1. The Perfect Circle Company manufactures manufactures bushings. Once each hour a sample of 125 finished bushings is drawn from the output; each bushing is examined by a technician. Those which fail are classified as defectie; the rest are satisfactory. !ere are data on ten consecutie samples ta"en in one wee"# $ample no. 1 2 % & 5 ' ( ) * 1+ ,efectie 15 1% 1' 11 1% 1& 2+ 25 %+ &5
a. -hat type of control chart should be used here b. -hat is the centerline of the chart c. -hat is the lower control limit /0C0 The upper control d. -hat statistic should be plotted on the control chart for e. ,raw the control chart on a piece of graph paper. f. s this system under control g. -hat should the 3uality control engineer do a. Use the p chart. This is attribute data with the categories of satisfactory and defective bushings.
b.
.
c.
.
d.
Sample No.
Statistic (p)
Sample No.
Statistic (p)
1
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f. No. Sample 1' falls above the U+,. g. /e should loo0 for an assignable cause for sample 1'. 2. se the data in Problem 61 in this problem. 7ssume that an assignable cause has been found for $ample 61+ and has been corrected. a. -hat is the alue of the centerline of the reised control chart b. -hat is the lower control limit of the reised chart c. -hat is the upper control limit of the reised chart d. Compare the reised control chart to the original control chart. a. The revised centerline will be obtained by deleting sample 1' and recalculating the value of
revised
on the basis of the remaining nine samples.
b. evised evised evised c. The revised control limits have lower values than the original control limits2 and they are slightly closer to the centerline. %. The Ta"e8Charge Company produces batteries. 9rom time to time a random sample of six batteries is selected from the output and the oltage of each battery is measured: to be sure that the system is under control. !ere are statistics on 1' such samples. $ample ean
a. -hat type of control chart should be used here -hy b. -hat is the centerline of the chart c. -hat is the lower control limit The upper control limit d. -hat statistic should be plotted on the control chart for each sample e. ,raw the control chart on a piece of graph paper. f. s this system under control g. -hat should the 3uality control engineer do a. Use the 3-bar chart4 this is measurement data.
b. (0 # the number of samples)
v.
c. 5ecause the value of the population standard deviation is un0nown2 use control chart factor.
v. v. v. d. The sample mean. e. U+,
and the !
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f. No2 sample 11 is out of control. g. /e should loo0 for an assignable cause for sample 11. &. se the data in Problem % to draw an < chart. a. -hat is the lower control limit The upper control limit b. -hat statistic should be plotted on the control chart for each sample c. ,raw the control chart on a piece of graph paper. d. s this system under control e. -hat should the 3uality control engineer do a. 5ecause s is un0nown2 use 8actors.
and the factors2 7% and 7& from the Table of +ontrol +hart
v. v.
b. The sample ranges. c. U+,
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d. 9es. e. No action is needed. 5. 7ssume that an assignable cause has been found and corrected for sample 6 11 in Problem %. a. -hat is the alue of the centerline of the reised control chart b. -hat is the lower control limit of the reised chart The upper control 0imit c. Compare the reised control chart to the original control chart.
a.
v.
b. ,+, # ".'% - .&(."%) # &. v. U+, # ".'% : .&(."%) # ".! v. c. The new control limits are lower but are still the same distance from the centerline. 6.Tin"er =elle Peanut =utter is sold in .5+ "ilograms >ars. The plant produces thousands of >ars of peanut butter per wor"ing day; the process is rather simple and 3uite standardi?ed: and is thought to be highly stable: with a standard deiation of . +1' "g. anagement has specified that the >ars should fall between .&&' "g and .55& "g. a. -hat is the process capability index b. s this process capable
a.
(upper specification - lower specification
# (.""& - .&&6)6(.'16) # 1.1!".
b. 9es2 but not by much. (. Occasionally: a random sample of fie >ars of Tin"er =elle Peanut =utter /see problem 6' is selected from the output and weighed: to be sure that the system is under control. !ere are data on ten such samples. easurements are in "ilograms. $ample 1 2 % & 5 ' ( ) * 1+ .5+ .5+ .5+ .51 .51 .51 .5+ .5+ .51 .5+ .&( .&) .&* .51 .5+ .5+ .51 .52 .&) .51 .5+ .&) .51 .52 .&* .52 .&* .&( .5+ .&* .&* .&) .&( .51 .52 .51 .5+ .&* .&* .5+ .51 .&( .&* .51 .5+ .51 .&) .&* .5+ .&( Total 2.&( 2.&1 2.&' 2.5' 2.52 2.55 2.&) 2.&( 2.&) 2.&(
a. -hat type of control chart should be used here -hy b. -hat is the centerline of the chart c. -hat is the lower control limit The upper control limit d. -hat statistic should be plotted on the control chart for each sample e. ,raw the control chart on a piece of graph paper. f. s this system under control g. -hat should the 3uality control engineer do a. Use the 3-bar chart4 this is measurement data.
b.
0g.
c. 5ecause the value of the population standard deviation is 0nown2 find the standard error of
the sample means and use ; # <%s.
0g. 0g. 0g.
d. The sample mean. /ere are the first few. Sample No. =ean
1
0g.
!
0g.
e. U+,
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f. 9es. g. No action is necessary. ). /One step beyond. se Table , in this study guide. se the data in Problem ' to construct an < chart. a. -hat is the lower control limit The upper control limit b. -hat statistic should be plotted on the control chart for each sample c. ,raw the control chart on a sheet of graph paper. d. s this system under control e. -hat should the 3uality control engineer do
a. 5ecause
is 0nown2 use the factors2 71 and 7!2 from the Table of +ontrol +hart 8actors
in this Study >uide.
0g. 0g.
b. ?lot the ranges. /ere are the first few of them. Sample No. ange () 1
0g.
!
0g.
c. U+,
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d. 9es. e. No action is necessary. *. The Poseidon 9abric Co. produces large beach towels /among other things# they are supposed to be brightly colored and hae a fringe on each end. 9rom time to time: a towel is selected from the finished goods and sub>ected to an intense inspection in search of any and all defects. 7 defect is a stain: a badly dyed spot: a
hole: a missing fringe: etc.: each occurrence counts as a distinct defect. !ere are data on 12 sample towels. Towel 1 2 % & 5 ' ( ) * 1+ 11 12 @umber of defects 2 1 % + 1 & + 1 % 2 % 1
a. -hat type of control chart should be used here -hy b. -hat is the centerline of the chart c. -hat is the lower control limit The upper control limit d. -hat statistic should be plotted on the control chart for each sample e. ,raw the control chart on a piece of graph paper. f. s this system under control g. -hat should the 3uality control engineer do a. Use a c-chart2 because the data consists of the number of defects per unit4 a unit is a towel.
b.
defects per towel
c. . d. The number of defects per towel. e. U+,
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f. 9es. g. No action is necessary.
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