s ? ( b)Howmanypar t swoul dhavebeenr emovedf r om t hel i neasdamagedduet obr eakdownsi f2000 p ar t swe r ec o mp l e t e d? ( c )Ho wma nyh ou r swo ul dha v ebe enr e qu i r e dt opr o du c et h e2 00 0c o mp l e t e dp ar t s ? 5 . 1 3.Th eAPSCI M Ma c hi n e&Fo un dr yop er a t e sana ut o ma t e dt r a ns f e rl i n ewi t h1 2s t a t i o ns .Th e l i nei sc ons i der edt oha veaneffic i enc yt hati sunac cept abl yl o w.Fi gur eP5. 13i sar epor tofas t udy ont hec ur r en tl i neo per a t i ons .APSCI M wou l dl i k et oi mpr o v et heeffic i en cybymak i ngt hef ol l o wi ng c hangesi nt hel i ne: Fi r s t ,c hang eo v erf r om t hec ur r entel ec t r omec hani c alr el a y –t y pec ont r ol st oapr og r amma bl e c ont r ol l er .I naddi t i ont oc ont r ol l i ngt hel i nei nt hes amewa yasbef or e,t henewc ont r ol l erwoul d r ed uc et h ea v er ag ed own t i meb ydi a gn os i n gt h ema l f u nc t i o n,t h usal l o wi n gr e pa i r st ob ema demor e qu i c k l y .I ti sex pec t edt hatt h ea v er a gedo wnt i mep ero cc ur r enc ewi l l ber ed uc edb y25% us i ngt hi s di agn os t i csy s t em. Sec ond,di v i det hec ur r entl i nec ons i s t i ngof12s t at i onsi nt ot wos t ages ,eac hc ons i s t i ngofs i x s t a t i on s.Ani n p r o c es ss t o r a geb uff erwo ul db eu se db et wee nt h es t a ge ss ot h ate ac hs t a gec o ul d oper at easani ndependentt r ans f erl i ne.Thi si sex pec t edt oi mpr o vet heo ver al lpr oduc t i onr at eand l i neeffic i enc y . Det er mi net hef ol l owi ng: ( a)Thepar amet er soft hel i neper f or manc easi tc ur r ent l yoper at es( wi t houtt hei mpr o vement s ) . Thes es houl di nc l udet hei dealc y cl et i me,t hef r equenc yofl i nes t ops ,t hel i neeffic i enc y ,andt he a ver agehour l ypr oduc t i onr at e. ( b )T heeff ec toft h et woc hang esi nt hel i neop er at i o nde sc r i bedabo v e.De t er mi net hee ffe cto fbo t h oft h ec hange st oge t herr a t he rt h ane ac hc hanges ep ar at e l y .Yo uran al y s i ss houl dr e sul ti nan as ses smentoft hel i neper f or manc ef oreac hs t age( i deal c y cl et i me,t hef r equenc yofl i nes t ops ,t he
l i neeffic i enc y ,andt hea ver agehour l ypr oduc t i onr at e) .Al s o,det er mi net heo ver al lper f or manc eof t h et wo s t a gesy s t e m.I ny ou ra na l y s i s ,a s su met h eu pp er b ou ndap pr o ac h .Ma k ea nyo t h er ad di t i onal as s ump t i onsnec es s ar yt os ol v et hepr o bl em. 5. 14.A14s t at i ont r ans f erl i nehasbeenl oggedf orat ot al of2400mi n.Thef ol l owi ngt abl ei dent i fi es t h et y p eo fd own t i meoc c u r r e nc e ,h owma nyo c c ur r e nc e s ,a ndho w mu c ht i mewa sl o s tf o re ac h t y p e . T y p eo fo c c ur r e nc e
Nu mb er
Ti mel o s t( mi n s )
T ool c h an ge sa ndf a i l ur e s
7 0
4 00
St at i onf ai l ur es :mec h.&el ec .
45
300
T r ans f ers y st em f ai l ur es
25
150
Thei dealc y cl et i mef ort hel i nei s0. 50mi n,i nc l udi ngt r ans f ert i mebet weens t at i ons .Hal foft he do wnt i meo cc ur r enc esf or“ t ool c hang esan df a i l ur es ”( 35oc c ur r enc esan d200mi n)i n v ol v ec as es wh er et h ep ar twa sda ma ge da ndha st ober e mo v e df r o mt h el i n e.Th eo t h erd own t i meoc c u r r e nc e s f ol l owt heas sumpt i onsoft heupper boundappr oac h.Det er mi net hef ol l owi ngc har ac t er i s t i c soft he l i neoper at i on. ( a )Ho wma nyac c e pt a bl ep ar t swe r ep r o du c edd ur i n gt h e2 40 0mi np er i o d? ( b )Wh atwer et h el i n ee ffic i e nc yan ddo wn t i mepr o por t i on ? ( c )Wh atwast hea v er ageac t u al pr oduc t i onr at eofac c ep t abl ep ar t si npar t sperhour ? ( d)De t er mi net hef r equenc ypas s oc i at edwi t ht het r ans f ers y st em f ai l ur es ? 5 . 1 5.Ap ar t i a l l yau t o ma t e dfl o wl i n eh asami x t ur eo fme ch an i z eda ndma nu alwo r k s t a t i o ns .Th er e ar eat ot al ofs i às t at i onsandt heov er al lt heor et i calc yc l et i mei s1. 0mi n.Thi si nc l udesat r ans f er t i meof6s .Thes i xst at i onspos ses sc har ac t er i s t i c sasf ol l ows: St at i o n
T y pe
Pr o ces st i me( s )
pg
1
Manual
30
0
2
Au t o ma t i c
1 5
0 . 0 1
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0 . 0 1
5
Manual
54
0
6
Manual
30
0
.
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Co stoft het r an sf erme chani s mi s$0. 10 / mi nt oo per at e.Co stt or unea choft heaut omat i c wor k headsi sfig ur edat$0. 12/ mi nf oreac ho ft het hr eeaut omat i cs t a t i ons .Lab orc os tt oo per at e ea choft hemanu al s t at i on si s$0 . 1 5/ mi nf ore ac hofs t at i ons1,5,a nd6 .I tha sbee npr opos edt o s ubs t i t ut eanaut omat i cwor k headf ort hec ur r entmanual s t at i on5.Thec os toft hi swor k headwi l l be 0. 25 / mi nan di t sbr eak do wnr at epwi l l b e0. 02,bu ti t spr oc es st i mewi l l b eonl y30sc omp ar edt o54 sf o rt h ec un en tl i n e.Th ea v er a gedo wn t i mepe rb r ea kd ownoft h ec un en ta ndpr o po se d c on figur a t i oni s3. 0mi n.Shou l dt hep r opos al beac c ep t ed? 5. 16.Amanualfl owl i nehassi xs t at i ons .Thet i mer equi r edt opr oc es st hepar tateac hs t at i oni s1. 0 mi n.Thepar t sar et r ans f enedb yhandf r om ones t at i ont ot hene xt ,andanaddi t i onal 12si sl os t eac hc yc l eduet ol ac kofoper at ordi s ci pl i ne.Henc e,t hec ur r entc yc l et i meont hel i nei s1. 2mi n. ’ I be f ol l owi ngt wopr opos al sha vebeenmade: . Fi r s t ,i ns t al l amec hani z edt r ans f ers y st em t opac et hel i ne. Sec ond,aut omat eoneormor eoft hewor k st at i onsont hel i ne,r es ul t i ngi napar t i al l yorf ul l y aut omat edl i ne.Thi sr equi r esi ns t al l at i onoft hemec hani z edt r ans f ers ys t em i nt hefi r s tpr opos al .The t r ans f ers ys t em al onewi l l br i ngdi s ci pl i net ot hel i neandc aus et hec yc l et i met ober educ edt o1. 0 mi n.Al l s i xs t at i onsar ec andi dat esf ora ut omat i on;howev er ,t her ear edi ffer enc esi nt her el i abi l i t y wi t hwhi c ht heaut omat eds t at i onswoul doper at e.Thi si smani f es t edi nt hev al ueofp,t hepr obabi l i t y ofas t at i onf ai l ur e.Thes epr obabi l i t yv al uesam gi v eni nt hef ol l owi ngt abl e. St at i on
Pr obabi l i t y p
St at i on
Pr obabi l i t y p
1
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4
0 . 0 4
2
0 . 0 2
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Th ea v e r a gedo wn t i me=3mi nwh enan yoft h es eau t o ma t e ds t a t i o nsb r e akd own .Th ei d ea lc y c l e t i mef o rea chaut omat edst at i oni s20s.Thecos toft heau t oma t edt r a ns f ermec ha ni s m( wh i c h s er v esal l s i xst at i ons )=$0. 10/ mi n.Thec os tperoper at oront hel i ne=$0. 20/ mi n;andt hec os tper aut omat e dwor k s t a t i on=$ 0. 25/ mi n .De t e r mi n ei fei t herorbo t hoft h epr o pos al ss hou l dbea cc ep t ed. I ft h es e co ndpr o po s ali sa c ce pt e d,h owma nys t a t i o nss ho ul db ea ut o ma t e d?Us eco s tp erp i e ceas t hec r i t er i onf ory ourdet er mi nat i ons . 5. 17.A16s t at i onaut omat i ct r ans f erl i nehast hef ol l owi ngoper at i ngc har ac t er i s t i c s: T c =0. 75mi n
Td =3 . 0mi n
01f oral l wor k st at i ons p =0. Ap r o po s alh asb ee ns ub mi t t e dt opl a ceas t o r a geb uff erb et we ens t a t i o ns8a nd9t oi mp r o v et h e o ver al leffic i enc yoft het r ans f erl i ne.Whati st hec ur r entl i neeffic i enc y( us et heupper bound a pp r o ac h) ,a ndwh ati st h ema xi mu mp os s i b l ee ffic i e nc yt h atwou l dr e su l tf r o mu s eo fast o r a ge b u ff e r ? 5. 18.I ft hec apac i t yoft hes t or agebufferi nPr obl em 5. 17i st obe10wor k par t s ,c al c ul at et hel i ne effic i enc yandt h ea v er ag ep r odu ct i o nr at eoft h et wos t a get r ans f erl i n e.As s umet hatdo wn t i me ( =3. 0mi n)i sac ons t a nt . Td 5. 19 .Sol v ePr o bl em 5 . 1 8as s umi ngt hatdo wn t i mei sgeo me t r i c al l yd i s t r i but e d. 5. 20.I nt het r ans f erl i neofPr obl em 5. 19,s uppos et hati ti smom t ec hni c al l yf eas i bl et opl ac et he s t or agebu ffe rb e t weens t at i ons6and7.Us i n gas t or agebuff erc apac i t yof10wor k par t s ,c al c ul at e t hel i n ee ffic i e nc yandt heav er agepr o duc t i onr at e.As s umet hatdo wnt i mei sc ons t ant . 5. 21 .Sol v ePr o bl em 5 . 2 0bu ta ss umet h atdo wnt i mei sgeome t r i c al l ydi s t r i but ed. 5. 22.As ync hr onoust r ans f erl i nehas20s t at i onsandoper at eswi t hani deal c y cl et i meof0. 5mi n.Al l s t a t i on sh av ea ne qu alp r o ba bi l i t yofb r ea kd own ,p=0 . 0 1.Wh enb r e ak do wn so c cu r ,t h ea v er a ge d own t i mei s5. 0mi na ndt h eu pp er b ou nda pp r o ac ha pp l i e s .Ap r o po s alh asbe enma det od i v i d et h e l i n ei nt ot woi nde pende nts t ag es ,eac hs t ageha v i ng1 0s t a t i ons ,wi t habuff ers t or ag ez onebe t ween t hes t at i ons .Thepr opos al i ndi c at est hateac hs t agec oul doper at ei ndependent l yt oi nc r eas e pr oduc t i onr at eoft heov er al l l i ne.I thasbeendec i dedt hatt hes t or agec apac i t ywi l l be 25uni t s . 1bec os tt ooper at eeac hs t at i oni s$4. 80/ 6pers t at i on.I ns t al l at i onoft hebuffers t or agez one woul di nc r eas et hel i neoper at i ngc os tby$12. 00/ h.I gnor emat er i alandt ool i ngc os t si nt hi spr obl em. ( a)De t er mi net hea ver agepr oduc t i onr at eperhourandt hec os tperuni tofpr oduc t i onf ort hec ur r ent 20s t at i onl i ne. ( b)Cal c ul at et hea ver agepr oduc t i onr at eperhourandt hec os tperuni tf ort hepr opos edt wos t age syst em. 5. 23.Ac er t ai n16s t at i ont r ans f erl i nec anbec onv eni ent l ydi v i dedi nt oat wos t agel i newi t habuffer s t or agez onebet weent heei ght handni nt hwor k st at i ons .Hepr obabi l i t yofaf ai l ur eatanys t at i oni s p =0. 01.Thei d eal c y c l et i mei s1. 0mi nan dt h edo wnt i meont hel i nei s10. 0mi ne v er yt i mea
l i n es t o po c cu r s .Hedo wn t i mes h ou l dbeco ns i d er e dt obeco ns t a nt ,a ndt h eu pp er b ou ndap pr o ac h s houl dbeas s umed.Thec os tofi ns t al l i ngt hebuff ers t or agez onei saf unc t i onofi t scapac i t y .The c os t=$ 0. 6 b/ h=$ 0. 0 1b / mi n ,wh er eb=t h eb uff erc ap ac i t y . Ho we v er ,t h es t o r a geb uff erc a no nl ybe bui l tt ohol di nc r ement sof10( i . e. ,c apac i t y=10or20or30,et c . ) .Hec os tt ooper at et hel i nei s$120 perhour .Mat er i al c os t sandt ool i ngc os t ss houl dbei gnor ed.Bas edonc os tperuni tofpr oduc t , de t er mi net hec apac i t yoft hebuff erz onet hatwi l l mi ni mi z et hepr oduc tc os t . 5. 24.Theoper at i onofacer t ai n20s t at i onl i nei sv er ypoorandt hemanagementi sl ook i ngt o i mp r o v et hel i ne ’ spe r f or manc e.Th ei dea lc y c l et i mei s48s ,andt heup t i mee ffic i enc yi sonl y40 %. Th ea v e r a ged own t i mep ero c c ur r e nc ei s3. 0mi n .As s u met h att h ef r e qu en c yo fb r e ak d own si se qu al f oral l s t at i onsandt hatt her epai rt i medi s t r i but i oni scons t ant .Oneoft heal t emat i v esunder c on si der at i oni st odi v i det h el i nei nt ot woe quals t a gesbymeansofas t o r agebuff er .Eac hs t age woul dha ve10wor k s t at i ons .Thec ompan yc ani ns t al l abuff erwi t ha15uni tc apac i t yi nt hel i nef or $14, 000.Thepr es entuni tc os tofpr oduc t i oni s$4. 00peruni tpr oduc ed( t hi si gnor esmat er i al and t ool i ngc os t s ) .Howman yuni t swi l l ha vet obepr oduc edi nor derf ort he$14, 000i nv es t menti nt he s t or agebuffert opayf ori t s el f ?
Aut omat edAss embl ySy st ems Th et e r ma ut o ma t e da s s emb l yr e f e r st ot h eu s eo fme c ha ni z e da nda ut o ma t e dd ev i c e st op er f o r m t hev a r i ou sf u nc t i onsi nanas s embl yl i neorc el l .Muc hpr o gr es sha sbeenmadei nt het e chnol og yof a ss e mb l yaut oma t i o ni nr e ce nty e ar s .So meo ft h i spr o gr e ssha sb ee nmo t i v a t e db yad v an ce si nt h e fi el do fr o bo t i c s .I n du s t r i a lr o bo t sar es ome t i me su s eda sc omp on en t si na ut o ma t e da s se mb l y s y st ems .Theappl i c at i onsofr obo t s ,i nc l udi ngt hos ei nas s embl yoper at i ons ,ar edes cr i bedi n Ch apt er13 .I nt h ec ur r entc hapt er ,west ud ya ut omat edas s embl yasasep ar at efiel dofaut omat i on . Al t h ou ght h ema nu al a s s emb l yme t h od sd es c r i b edi nCh ap t e r6wi l l n od ou btb eu s edf o rma n y y ear si nt ot hef ut ur e,s i gni fi cantoppor t uni t i esf orp r oduc t i v i t ygai nsex i s ti nt heus eofaut omat ed me t hods .Fort her eaderi nt er es t edi npur s ui ngt hi st opi cofaut omat edas sembl yi nmor ede t ai l ,t her e ha v ebe ens ev e r a lbo ok swr i t t eni nt hel as tf e wy e ar st hatwer ec ommend[ 1 , 3, 9] .
I tt ur nsoutt hatt hepr oduc t ’ sdes i gnhasas i gni fi canti mpac tont heeas ewi t hwhi c hi t sas sembl y c anbeaut omat e d.Webe gi nourc ha pt erwi t ht hi st opi c .
DESI GNFORAUTOMATEDASSEMBL Y On eo ft h ei mp ed i me nt st oau t o ma t e da s se mbl yi st h atma nyoft h et r a di t i o na la s se mbl yme t h od s d es c r i b edi nCh ap t e r6e v o l v e dwh enhu ma nb ei n gswe r et h eo nl ya v ai l a bl eme an sofa s s emb l i n ga pr o du ct .Man yoft hemec han i c alf a st ener sc ommonl yus edi ni ndu st r yt oda yal mos tr equi r et he s pe ci al an at omi c al a nds ens or yc ap abi l i t i esofhumanbe i ngs .Con si der ,f o re x amp l e,t h eus eofa s c r e w,al oc kwas her ,a ndan utt of a st ent wos hee tme t al par t sonap ar t i al l ya ss emb l edc abi ne t . Thi st y peofoper at i oni st y pi c al l yac c ompl i s hedmanual l yatei t heras i ngl eas sembl yst at i onoronan as sembl yl i ne.Thec abi neti sl oc at edatt hewor k s t at i onwi t ht het wos hee tme t al par t st obef as t ened atana wk war dpos i t i o nf ort heope r at ort or eac h.Theoper at orpi c k supt hes c r e w,l o ckwas her ,and nu t ,s ome ho w mani pul at i ngt he mi nt opos i t i o no nopp os i t es i desoft het wopa r t s ,an dpl ac est h el oc k was herandt hent henutont ot hes c r ew.Asl uc k,woul dha vei t ,t het hr eadsoft henuti ni t i al l ybi ndon t hes c r e wt hr eads ,s ot heoper at ormus tuns cr ews l i ght l yandr es t ar tt hepr oc es s,us i ngawel l d ev e l o peds en seoft o uc ht oen s ur et h att h et h r e ad sar ema t c hi n g.On c et h es c r e wa ndn uth av e beent i ght enedwi t hfi nger s ,t heoper at orr eac hesf ort heappr opr i at es cr e wdr i v er( t her ear ev ar i ous s i z esofs cr e wswi t hdi ff er ent s hapedheads )t ot i ght ent hef as t ener . Th i st y peofma nu al o pe r a t i onha sbe enu s edco mmo nl yan ds uc c es s f u l l yi ni n du s t r yf o rma nyy e ar s t oas s embl epr oduc t s .Thehar dwar er equi r edi si ne xpens i v e,t hes hee tme t al i sr eadi l yper f or at edt o pr o vi det h emat c hi n gc l ea r an cehol e s,andt heme t hodl en dsi t s el ft ofi el ds er v i c e.Whati sbec omi ng v er yex pens i v ei st hemanuall aboratt heas s embl ywor k s t at i onr equi r edt oac compl i s ht hei ni t i al f a st en i ng .Thehi ghc os tofmanu all a borhasr es ul t edi nar ee x ami na t i onofas s embl yt ec hn ol o gy wi t hav i e wt o wa r dau t o ma t i o n.Ho we v er ,a ut o ma t i n gt h ea s se mbl yop er at i o nd es c r i b edab ov ewo ul d bev er ydi ffic ul t .Fi r s t ,t hepos i t i onsoft hehol est hr oughwhi c ht hes cr ewmus tbei ns er t edar e di ffer entf oreac hs cr e w,andt hepos i t i onma ybedi ffic ul tf ort heoper at ort or eac h.Sec ond,t hesc r e w ho l esbe t weent het wos hee tme t a lpa r t sma yno tmat c huppe r f ec t l y ,n ec es s i t at i ngt heope r at ort o r epos i t i ont het wopar t sf orabe t t ermat c h.Thi r d,t heoper at ormus tj uggl et hr ees epar at ehar dwar e
i t ems( s cr ew,l oc kwas her ,andnut )t oper f or mt hef as t eni ngoper at i on.Four t h,as ens eoft ouc hi s r equi r edt omak es ur et hatt henuti sst ar t edpr oper l yont ot hes cr e wt hr ead.Eac hoft hes ef our pr o bl emsmak esaut omat i onoft heoper at i ondi ffic ul t .Al l f o urp r obl emst og et hermak ei tnea r l y i mp os s i b l e .Asac o ns eq ue nc e,a t t e mp t sata s se mb l yau t oma t i o nh av el e dt oa ne x ami n at i o no ft h e me t h od ss pe c i fi e db yt h ed es i g ne rt of a st e nt o ge t he rt h ev a r i o usco mp on en t sofap r o du ct . Thefi r s tan dmos tg ener al l e ss on,ob vi ou sf r o mt hee x ampl eab ov e ,i st hatt heme t hodst r a di t i onal l y u s edf o rma nu ala s s emb l yar en otn ec e s s ar i l yt h eb es tme t h od sf o ra ut o ma t e da s s emb l y .Hu ma n bei ngsar et hemos tde xt er ousandi nt el l i gentmac hi nes:abl et omo v et odi ffer entpos i t i onsi nt he wor k s t a t i on,a bl et oadap tt ou ne xp ec t edp r obl emsandne ws i t u at i on sdur i ngt hewor kcy c l e,c apab l e ofmani pul at i ngandc oor di na t i ngmu l t i pl eobj e ct ssi mul t aneo us l y ,anda bl et omak eus eofawi de r a ngeo fs e ns esi np er f o r mi n gwo r k .Fo ra s s emb l yaut o ma t i o nt ob ea c hi e v ed ,f a s t e ni n gp r o c ed ur e s mu s tb ed ev i s e da nds pe ci fi edd ur i ngp r o du ctd es i g nt h atd on otr e qu i r ea l l o ft h es eh uma n c apabi l i t i es .
TYPESOFAUTOMATEDASSEMBL YSYSTEMS As s umi ngt ha tt h ep r o duc td es i gni sc ompat i bl ewi t haut omat edas s embl y ,t her ea r es ev er al di ff er ent wa y st oc ha r a ct e r i z et h eo pe r a t i o na ndc o nfi gu r a t i o no ft h ea ut o ma t e da s se mb l ys y s t e m.On ewa yt o c l as si f yt hes y st em i sbyt het y peofwor kt r ans f ers y st em t hati sus edi nt hes y st em.Thet y pesar e: •
Cont i nuoust r ans f ers y st em
•
Sy nc hr onoust r ans f e rs y s t e m
•
As y nc hr o no ust r a ns f e rs y s t em
•
St at i onar ybas epar ts y st em
Thefi r s tt hr eet y pesi n vol v et hesamemet hodsofwor kpar tt r ans por tdes cr i bedi nSec t i on4. 2.I nt he s t at i onar ybas epar ts y s t em,t h ebas epar t( t owhi c ht heo t he rc omponent sar ead dedi spl ac edi na
fi x edl oc at i on ,wh er ei tr emai nsdur i ngt heas s embl ywor k . Ano t herwa yofc l as s i f y i ngaut omat eda ss embl ysy s t emsi sbyt hei rph y si c al c onfi gur at i on.The pos si bl ec onfi gur at i onsi nc l ude: •
Di a l t y peas s emb l yma c hi n e
•
I nl i n ea ss emb l yma chi ne
•
Ca r o us e la s s emb l ys y s t e m
•
Si n gl e s t a t i onas s embl ymac hi ne
Thedi al t y pemac hi nei ssho wni nFi gur e7. 1.I nt het y pi c al appl i c at i on,bas epar t sar el oadedont o fi x t ur esornes t st hatar eat t ac hedt ot hec i r c ul ardi al .Component sar eaddedand/ orf as t enedatt he v ar i ouswor kst at i onsl oc at edar oundt heper i pher yoft hedi al .Thedi ali nde xi ngmac hi nei st hemos t c ommons y s t em i nt h i scat ego r y .I to per at eswi t has y nc hr ono usori n t er mi t t entmo t i on,wh er et h e c y c l ec ons i s t soft hepr o ces st i mepl usi nd ex i ngt i me.Se v er alo ft h emec ha ni s msde sc r i bei nSe ct i on 4 . 3c a nb eu s edt op r o v i det h i smo t i o n.Al t h ou ghl e s sc o mmo n,d i a l t y pea ss e mb l yma c hi n esar e s ome t i me sdes i gnedt ous eacont i nuousmo t i o nr at he rt hanani nt e r mi t t en tmo t i on. Thei nl i neas sembl ymac hi nec ons i s t sofas er i esofaut omat i cwor kst at i onsl oc at edal ongani nl i ne t r ans f ers y s t e m.I ti st heaut omat e dv e r s i onoft hema nua las s embl yl i ne.Con t i nuo us ,s y nc hr on ous , oras y nc hr onou st r an sf ers y s t emscanb eus edwi t ht hei nl i n ec on figur at i on. Theoper at i onofdi al t y peandi nl i neas sembl ysy st emsi ssi mi l art ot heoper at i onoft hei r c ou nt e r p ar t sdes c r i bedi nChap t er4f ormac hi ni n g( ando t he rp r oc es s i ng)ope r at i on s.Sub as s embl i e satv a r i ou ss t ag esofc ompl e t i onar epr oc es s eds i mul t an eo us l yats epar a t ewor kst at i ons . Fors y nc hr onoust r ans f erofwor kbet weens t at i ons ,t hei dealc y cl et i meequal st heoper at i ont i meat t hes l o wes ts t at i onpl ust het r ans f ert i mebe t weens t at i ons .Thepr oduc t i onr at e,at100% upt i me,i s t her ec i p r oc al oft hei deal c y c l et i me .Owi n gt oj amsoft hec ompon ent satt hewo r k s t a t i onsan do t her mal f u nc t i ons ,t h es y s t e m wi l l pr obabl yno to per a t eat10 0% upt i me.Wewi l l a nal y z et heo per a t i onof t h es ea ut o ma t e da s se mbl ys y s t e msi nas u bs eq ue nts e ct i o no ft h i sc ha pt e r .
I nas e ns e,t h ec ar o us ela s se mb l ys y s t e m r ep r e se nt sah y br i db et we ent h ec i r c ul a rfl o wo fwo r kpr o v i d edb yt h ed i a la s se mb l yma ch i nea ndt h e s t r ai ghtwor kfl owoft hei nl i nes ys t em.Thec ar ous el c onfi gur at i oni si l l us t r at edi nFi gur e7. 2.Thi s t y pea s se mb l ys y s t e mc a nb eo pe r a t e dwi t hc o nt i n uo us ,s y nc hr o no us ,o ra s yn ch r o nou st r a ns f e r me c ha ni s mst o mo v et h ewo r ka r o un dt h ec a r o us e l .Th ec a r o us e lc o nfi g ur a t i o nwi t hs y nc h r o no us t r ans f erofwor ki sof t enus edi npar t i al l yaut omat edas sembl ysy s t ems .I nChapt er15wewi l l de sc r i beho w wo r k i n p r o ces ss t or agei si nc or por at edi nt ot hedes i gnoft hec ar ous elas s embl y syst em.
I nt hes i ngl es t at i onas sembl ymac hi ne,t he as sembl yoper at i onsar eper f or medatas i ngl el oc at i on( s t at i onar ybas epar ts y st em) .Thet y pi c al op er a t i oni n v ol v e st hepl ac ementoft h eba separ tatt h ewo r k s t at i o nwh er ev a r i ou sc omponen t sar e a dd edt ot h eb as e .Th ec o mp on en t sa r ede l i v e r e dt ot h es t a t i onbyf e ed i n gme c ha ni s ms ,a ndon eo r mor ewo r khea dsper f or mt hev ar i o usas s emb l yandf as t en i ngope r at i on s.Thes i ngl e s t at i onc el l i s s omet i messel ec t edast hec onfi gur at i onf orr obo t i cas s embl yappl i c at i ons .Par t sar ef edt ot hes i ngl e s t at i ona ndt her o bo tadd st hem t ot heba sepa r tandp er f or mst hef as t e ni n gop er at i ons . T abl e7. 1pr es ent sal i s t i ngoft hepos s i b l ec ombi nat i o nsofwo r kt r a ns f ers y s t emsan das s embl y s y s t e mc on fig ur a t i o ns .
PARTSFEEDI NG DEVI CES I ne ac ho ft h ec on fig ur a t i o nsde sc r i b eda bo v e,ame an so fd el i v e r i n gt h ec ompo ne nt st ot h e a ss e mb l ywo r k he admu s tb ed es i g ne d.I nt h i ss ec t i o nwed i s c us st h es ed ev i c e sa ndt h ei ro pe r a t i o n. El e me nt soft hepa r t sde l i v er ysy st e m
Th eh ar d wa r es y s t e mt h atd el i v e r sc o mp on en t st ot h ewo r kh ea di nanau t o ma t e da s s emb l ys y s t e m t y pi c al l ycons i s t soft hef ol l owi ngel ement s : •
Hop per .Thi si st h ec on t a i neri nt owhi c ht hec omponent sar el oad eda tt hewor ks t at i on.A s ep ar at eho ppe ri su s edf o re ac hco mp one ntt y p e.Th ec omp on en t sa r eus ua l l yl o ade di n t o t hehopperi nbul k .Thi smeanst hatt hepar t sar er andoml yor i ent edi ni t i al l yi nt hehopper .
•
Pa r t sf e ed er .Th i si s ame c ha ni s mt h atr e mo v e st h ec o mp on en t sf r o mt h eh op pe ro neata t i mef ordel i v er yt ot heas s embl ywor khead.Thehopperandpar t sf eederar eof t en c ombi nedi nt ooneoper at i ngmec hani s m.Thevi br at or ybowlf eeder ,pi c t ur edi nFi gur e7. 3,i s av e r yc o mmo ne x a mp l eoft h eh op pe r f e ed erc o mb i n at i o n.
•
Sel ec t orand/ oror i ent or .Thes eel ement sof t hedel i v er ys ys t em es t abl i s ht hepr operor i ent at i onoft hec omponent sf ort heas s embl y wor k head.As el ec t ori saadv i c et hatac t sasafi l t er ,per mi t t i ngonl ypar t st hatar ei nt he c or r ec tor i ent at i ont opas st hr ough.Component st hatar eno tpr oper l yor i ent edar er ej ec t ed bac ki nt ot hehopper .Anor i ent ori sadev i c et hatal l owspr oper l yor i ent edpar t st opas s t hr oughbutpr ov i desar eor i ent at i onofc omponent st hatar enotpr oper l yor i ent edi ni t i al l y . Sev er al s el ec t orandor i ent ors chemesar ei l l us t r at edi nFi gur e7. 4.Sel ec t orandor i ent or d ev i c esar eo f t e nc o mb i n eda ndi n c or p or at edi n t oo neh op pe r f e ed ers y s t e m.
•
Fe edt r a c k.Th ep r e ce di n ge l e me nt soft h e d el i v e r ys y s t e ma r eu s ua l l yl o c at e ds omed i s t a nc ef r o mt h ea s se mb l ywo r khe ad .Af e ed t r ac ki sus edt ot r ans f ert hec omponent sf r om t hehopperandpar t sf eedert ot hel oc at i onof t heas s embl ywor khead,mai nt ai ni ngpr operor i ent at i onoft hepar t sdur i ngt het r ans f er . Ther ear et wogener al c at egor i esoff eedt r ac ks:gr a vi t yandpower ed.Thegr a vi t yf eedt r ac k i smo stc ommon.I nt hi st y pet h eh oppe ra ndpa r t sf e ederar el oc at eda tane l e v at i o nt h ati s abo v et heel e v at i onoft hewor khead .Thef or c eofg r a vi t yi sus edt ode l i v ert hec ompo ne nt s t ot hewor khead .Th epo wer edf e edt r ac ku sesv i br at or yac t i o n,ai rp r e ss ur e,oro t hermeans t of or c et hepar t st ot r a v ela l ongt hef ee dt r ac kt o wa r dt heas s embl ywor khe ad.
•
Escapementandpl acementdevi ce.The p ur p os eo ft h ee s c ap eme ntd ev i c et or e mo v ec o mp on en t sf r o mt h ef e edt r a c ka tt i me
i nt er v al st ha ta r ec ons i s t entwi t ht hec y c l et i meoft hea ss embl ywor khe ad.Thep l ac ement dev i c ephy si c al l ypl ac est hec omponenti nt hec or r ec tl oc at i onatt hewor k st at i onf ort he a s s emb l yo pe r a t i o nb yt h ewo r kh ea d.Th es eel e me nt sa r es ome t i me sc omb i n edi n t oa s i ng l eop er at i ngmec hani s mi no t herc as es ,t he ya r et wos ep ar at ede vi c es .Se v er alt y pe so f e sc ap emen ta ndp l a ce me ntd ev i c esar epi c t ur e di nFi g ur e7 . 5 . Theel ement soft hepar t sdel i v er ysy st em ar ei l l us t r at eds chemat i c al l yi nFi gur e7. 6.Apar t ssel ec t or i si l l us t r at edi nt hedi agr am.I mpr oper l yor i ent edpar t sar ef edbac ki nt ohopper .I nt hec as eofapar t s or i ent or ,i mpr oper l yor i ent edpar t sar er eor i ent edanpr oc eedt ot hef eedt r ac k.Amor edet ai l ed des cr i pt i onoft hev ar i ousel ement soft hedel i v er ysy st em i spr ov i dedi nr ef er enc e[ 3] . Oneo ft her ec entde v el opme nt si nt het ec hnol og yofpa r t sf e ed i nga nddel i v ers y s t e msi st h e p r o gr a mma bl ep ar t sf e ed er[ 5 , 7 ] .Th ep r o gr a mma bl ep ar t sf e ed eri sc ap ab l eo ff e ed i n gc o mp on en t s o fv a r y i n gg eo me t r i e swi t ho nl yaf e w mi n ut e sr e qui r e dt oma k et h ea dj u s t me nt s( c ha ng et h e pr ogr am)f ort hedi ff er enc es .Thi st y peoff eederwoul dpos ses st hefl ex i bi l i t yt obeus edi nbat c h p r o du c t i o na ss e mb l ys y s t e ms .Mo s tp ar t sf e ed era r ede si g nedasfi x e da ut o ma t e ds y s t e msf o rh i g hp r o du c t i o na ss e mb l y .
Qua nt i t a t i v ea na l y si soft hede l i v er ys y st e m ope r a t i on
Thepar t sf eedi ngmec hani s mi sc apa bl eofr emo vi ngpar t sf r om t hehopperatace r t a i nr at e ,f .Th es e par t sar eas s umedt obei nr andom or i ent at i oni ni t i al l y ,andmus tbepr es ent edt ot hes el ec t oror or i ent ort oes t abl i s ht hec or r ec to r i ent at i on.I nt hec as eoft hes el ec t or ,ac er t ai npr opor t i onoft he par t swi l l bec or r ec t l yor i ent edi ni t i al l yandt hes ewi l l beal l owedt opas st hr ough.Ther emai ni ng pr opor t i on,whi c har ei nc or r ec t l yor i ent ed,wi l l ber ej ec t edbac ki nt ot hehopper .I nt hec as eoft he or i ent or ,t hepar t st hatar ei nc or r ec t l yor i ent edwi l l ber eor i ent ed,r es ul t i ngi deal l yi na100% r at eof par t spas si ngt hr ought heor i ent ordev i c e.I nman ydel i v er ysy s t em des i gns ,t hef unc t i onsoft he
s el ec t orandt heor i e nt orwi l l bec ombi ned.L etusde fine9t obet hep r op or t i onofc omponent st hat pas st hr ought hes el ec t or or i ent orpr oc es sandar ec or r ec t l yor i ent edf ord el i v er yi nt ot hef eedt r ac k. Henc et heeff ec t i v er at eofdel i v er yofc omponent sf r om t hehopperi nt ot hef eedt r ac kwi l l be f e θ.Th r emai ni ngpr opor t i on,( 1–θ) ,wi l l beac i r c ul at edbac ki nt ot hehopper .Obv i ousl y ,t hedel i v er y θ r at ef o fc o mp on en t st ot h ewo r khe admu s tb es u ffic i e ntt ok e epu pwi t ht h ec y c l er a t eo ft h e
assembl ymachi ne.
θ As s umi ngt ha tt h ed el i v er yr a t eofc omp onent sf i sgr eat ert hant hec yc l er at eRc o ft h ea s se mbl y
mac hi ne,ameansofl i mi t i ngt hes i z eoft hequeuei nt hef eedt r ac kmus tbees t abl i s hed.Thi si s gener al l yac compl i s hedbypl ac i ngas ens or( e. g. ,l i mi ts wi t c h,opt i c al s ens or ,et c . )neart het opoft he f eedt r ac k,whi c hi sus edt ot ur nofft hef eedi ngmec hani s m whent hef eedt r ac ki sf ul l .Thi ssens ori s r ef er r edt oast hehi ghl ev els ens or ,andi t sl oc at i ondefi nest heac t i v el engt hLf2 oft hef eedt r ac k .I f t hel engt hofac omponenti nt hef eedt r ac ki sLc,t hen umberofpar t st h atc anbehel di nt hef ee d Lf2 Lc.Th t r ac ki snf2 = / el e ng t hoft h ec o mp on en t smu s tb eme as u r e df r o m apo i n to nagi v e n
c omp on en tt ot h ec or r e sp ond i n gp oi n to nt h en ex tc o mp on en ti nt h eq ue uet oa l l o wf o rp os s i b l e o ver l apofpar t s .Thev al ueofnf2 i st hec apac i t yoft hef eedt r ac k. Ano t hers en sori spl a cedal ongt h ef eedt r ac kats omedi s t anc ef r om t hefi r s ts en soran di sus edt o r es t ar tt hef eedi ngmec hani s magai n.Defi ni ngt hel oc at i onoft hi sl o w-l e vels ens orasLf1,t he Lf1 Lc. nu mbe ro fc ompo nent si nt hef ee dt r ac katt hi spo i nti snf 1= /
Ther at eatwhi c ht hequant i t yofpar t si nt hebufferwi l l ber educ edwhent hehi ghl e vel s ens ori s a ct u at e d=Rc,wh er eRc i st het heor e t i c al c y cl er at eoft heas sembl ymac hi ne.Ona ver age,t her at eat θ–Re.Ho whi c ht hequant i t yofpar t swi l l i nc r eas euponac t uat i onoft hel owl ev el s ens ori sf we v er ,
t her at eofi nc r eas ewi l l notbeuni f or m duet ot her andom nat ur eoft hef eeder s el ec t oroper at i on. Ac cor di ngl y ,t hev al ueofnf1 mus tbemadel ar geenought ov i r t ual l yel i mi nat et hepr obabi l i t yofa s t oc koutaf t ert hel o wl e vel s ens orhast ur nedont hef eeder .
EXAMPLE7. 1 Th ec y c l et i mef o ragi v e na s se mb l ywo r khe ad=0 . 2mi n .Th ep ar t sf e ed erh asaf e edr a t e=2 0 c omponent s / mi n.Thep r obabi l i t yt h atagi v e nc omponentf e db yt hef eed erwi l l pas st h r ought he s el ec t ori sθ =0. 3.Thenumberofpar t si nt hef eedt r ac kcor r es pondi ngt ot hel o wl ev els ens or i snf1 =6.Thec apac i t yoft hef eedt r ac ki snf2 =1 8p ar t s . ( a)Det er mi nehowl ongi twi l l t ak ef ort hes uppl yofpar t si nt hef eedt r ac kt ogof r om nf2 t onf1. ( b)De t er mi neho wl ongi twi l l t ak eona ver agef ort hes uppl yf orpar t st ogof r om nf1 t onf2. Sol ut i on: ( a)Ther at eofdepl et i onofpar t si nt hef eedt r ac k,s t ar t i ngf r om nr 2,wi l l be Rc =1 / 0 . 2 =5 par t s / mi n.Thet i met odepl et ei s
( b)Ther at eofpar t si nc r eas ei nt hef eedt r ac k,onc et he l o wl e v el s ens orhasbee nr eac hed ,i s f θ–Rc =( 2 0) ( 0 . 3 ) –5 =6 –5 = 1p ar t / mi n .Th et i met og of r o m nf1 t onf2 i s
ANAL YSI SOFMUL TI STATI ONASSEMBL YMACHI NES
I nt h i ss e ct i o nweex a mi n et h eo pe r a t i o na ndpe r f o r man c eo fa ut o ma t e da s se mbl yma ch i n est h at ha v es ev er al wor k s t at i o nsandus eas y nc hr onoust r ans f e rs y s t e m.Thet y pesi n cl udet h edi a l i n de x i n gma c hi n e,ma nyi n l i n ea s se mb l ys y s t e ms ,a ndc e r t a i nc ar o us el s y s t e ms . Th eme as ur e sofp er f o r ma nc ea r epr o du ct i o nr a t e ,u pt i meeffic i e nc ya ndco s t . Th ea na l y s i sofa na ut o ma t e da s s emb l yma c hi n ewi t hmu l t i p l es t a t i o nss ha r e smu c hi nc o mmo nwi t h t h eu pp er b ou nda pp r o ac hu se df o rme t a lma ch i n i n gt r a ns f e rl i n esf r o m Ch ap t e r5 .So me mo di fi c at i o nsi nt h ea na l y s i smu s tb ema det oa c co un tf o rt h ef a c tt h atc omp on ent sar eb ei n ga dd ed att h ev a r i ou swor k s t at i on si nt h eas s embl ysy s t em.Thege ner a lop er at i onoft heas s embl ys y st em i s pi c t ur edi nFi gur e7. 7.I nde vel opi ngt heequat i onst hatgo ver nt heoper at i onoft hes y st em,wes hal l f o l l o wt h eg ene r a la ppr o ac hs u gg es t e db yBo ot hr o y da ndRe df or d[ 2 ] .
Weas s umet hatt h et y pi c al . op er a t i ono cc ur r i ngata wo r k s t a t i o no fa na s se mb l yma c hi n ei so nei nwh i c hac omp on en ti sa dd edorj o i n edi nso mef a s hi o n t oane x i s t i n gas s embl y .Theex i s t i n ga ss embl yc ons i s t sofaba sepa r tpl ust hec omponent s as sembl edt oi tatpr e vi ouss t at i ons .Thebas epar ti sl aunc hedont ot hel i neei t heratorbef or et he fi r s twor k s t at i on.Th ec ompone nt st hata r eadd edmu stbecl ean,u ni f o r mi nsi z ea ndsha pe,ofhi g h q ua l i t y , a ndc on si s t e nt l yor i e nt e d.Wh ent h ef e edme ch an i s ma nda s se mb l ywo r khe ada t t emp tt o j oi nac omponentt hatdoesnotmeett hes es pec i fi c at i ons ,t hes t at i onc anj am.Wh ent hi soc c ur s ,i t c anr es ul ti nt hes hut downoft heent i r emac hi neunt i l t hef aul ti sc or r ec t ed.Thus ,i naddi t i ont ot he ot hermec hani c al andel ec t r i c alf ai l ur est hati nt er r uptt heoper at i onofafl owl i ne,t hepr obl em of de f ec t i v ec omponent si sonet h ats pec i fi c al l ypl agu est h eop er a t i ono fana ut omat i cas s embl y mac hi ne .Th i si st h epr o bl e m wep r opo set odeal wi t hi nt hi sse ct i on . Theassembl ymachi neasagameofchance
Def ec t i v epar t sar eaf ac to fmanuf ac t ur i ngl i f e.Def ec t soc curwi t hac er t ai nf r ac t i ondef ec t i v e r at e,q.I nt heop er at i onofana ss embl ywor k s t at i o n,q c anbec ons i der edast hepr obabi l i t yt hatt he n ex tc ompo nen ti sd ef e ct i v e .Wh enanat t e mp ti sma det of e edan da s se mb l ead ef e ct i v e c omponent ,t h edef ec tmi g htormi g htno tc aus et hes t at i ont oj am.Le tm equalt hepr obabi l i t yt hata def ec twi l l r es ul ti nt hemal f unc t i onands t oppageoft hewor k st at i on.Si nc et hev al ues ofq andm ma ybedi ff er entf ordi ff er ents t at i ons ,wes ubs cr i ptt hes et er msasqi andmi,wher ei =1, 2,...,n,t henumberofs t a t i onsont heas s embl ymac hi ne. Cons i der i ngwhathappensatapar t i c ul arwor k st at i on,s t at i oni ,t her ear et hr eepos si bl eev ent st hat mi g hto c c urwh ent h ef e edme c ha ni s ma t t e mp t st of e edt h ec o mp on en ta ndt h ea s s emb l yd e v i c e at t empt st oj oi ni tt ot heex i s t i ngas sembl y: 1 .Th ec o mp on en ti sde f e ct i v ea ndc au se sas t a t i o nj a m. 2 .Th ec o mp on en ti sde f e ct i v eb utd oe sn otc a us eas t a t i o nj a m. 3.Theco mpon en ti sno tde f ec t i v e.
qi, Thepr obabi l i t yoft hefi r s tev enti st hepr oduc toft hef r ac t i ondef ec t i v er at ef ort hes t at i on,
mul t i pl i edbyt hepr obabi l i t yt hatadef ec twi l l c aus et hes t at i ont os t op,mi.Thi spr oduc ti st hes ame a st h et e r m t i on5. 2,t hepr obabi l i t yt hatapar t wi l l j am ats t at i oni .Fo ra na s s emb l y pi,ofSec machi ne, I nt h i sc as ewh er et h ec omp on en ti sde f e c t i v ea nd c au sesas t a t i o nj am,t hede f ec t i v ec omponen twi l l bec l e ar edandt hene xtc ompo nen twi l l be a l l o we dt of e eda ndb ea s se mb l e d.Weas s umet h att h i sn ex tc omp on en ti sn otd ef e ct i v et h e 2 pr obabi l i t yoft woc ons ec ut i v edef ec t si sv er ys mal l ,equalt oq .
Th es e co ndpo ss i b l ee v en t ,wh ent h ec omp on en ti sde f e ct i v eb utd oe sn otc au s eas t a t i o nj a m,h as apr obabi l i t ygi v enby
Wi t ht hi sout c ome,abadpar ti sj oi nedt ot hee xi s t i ngas s embl y ,per haps r ender i ngt heent i r eas s embl ydef ec t i v e.
Thepr obabi l i t i esoft het hepos si bl ee vent smus ts um t ouni t y . Fo rt h es pe c i a lc a sewh er emi=m andqi=q f or al li ,Eq.( 7. 2)r educ est o T odet er mi net hec ompl et edi s t r i but i onofpos s i bl e out comest hatcanoccuronann s t at i onas s embl ymac hi ne,wec anmu l t i pl yt het er msofEq.( 7 . 2 ) t oget herf oral ln s t at i ons:
I nt hes pec i al c as eofEq.( 7. 3) ,wher eal lmi ar e equalandal lqia r eequal ,Eq.( 7. 4)be comest h emul t in omi al e x pa ns i on Ex pans i onofEq.( 7. 4)or( 7. 5)wi l l r ev eal t he pr o ba bi l i t i e sf ora l l pos s i b l es equen cesofe v en t swh i c hc ant ak epl ac eont h ea ss emb l yma chi ne . Unf or t un at el y ,t hen umberoft er msi nt hee x pan si onofEq.( 7. 4)b ec ome sv er yl ar g ef oramac hi ne wi t hmor et hant wos t at i on s.Thee x ac tnu mbe ro ft er msi seq ual t o3n,wh er en i st h en umb ero f s t at i ons .Foranei ght s t at i onl i ne,t henumberoft er msi sequal t o6561,eac ht er mr epr es ent i ngt he
p r o ba bi l i t yofo neo ft h e6 56 1p os s i b l es e que nc esont h ea s se mb l yma ch i n e. Measur esofper f or mance
Fo r t una t el y , wear en otr equi r edt oc al c ul a t ee v er yt er mt omak eu seoft hec onc ep to fas s emb l y mac hi neoper at i onpr o vi dedb yEqs .( 7. 2)and( 7. 4) .Oneoft hec har ac t er i s t i c sofper f or manc et hat wemi gh twan tt ok no wi st hepr op or t i onofas s embl i e st hatc ont ai noneo rmor ede f ec t i v e c omponent s .T wooft het hr eet er msi nEq.( 7. 2)r epr es ente vent st hatr es ul ti nt headdi t i onofgood c omponent satagi v ens t at i on.Thefi r s tt er mi smiqi,whi c hi ndi c at esal i nes t opbutal s omeanst hata d ef e ct i v ec omp on en th asn otb ee na dd edt ot h ea ss emb l y . Th eo t h ert e r mi s( 1– qi) ,whi chmeans t h atag oo dc o mp on en th asbe ena dd eda tt h es t a t i o n.Th es u mo ft h es et wot e r msr e pr e s en t st h e pr obabi l i t yt hatadef ec t i v ec omponentwi l l no tb eaddedats t at i oni .Mul t i pl y i ngt hes epr obabi l i t i esf or al ls t at i ons ,wegett hepr opor t i onofac cept abl epr oduc tc omi ngofft hel i ne,Pap,
I ft hi si st hepr opor t i onofas sembl i eswi t hno def ec t i v ec omponent s ,t hepr opor t i onofas sembl i est hatc ont ai natl eas tonedef ec ti sgi v enby
I nt h ec a s eo fe qu almean de qu alqi,t he set wo equa t i onsbe come ,r es pec t i v el y ,
Thepr opor t i onspr o vi dedb yEq.( 7. 6)or( 7. 8)gi v e t he“ y i e l d”o ft heas s embl ymac hi n e,c er t ai nl yonei mpor t an tme as ur eo ft hema chi ne ’ sper f or ma nc e. Thep r op or t i on sofa ss embl i e swi t ho neormor ed ef ec t i v ec ompo nent s ,gi v enb yEq.( 7. 7)or( 7 . 9 ) , mus tbec ons i der edal i abi l i t yoft hemac hi ne ’ soper at i on.Ei t hert hes eas sembl i esmus tbei dent i fi ed t hr ou ghani n spec t i onpr oc es san dpo ss i bl y r epai r ed,ort he ywi l l be comemi x e di nwi t ht h ego od as s embl i e s.Thel at t erp os s i bi l i t ywoul dl ea dt ound es i r ab l ec ons equen ceswhe nt heas s embl i esar e pl ac edi ns er v i c e. I na dd i t i o nt ot h ep r op or t i o nsofg oo da ndb ada s se mbl i e sa sme as u r e so fp er f o r ma nc ef o ra n as s embl yma chi n e,wear eal s oi nt er e st edi nt h emac hi ne ’ sp r oduc t i o nr a t e,pr op or t i onsofupt i me a ndd own t i me ,a nda v e r a gec o s tp eru ni tp r o du c ed .
T oc al c ul at epr odu ct i onr a t ewemus tfi r s tde t e r mi net h ef r equ en cyofdo wnt i meoc c ur r enc esper c y cl e,F.I fe ac hs t at i onj a mr e sul t si namac hi ned ownt i meo cc ur r en ce,F c anb ef o un db yt a ki n gt h e e xpec t ednumberofs t at i onj amsperc y cl e.Mak i ngus eofEq.( 7. 1) ,t hi sv al uei sgi v enb y
I fa l l i ar eequalandal lmi ar eequal ,Eq.( 7. 10) p be c omes Th ea v er ag ep r o du ct i o nt i mepe ra ss emb l yi s t her ef or egi v enby
wher e Tc =i dealc y cl et i me
=a v er a gedo wn t i mepe ro c c ur r e nc e Td Fo rt h ec a s eo fe qu al mi a nde qu alqi, Fr o mt h ea v er a gepr o du ct i o nt i mepe ra s se mbl y , we obt ai nt hepr oduc t i onr at ef r om Eq.( 5. 3) ,r epeat edher ef orc on veni enc e:
Ho we v e r ,i tmu s tb er e me mb er e dt h atu nl e s smi =1f ora l l s t at i ons ,t he pr o du ct i onofas s emb l i eswi l l i nc l udes omeu ni t swi t ho neormo r edef ec t i v ec omponen t s . Ac cor di ngl y ,t hepr oduc t i onr at es houl dbec or r ec t edt ogi v et her at eofout putofas sembl i est hat c ont ai nnodef ec t s .Wes hal l c al l t hi sRap t her at eofpr oduc t i onofac cept abl epr oduc t .Byc ombi ni ng Eqs .( 5. 3)and( 7. 6) ,weobt ai n
Us i ngEq.( 7. 8)r at hert hanEq.( 7. 6) ,wegett he c or r e spondi ngr a t eofpr o duc t i onwhe nmi ar eal l equalandqi ar eal l equal:
He nc e,Eq .( 5. 3)pr o vi dest hea v er agepr oduc t i on c y c l er at ef oranas s embl ymac hi ne,wh i c hi nc l udespr o duc t i o nofbo t hgo odandbadpr o du ct . Equat i ons( 7. 14)and( 7. 15)gi v ev al uesofa v er agepr oduc t i onr at ef orgoodpr oduc tonl y . Thel i neeffic i enc yi scal c ul at edast her at i oofi dealc y cl et i met oav er agepr oduc t i ont i me.Thi si st he s ameasEq.( 5. 5) ,e x c ep tt ha ta v er ag epr o duc t i o nt i me,T i sgi v enb yEq.( 7. 12)or( 7. 13) .Us i ngEq. p ( 7. 13)asani l l us t r at i on,
Th ep r o po r t i o no fdo wn t i me ,D,i st hea ver age do wnt i mep erc y c l edi v i dedb yt hea v er agepr oduc t i ont i me.Fo re x ampl e,f ort h ec as eofequal mi andequalqi,t hev al ueofD wo ul dbegi v e nb y Noa t t e mp th asbe enma det oc or r e c te i t h ert h el i n ee ffic i e nc yE,ort hepr opor t i ondo wnt i meD,f or t h ey i e l do fg oo da s se mb l i e s.Wea r et r e at i n gt h ea s se mb l yma ch i n ee ffic i e nc ya ndt h eq ua l i t yof un i t spr odu cedass epar at ei s s uesi nt hec ompu t at i onofEandD. Thec os tpe ras s embl ypr o duc ed,ont heo t herhan d,mus tt ak eac c ou ntoft heo ut putqu al i t y . Ther ef or e,t hegener al c os tf or mul a,gi v enb yEq.( 5. 8) ,mus tbeamendedt oi nc l udeacor r ec t i onf or y i el dpl usanyaddi t i onal c os t ssuc hasi ns pec t i ont oi dent i f ydef ec t i v eas sembl i es .Asani l l us t r at i on, t hec or r ec t i onf ory i el dofgoodpr oduc twoul dbei nc or por at edi nt ot hec os tf or mul aasf ol l o ws:
wh er et h ec o s tt e r msi nt h en ume r a t o rwe r ed efi n ed i nSec t i on5. 1.TheCm t e r mi n cl u de st h ec os t soft h eb as ep ar ta nda l l c omp on en t sad de db yt h e a ss e mb l ys y s t e m.Th ed en omi n at orwo ul dt e ndt oi n cr e as et h ec o sto ft h ea s se mbl y . Th us ,a st h e qual i t yofi ndi v i dual c omponent sdet er i or at es ,t hi sr es ul t si nani nc r eas eda ver agec os tperas sembl y produced. I ti sap pr op r i a t et oc onc l udet hi sl i s t i ngofequa t i onsonas s embl yma chi neper f o r manc ewi t hs ome e xampl es .I naddi t i ont ot het r adi t i onal wa ysofi ndi c at i ngl i neper f or manc e( e. g. ,pr oduc t i onr at e, pr opor t i onupt i me,c os tperuni t ) ,wes eeanaddi t i onal di mens i onofper f or manc ei nt hef or m oft he
y i el d.Whi l et hey i el dofgoodpr oduc ti sani mpor t anti s suei nan yaut omat edpr oduc t i onl i ne,wes ee t hati tc anbee x pl i c i t l yi nc l u dedi nt h ef o r mul asf oras s embl ymac hi neper f o r man ceb ymean s ofq andm. EXAMPLE7. 2
A10s t at i oni nl i neas sembl ymac hi nehasa6si deal c y cl et i me.Thebas epar ti saut omat i c al l y l oadedpr i ort ot hefi r s ts t at i on,andc omponent sar eaddedateac hoft hes t at i ons .Thef r ac t i on def ec tr at eateac hoft he10s t at i onsi sq =0. 01,andt hepr obabi l i t yt hatadef ec twi l l j am i sm =0. 5. Wh enaj a mo c cu r s ,t h ea v er a ged own t i mei s2mi n .De t e r mi n et h ea v er a gep r o du c t i o nr a t e ,t h ey i e l d o fg oo da s s emb l i e s ,a ndt h eu pt i meeffic i e nc yo ft h ea s s emb l yma c hi n e. Sol ut i on: Thea v er agepr o duc t i onc y c l et i mei s Thepr oduc t i onr at ei st her ef or e
They i el di sgi v enbyEq.( 7. 8): Thi si st hepr o por t i o no fas s emb l i esc omi n go fft h e mac hi net hatc ont ai nnodef ec t i v epar t s .Ther ef or e,t hepr opor t i onofas sembl i est hatc ont ai noneor mor edef ec t si s
Th ee ffic i e nc yo ft h ea s s emb l yma c hi n ei s
EXAMPLE7. 3 L etu se x a mi n eh owt h ep er f o r ma nc eme as u r e si nEx a mp l e7 . 2a r ea ffe c t e db yv ar i a t i o nsi n qandm. Fi r s t ,f orm =0. 5,det er mi net hepr oduc t i onr at e,y i el d,andeffic i enc yf ort hr eel ev el sofq:q =0 ,q= 0 . 0 1,a ndq =0. 02.Sec on d,f orq =0. 01,det er mi net hepr oduc t i onr at e,y i el d,andeffic i enc yf ort hr ee l e v el sofm:m =0 . 2 ,m =0 . 5 ,a ndm =0 . 8 .Co mp ut a t i o nss i mi l a rt ot h os ei nEx a mpl e7 . 2p r o v i d et h e f ol l owi ngr es ul t s:
I ts eemsappr opr i at et odi s cus st her es ul t sof Ex ampl e7. 3.Theeff ec tofc omponentqual i t y ,asi ndi c at edi nt hev al ueofq,i spr edi c t abl e.Ast he f r ac t i ondef ec tr at ei nc r eas es ,meani ngt hatc omponentqual i t yget swor s e,al l t hr eemeas ur esof per f or manc es uff er .Pr oduc t i onr at edr ops ,t hey i el dofgoodpr oduc tge t sl ower ,andt hepr opor t i on u pt i mede c r e as e s . Th ee ff ec to fm,t hep r o ba bi l i t yt hatade f ec twi l l j am t hewor kheadandc aus et hea ss embl ymac hi ne t os t op,i sl es sobv i ous .Atl owv al uesofm ( e. g. ,m =0. 2)f ort hes amec ompo ne ntqual i t yl e v el( q= 0. 01) ,t hepr oduc t i onr at eandmac hi neeffic i enc yar ehi gher ,butt hey i el dofgoodpr oduc ti sl ower . I ns t eado fi n t er r up t i ngt heas s embl yma chi neope r at i onan dc aus i n gdo wn t i me ,def e ct i v e c omp on en t sa r epa ss i n gt h r o ug ht h ea s se mb l yp r o ce sst obe co mepa r t o ft h efi n al p r od uc t .Ast h e v a l ueofm i n cr e as es ,pr o duc t i onr at eandmac hi neeffic i e nc ydr op,b utt hey i el di n cr e as es . I nCha pt er4,wed i s c us s edt wot y pesofc ont r ol ,i ns t ant aneousc on t r ol andme mor yc on t r ol .The memor yc ont r ol s c hemei sp ar t i c ul ar l yappr opr i at ef ora ut o mat edas s emb l yma chi neope r at i on.Wi t h memor ycont r ol ,t h eas s embl yma chi nei spr o v i de dwi t hl ogi ct hati d ent i fi eswh enade f ec t i v e c omponenti sen count er ed,b uti td oesno ts t opt hemac hi n e.I n st e ad ,i tr ememb er st hepos i t i onof t heas sembl yt hati saffec t edbyt hedef ec t ,l oc ki ngi toutf r om addi t i onal as s embl yoper at i onsat s ubs equentwor k s t at i ons ,andr ej ec t st heas sembl yaf t ert hel as ts t at i on.Byc ont r as t ,i ns t ant aneous c on t r o ls t opst hea ss embl ymac hi newhenad ef ec t( o ro t he rmal f un ct i on)oc c ur s .Wi t ht he i nt r oduc t i onoft hev ar i abl em,wea r en owi napo si t i ont oc omp ar et h ep er f o r ma nc eo ft h et wo c ont r olt y pes . EXAMPLE7. 4 L etu sa ddc os td at at oou re x ampl e .Su pp os et h att h ec os to ft h ec omp on en t si s$0 . 0 2p er c omponenta teac hoft he10st at i onsan d$0 . 1 0f o rt heba separ t .Th et o t al c omponen tc os ti s t her ef or e$0. 10+10( $0 . 0 2)=$0 . 30pe ru ni t .Wewi l l a ss umet h att hes ec os tda t ai nc l u dea n al l o wanc ef ort hef r ac t i onofdef ec t i v ec omponent s .Howe ver ,i tdoesno ti nc l udeanal l owanc ef or fi na lpr oduc t st ha tmi ghtbes po i l eddur i nga ss embl yb yt hei nc l us i o nofdef ec t i v ec ompon en t s .I n
o t herwor ds ,i tdo esno tc ons i d ert h ey i e l dofgoo dpr o duc tf r om t h eas s embl yma chi ne.Th ec os tt o op er a t et hea ss embl ymac hi neus i n gi n st ant aneousc on t r o li s$60/ ho r$1. 00/mi n.Bec aus eo fi t s gr eat erc ompl e xi t y ,t hec os tofoper at i ngt hememor ycont r oli s$1. 10/mi n.Ot herc os t sar e negl i gi bl e. Sol ut i on: Wewi l l c omput et hea ver agepr oduc t i ont i me,y i el d,andc os tf ori ns t ant aneouscont r ol fi r s t .
Hence,t hecostperassembl ypr oducedcanbe d et e r mi n ed . Next ,t hesameper f or mancemeasur esf ormemor y c ont r ol .
Th ec os tp era ss emb l yi s
Al t ho ug ht h ec os tofc omponent si shi gher ,t h e o pe r a t i n gc o st sar er ed uc edb ec au s eo fn od own t i me ,a ndt h er e su l t i n gc o stp era s se mb l yi s s i gni fi cant l yl o wer .Memor yc ont r ol hast hecl earc os tadv ant agei nt hi se xampl e. I npr ac t i c e,t het heor et i c alv al uesofm wi l l notber eal i z edf ort het woc ont r olt y pes .Wi t h i ns t ant aneousc ont r ol ,apor t i onoft hedef ec t i v ec omponent swi l l s l i pt hr oughundet ec t edt obec ome i nc l udedi nt hefi nal pr oduc t ,s ot hatt heac t ualv al ueofm wi l l bel es st han1. 0.Wi t hmemor ycont r ol , t her ewi l l bec as esofl i n es t opsr e sul t i ngf r o m def ec t i v ec omp on ent sj ammi n gt hema chi nei ns uc ha wa yt hati tc anno tc ont i nueoper at i on.Henc e,t heac t ualv al ueofm un de rme mo r yco nt r o lwi l l b e gr eat ert hant het heor e t i c al v al ueofz er o.Thes er eal i t i eswer ei gnor edi nEx ampl e7. 4.
ANAL YSI SOFASI NGLESTATI ONASSEMBL YMACHI NE
Th es i n gl e s t a t i onas s emb l yma ch i n ec a nb e p i c t u r e da ss ho wni nFi g ur e7. 8 .Weas s umeas i n gl ewo r kh ea d,wi t hs ev e r a lc o mpo ne nt sf e ed i ng i nt ot hes t at i ont obeas s embl e d.Le tusus ent or epr es entt henu mberofdi s t i nc ta ss embl yel ement s t h ata r ep er f o r me do nt h ema c hi n e.Ea c he l e me nth asa ne l e me ntt i me ,Tei,wh er ei=1 , 2,...,n. Thei deal c y cl et i mef ort hes i ngl es t at i onas sembl ymac hi nei st hes um oft hei ndi v i dual e l e me ntt i me so ft h ea s se mb l yop er a t i on st ob ep er f o r me do nt h ema c hi n e,p l u st h eh an dl i ngt i met o l o adt hebas ep ar ti nt op os i t i onandunl o adt hec ompl e t eda ss embl y . Wec ane x pr es st hi si de alc y c l e t i mea s wher eTh i st hehandl i ngt i me. Ma nyoft h ea ss emb l yel e me nt si n v ol v et h ea dd i t i ono fac omp on en tt ot h ee x i s t i n gs uba s se mb l y .As i nouranal y s i soft hemul t i pl es t at i onas sembl ys ys t em,eac hc omponentt y pehasac er t ai nf r ac t i on def ec tr at e,qi,andt her ei sac er t ai npr obabi l i t yt hatadef ec t i v ec omponentwi l l j am t he wor k st at i on,mi.Wh enaj a mo c c ur s ,t h ea s s emb l yma c hi n es t o ps ,a ndi tt a k esa na v e r a geTd t oc l ear t hej a m andr e st ar tt hes y s t e m.Th ei nc l us i ono fd ownt i mer es ul t i ngf r om j a msi nt hemac hi n ec y c l e t i megi v es Forel ement st hatdonoti nc l udet headdi t i onofa c omp on en t ,t h ev a l u eo fqi=0.Thi smi ghtoc cur ,f ore xampl e,whenaf as t eni ngoper at i oni s per f or medonacomponentaddeddur i ngapr evi ousel ement . Fo rt h es pec i a lc as eo fequalq andequalm v al u esf o ra l l c ompo ne nt sad de d,Eq .( 7 .I8 )b e c ome s
Det er mi nat i onofy i el d( t hepr opor t i onofas sembl i es t hatc on t ai nnodef e ct i v ec omp onent s )f ort h es i ng l es t at i onas s embl ymac hi nema kesus eo ft he s ameequ at i o nsasf o rt h e
mul t i p l es t at i onsy s t ems .Upt i mee ffic i e nc yi sc omput edasE=Tc /T us i ngt hev al ue s p ofTcandT f r o m Eqs .( 7. 17 )a nd( 7. 18 ) . p EXAMPLE7. 5 As i n gl e s t a t i o na s se mb l yma c hi n ep er f or msfi v ewo r ke l e me nt st oas s emb l ef o urc omp one nt st o As i n gl e s t a t i o na s s emb l yma c hi n ep er f o r msfi v ewo r kel e me nt st oa s s emb l ef o urc o mp on en t st oa bas epar t .Theel ement sar el i s t edbel ow,t oget herwi t ht hef r ac t i ondef ec tr at eandpr obabi l i t yofa j am f oreac hoft hec omponent sadded.
Th et i met ol o adt h eb as ep ani s3san dt h et i met o u nl o adt h ec o mp l e t e da s s emb l yi s4s ,gi v i ng at ot al l oad/ unl oadt i meofTh =7s .Whenaj am oc c ur s ,i tt ak esana v er ag eo f1. 5mi nt oc l ea rt h ej am a ndr es t ar tt hemac hi ne.De t er mi net he pr o du ct i onr at e,t heyi el d,an dt h eupt i meeffic i en cyoft h eas s emb l yma chi ne . Sol ut i on: Thei dea lc y c l et i meoft heas s embl yma chi nei s Ad di n gt h ea v e r a ged own t i med uet oj a msy i e l d s Thepr oduc t i onr at ei s
Theyi el dofgoodpr oduc ti s a ndt h eu pt i meeffic i e nc yi s
Asou ranal y s i ss ugges t s ,i n cr eas i ngt h en umbe rof el ement si nt heas sembl ymac hi necy c l er es ul t si nahi gherc y cl et i me,t her ef or edec r eas i ngt he pr oduc t i onr at eoft hemac hi ne.Ac cor di ngl y ,appl i c at i onsoft hes i ngl es t at i onas s embl ymac hi near e us ual l yl i mi t edt ol ower v ol ume,l ower pr oduc t i onr at es i t uat i ons .Forh i gherpr oduc t i onr at es ,oneof t hemul t is t at i onas s embl ys y st emsi sgener al l ypr ef er r ed.
PROBLEMS 7 . 1 .Af e ed ers el e c t o rd e v i c ea to neo ft h es t a t i o nsofa na ut o ma t e da s se mb l yma ch i n eh asaf e ed r at ef =25par t s/mi nandpr o vi desat hr oughputofonepar ti nf our(θ=0. 25) .Thei deal c y cl et i me oft h ea ss embl yma chi nei s10s .Th el o wl e v els en soront hef eedt r a cki sse tat10par t s ,a ndt he hi ghl ev el s ens ori ss etat20par t s .
( a)Howl ongwi l l i tt ak ef ort hes uppl yofpar t st obedepl et edf r om t hehi ghl ev el s ens ort ot hel owl e vels ens oronc et hef eeder –s el ec t orde vi c ei st ur nedoff? ( b)Howl ongwi l l i tt ak ef ort hepar t st ober es uppl i edf r om t hel owl ev el s ens ort ot hehi ghl ev el s ens or ,ona ver age,af t ert hef eeder s el ec t orde vi c ei st ur nedon? ( c )Whatpr opor t i onoft het i met hatt heas sembl ymac hi nei soper at i ngwi l l t hef eeders el ec t orde vi c e bet ur nedon?Tur nedoff? 7 . 2 .DoPr o bl e m7 . 1b utu s eaf e edr a t ef =3 2pa r t s/mi n .No t et h ei mpor t an ceoft u ni ngt hef ee de r s el ec t orr at et ot hec y cl er at eoft heas s embl ymac hi ne. 7. 3.Adi al i nde xi ngmac hi nehassi xst at i onst hatper f or mt hef ol l o wi ngas sembl yoper at i onst ot he ba sepa r t(a l s ogi v ena r eel eme ntt i me s,andq andm v a l u esf o rt h ec o mp on en t sad de d):
Thei nde xi ngt i mef ort hedi al t abl ei s2s .Whena j am oc c ur s ,i tr equi r es1. 5mi nt or el eas et hej am andputt hemac hi nebac ki noper at i on.Det er mi ne t hepr oduc t i onr at ef ort heas sembl ymac hi ne,t hey i el dofgoodpr oduc t(fi nal as s embl i esc ont ai ni ng nodef ec t i v ec omp on ent s) ,andt hepr opor t i onupt i meoft h es y s t e m. 7. 4.Anei gh t s t a t i o nas s embl yma chi nehasani de alc y c l et i meo f6s .Thef r ac t i ondef ec tr at eat eac hoft he8s t at i onsi sq =0. 0 15andt hes y s t em op er at esu si n gt h ei ns t an t aneouscon t r o ls t r at egy . Whe nabr e ak do wnoc c ur s ,i tt a k es1mi n ,onav er ag e,f ort hesy s t em t obeputb ac ki nt oop er at i on. De t e r mi net h epr o duc t i o nr at ef ort heas s embl ymac hi ne,t hey i e l dofgoo dpr o du ct( fi na las s embl i es c on t a i ni ngnodef ec t i v ec omp on en t s ) , andt hep r opor t i onupt i meoft hes y s t em. 7. 5.Sol v ePr obl em 7. 4b uta ss umi ngt ha tme mor yc ont r ol i sus edr at hert ha ni n st ant a ne ousc on t r ol . Th eo t h erd at aar et h es a me . 7 . 6 .So l v ePr o bl e m7 . 4o nl yas s umi n gt h atm =0. 6f oral l s t at i ons .Ot herdat aar et hes ame. 7. 7.As i ngl es t at i onas sembl ymac hi nei st obec ons i der edasanal t er nat i v et ot hedi ali nde xi ng mac hi nei nPr ob l em 7 . 3 .Us et hed at agi v eni nt het a bl eo fPr obl em 7. 3t ode t er mi net hepr od uc t i on r at e,t heyi el dofgoodpr oduc t(fi nalas s embl i esc ont ai ni ngnodef ec t i v ec omponent s) ,andt he pr o po r t i onu pt i meoft hes y s t em.Theh and l i ngt i met ol o adt hebas ep ar tandu nl oadt hefi ni s hed a s s emb l yi s7s andt hedownt i meaver ages1. 5mi never yt i meacomponentj ams.Whyi st he pr o po r t i onu pt i mes omuc hh i ghe rt h ani nt hecas eoft hedi a li nde xi ngmac hi nei nPr obl em 7. 3? 7. 8.As i x s t at i ona ut o mat i cas s emb l yma chi nehasani deal c y c l et i meof12s .Do wn t i meo c cu r sf o r t wor eas ons .Fi r s t ,mec hani c al andel ec t r i c al f ai l ur esoft hewor kheadsoc curwi t haf r equenc yof o nc epe r5 0c y c l e s .Av e r a gedo wn t i mef o rt h es eca us esi s3mi n .Se co nd ,d ef e ct i v ec omp on en t s al s or e sul ti nd ownt i me.Thef r ac t i ondef e ctr at eofea choft hes i xco mpon en t sad dedt ot heb as e par t att hes i xs t at i onsi sq =2%.Thep r obabi l i t yt h atade f ec t i v ec ompo nen twi l l c aus eas t at i onj am i sm
=0. 5f oral ls t at i ons .Do wnt i meperoc cur r enc ef ordef ec t i v epar t si s2mi n.De t er mi net he
y i el dofas sembl i est hatar ef r eeofdef ec t i v ec omponent s .t hepr opor t i onofas s embl i est hatc ont ai n atl ea stoned ef ec t i v ecomp one nt ,t heav er agep r oduc t i o nr at e,andt heupt i meeffic i e nc y . 7. 9.Anei gh t s t a t i o nau t omat i cas s embl ymac hi nehasani d eal c y c l et i meof10s .Do wn t i mei s c au sedbyde f ec t i v ep ar t sj ammi ngatt hei nd i v i dualas s embl ys t at i ons .Theav er agedo wn t i mepe r oc cur r enc ei s3. 0mi n.Thef r ac t i ondef ec tr at ei s1. 0% andt hepr obabi l i t yt hatadef ec t i v epar twi l l j am atagi v ens t at i oni s0. 6f oral l s t at i ons .Thec os tt ooper at et heas s embl ymac hi nei s$90. 00/ h an dt hecos to fc omp on ent sbe i ngas s embl edi s$ 0. 60/ uni ta ss embl y .I g nor eot he rc os t s . ( a )De t er mi net hey i el do fgo oda ss embl i e s. ( b )De t e r mi n et h ea v er a gep r o du ct i o nr a t eo fg oo da s se mb l i e s. ( c )Wh atp r opor t i onofas s embl i e swi l l ha v eatl e as to ned ef ec t i v ec omponent? ( d )De t er mi net heu ni tc os to ft h eas s emb l edpr od uc t . 7 . 1 0.As y nc hr o no usa s se mb l yma c hi n eh ase i g hts t a t i o nsa ndmu s tp r o du ceatar a t eof4 00 c o mp l e t e da s s emb l i e spe rh ou r .Av e r a gedo wn t i mepe rj a mi s2 . 5mi n .Wh enab r e ak d ownoc c u r s , al ls ubs y s t ems( i nc l u di n gt h ef eede r )s t op .Th ef r equenc yofbr ea kdo wn soft hemac hi nei sonc e e v er y50pa r t s .Oneoft heei gh ts t at i on si sanaut omat i cas s embl yope r at i ont h atu ses af e eder s el ec t or .Thec omponent sf edi nt ot hes el ec t orc anha vean yoffi v epos si bl eor i ent at i ons ,eac hwi t h equalpr obabi l i t y ,butonl yoneofwhi c hi scor r ec tf orpas sagei nt ot hef eedt r ac kt ot heas sembl y wo r khe ad .Pa r t sr e j e ct e db yt h es el e ct o ra r ef e db ac ki n t ot h eh op pe r .Wh atmi n i mu mr a t emu s tt h e f e ede rd el i v erc omponent st ot hes el e ct ordur i ngs y s t em upt i mei nor de rt ok e epupwi t ht h e assembl ymachi ne? 7 . 1 1.Ana ut oma t e da ss emb l yma c hi n eh asf o urwor k s t a t i o ns .Th efi r s ts t a t i o np r e se nt st h eb as e par tf ort heas sembl y ,andt heot hert hr ees t at i onsaddpar t st ot hebas e.Thei dealc y cl et i mef ort he ma c hi n ei s1 5s a ndt h ea v er a ged own t i mewh enaj a mr e s ul t sf r o m ade f e c t i v ep ar ti s3. 0mi n .Th e f r ac t i ondef ec t i v er at esandpr obabi l i t i est hatadef ec t i v epar twi l l j am t hes t at i onar egi v eni nt he f ol l owi ngt abl e. Wor k st at i on
Par ti dent i fi cat i on
q
0. 01
m
1
Base
1. 0
2
Br ac k et
0 . 0 2
3
Pi n
0. 03
1. 0
4
Re t ai n er
0 . 0 4
0. 5
1. 0
Quant i t i esof100, 000f oreac hoft hebas es ,br ac k et s ,pi ns ,andr et ai ner sar eus edt os t oc kt he as sembl yl i nef oroper at i on. ( a)De t er mi net hepr opor t i onofgoodpr oduc tt ot ot alpr oduc tc omi ngofft hel i ne. ( b)De t er mi net hepr oduc t i onr at eofgoodpr oduc tc omi ngofft hel i nedur i ngs t eady s t at eoper at i on. ( c )Wi t ht hequ an t i t i e sofc ompon en t sgi v enabo v e,de t er mi net het o t a lnu mbero ffi na las s embl i es t hatwi l l bepr oduc ed .Oft het o t a l ,ho w man ywi l l beg oodpr od uc t ,a ndh owma nywi l l bepr o duc t s t hatc on t ai natl ea stonedef ec t i v ec omp on ent?
( d )Oft henumb erofd ef ec t i v eas s embl i esde t e r mi nedi npar t( c ) ,ho w man ywi l l ha v edef e ct i v eb as e p ar t s ?Ho w ma nywi l l ha v ed ef e ct i v ebr a ck e t s ?Ho w ma nywi l l h av ede f e ct i v epi n s?Ho w ma nywi l l hav edef ec t i v er et ai ner s? 7. 12.As i x s t at i onaut omat i cas sembl ymac hi nehasani dealc y cl et i meof6s .Ats t at i ons2t hr ough 6,pa r t sf e eder sde l i v erc ompo ne nt st obeas s embl edt oabas epar twhi c hi sad dedatt hefir s t s t at i on.Eac hofs t at i ons2t hr ough6i si dent i c alandt hefi vec omponent sar ei dent i c al .Thati s ,t he c omp l e t e dp r o du ctc on s i s t soft h eb as ep ar tp l u st h efi v eco mp on en t s .Th eb as ep ar t sha v ez er o def ec t s ,butt heot herc omponent sar edef ec t i v eatar at eq.Whenanat t empti smadet oassembl ea d ef e ct i v ec omp on en tt ot h eb as ep ar t ,t h ema ch i n es t o ps(m =1. 0) .I tt ak esana ver ageof2. 0mi nt o mak er epai r sands t ar tt hemac hi neupaf t e re ac hs t opp ag e.Si nc eal l c omponent sar ei d ent i c al ,t he y ar epur c has edf r om as uppl i erwhoc anc ont r olt hef r ac t i ondef ec tr at ev er ycl os el y .Howev er ,t he s up pl i e rc har g esapr emi um f o rb et t e rq ual i t y .Th ec os tp erc ompone nti sde t er mi nedb yt hef ol l o wi ng equa t i on:
wher eq i st hef r ac t i ondef ec tr at e.Cos toft hebas e par ti s20c ent s .Ac cor di ngl y ,t het ot alc os toft hebas epar tandt hefi v ec omponent si s
Th ec os tt oo pe r a t et h ea ut o ma t i cas s emb l y ma ch i nei s$1 50 . 0 0/h.Th ep r o bl e mf a c i ngt h ep r o du ct i o nma na ge ri st h i s:Ast h ec o mp on en t qual i t ydec r eas es( i nc r ea ses ) ,t h edo wn t i mei nc r ea seswhi c hdr i v e spr oduc t i onc os t sup.Ast h e q qual i t yi mpr o ves( dec r ea ses ) ,t h emat e r i al c os ti nc r ea sesbe caus eo ft hep r i c ef o r mul aus edb yt h e q s uppl i er .T omi ni mi z et ot al c os t ,t heopt i mum v al ueofq mus tb ede t e r mi ned.De t e r mi nebyana l y t i c al met hods( r at hert hant r i al ander r or )t hev al ueofq t hatmi ni mi z est het ot alc os tperas sembl y .Al s o de t er mi net hea ss oc i at e dc os tp eras s embl yandpr od uc t i onr at e.(I gnor eo t h erc os t s) . 7. 13.As i x s t at i ondi al i nde xi ngmac hi nei sdes i gnedt oper f or mf ouraut omat i cas sembl yoper at i ons ats t at i ons2t hr ough5af t erabas epar thasbeenmanual l yl oadedats t at i on1.St at i on6i st he un l oa ds t at i on.Ea choft heas s embl yop er at i o nsi n v ol v est hea t t ac hmentofac omponentt ot he e xi s t i ngbas e.Ateac hoft hef ouras sembl ys t at i ons ,ahopper f eederi sus edt odel i v erc omponent s t oas e l e ct o rd e v i c ewh i c hs ep ar a t e sc omp on en t st h ata r ei mp r o pe r l yor i e nt e da ndd r o pst h em b ac k i nt ot heh opper .Thes y s t em wa sd es i gnedwi t ht hef ol l o wi ngo per a t i ngpar ame t er sf ors t at i ons2 t h r o ugh5.
atac er t ai nhour l yr a t e,whi c ht ak esi nt oac countt he
