Experimental Experimental Design Design For For Injection Injection Molding Molding Launsby Launsby Consulting Consulting 2009 2009
4/2/2009
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Launsby Consulting
Bob Bob Launsby Launsby
[email protected]
•• Taught Taught experimental experimental design design to to several several thousand thousand people people •• Participated Participated in in numerous numerous actual actual experiments experiments •• Application Application is is key key •• Co-developer Co-developer of of DOE DOE Wisdom Wisdom software software •• Co-Author Co-Author of of “DOE “DOE for for Injection Injection Molding” Molding” www.launsby.com 4/2/2009
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Introductions Introductions •• •• ••
Name Name Title Title Background Background in in Injection Injection Molding Molding –– Previous Previous Courses Courses –– Cavity Cavity Pressure Pressure Control? Control?
•• Previous Previous Experiences Experiences with with Experimental Experimental Design Design and and Statistics Statistics
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Course Course Guidelines Guidelines •• •• •• •• ••
Start Start and and Stop Stop Times Times Breaks Breaks Active Active Participation Participation You You are are Responsible Responsible for for Learning Learning Importance Importance of of Applications Applications
•• Having Having Fun Fun and and Learning Learning
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Module Module One One •• Goals: Goals: –– Understand Understand the the Building Building Blocks Blocks for for aa Fundamentally Fundamentally Robust Robust Molding Molding Process Process –– Understand Understand the the Need Need for for Modern Modern Design Design of of Experiments Experiments Techniques Techniques –– Recognize Recognize the the Power Power and and Applicability Applicability of of These These Approaches Approaches to to Injection Injection Molding Molding –– Understand Understand the the Basics Basics
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The Injection Molding Challenge
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The The Challenge Challenge (Cont.) (Cont.) •• •• •• •• •• •• •• •• 4/2/2009
Complex Complex Part Part Geometry,Many Geometry,Many Finishes Finishes Varying Varying Wall Wall Thickness Thickness Snap Snap Fits, Fits, Threads Threads No No Secondary Secondary Operations Operations Consistency, Consistency, High High Prod. Prod. Rates Rates Regrind Regrind Tight Tight Tolerances, Tolerances, Cost Cost Competition Competition QS QS 9000, 9000, Process Process Validation Validation 7
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The The Process Process Diagram Diagram
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Process Process Diagram Diagram PROCESS DIAGRAM FOR INJECTION MOLDING
Some Potential Factors
Potential Responses
Material Lot
Dimensions
Material Variation
Color
% Regrind
Black Specks
Hold Pressure
Warpage
Pellet Geometry
Blisters
Plastic Temperature
Blush
Screw RPM
Knit Lines
Injection Velocity
Sinks
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Basic Basic Understandings Understandings Before Before Doe Doe •• Non-Newtonian Non-Newtonian Behavior Behavior of of Plastic Plastic –– Static Static Pressure Pressure Loss Loss –– Relative Relative Viscosity Viscosity Curves Curves
•• •• •• •• •• 4/2/2009
Semi-Crystalline Semi-Crystalline Vs. Vs. Amorphous Amorphous Materials Materials Hygroscopic Hygroscopic and and non-hygroscopic non-hygroscopic Materials Materials Shear Shear Heating Heating Fountain Fountain Flow Flow Four Four Plastic Plastic Variables Variables 10
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Static Static Pressure Pressure Loss Loss
CAVITY
SCREW
RUNNERS
SPRUE
TRANSDUCERS
Where is Plastics Pressure Greatest? Where is it the Least?
Source: RJG, Inc. 4/2/2009
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Relative Relative Viscosity Viscosity THICK
VISCOSITY
High sensitivity to machine fill speed fluctuation Crossover point
Low sensitivity to machine fill speed fluctuation
THIN SLOW 4/2/2009
FLOW RATE
Source: RJG, Inc. 12
FAST Launsby Consulting
Crystalline Crystalline Vs. Vs. Amorphous Amorphous •• Crystalline Crystalline (Semi-Crystalline) (Semi-Crystalline) –– Melt Melt is is Amorphous Amorphous -- Forms Forms Crystals Crystals on on Cooling Cooling –– More More Crystalline Crystalline == More More Shrinkage Shrinkage –– Fast Fast Cooling Cooling --> --> Less Less Time Time to to Form Form Crystals Crystals --->> Less Less Crystallinity Crystallinity --> --> Less Less Shrinkage Shrinkage
•• Amorphous Amorphous –– Both Both Melt Melt and and Solid Solid are are Amorphous Amorphous –– Cooling Cooling Rate Rate Not Not Related Related to to Shrinkage Shrinkage Source: RJG, Inc. 4/2/2009
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Fountain Fountain Flow Flow •• Fountain FountainFlow, Flow,Skin SkinLayer, Layer,and andAlignment Alignment
Source: RJG, Inc. 4/2/2009
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Four Four Plastic Plastic Variables Variables •• •• •• ••
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Plastic Plastic Flow Flow Rate Rate Plastic Plastic Temperature Temperature Plastic Plastic Cooling Cooling Plastic Plastic Pressure Pressure Gradient Gradient
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Before Before Attempting Attempting DOE DOE •• •• •• •• •• •• •• •• 4/2/2009
Is the materials dry?
Set Set Melt Melt Temps Temps at at Nominal Nominal Check ring leakage? Position Position Transfer Transfer Fill Fill Fast Fast (But (But No No Faster), Faster), Fill Fill With With Ample Ample First First Stage Stage Pressure Pressure –– Relative Relativeviscosity viscositycurve curve
Fill Fill 95% 95% to to 99%, 99%, Then Then Transfer Transfer to to Pack Pack Hold Hold Plastic Plastic in in Tool Tool Understand Understand When When Gate Gate Seals Seals (gate (gate seal seal test) test) Clogged cooling Cool Efficiently Cool Efficiently lines??? Demold Demold Quickly Quickly and and Consistently Consistently 16
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What What Is Is A A Designed Designed Experiment? Experiment? •• Systematic, Systematic, Controlled Controlled Changes Changes of of the the Inputs Inputs (factors) (factors) to to aa Process Process in in Order Order to to Observe Observe Corresponding Corresponding Changes Changes in in the the Outputs Outputs (responses). (responses).
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Types Types Of Of Factors Factors •• •• ••
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Constant Constant Factors Factors Control Control Factors Factors Noise Noise Factors Factors (Robustness) (Robustness)
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What What Do Do We We Learn Learn From From Designed Designed Experiments? Experiments? •• Best Best Settings Settings
•• Sensitivity Sensitivity
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Why Why Do Do Designed Designed Experiments? Experiments?
•• 50 50 Per Per Cent Cent Improvement Improvement in in Efficiency Efficiency and and Effectiveness Effectiveness
•• 11 ++ 11 == 10 10 4/2/2009
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How How To To Be Be Good Good At At ItIt •• Attend Attend Training Training •• Read Read •• 510 510 Rule Rule
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Engineering Engineering Experimental Experimental Design Design •• Not Not aa Substitute Substitute For For Knowledge Knowledge of of Technology Technology •• Incorporates Incorporates Current Current Understanding Understanding
•• Physics Physics First First •• IfIf You You Do Do Not Not Understand Understand the the Basics, Basics, You You Will Will Do Do EVIL EVIL Things Things With With DOE DOE
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Examples Examples Of Of Poorly Poorly Done Done Doe’s Doe’s •• Quality Quality Digest Digest of of 1999 1999 –– Injection Injection Press Press –– Gates Gates –– Barrel Barrel Temps Temps –– Moisture Moisture Content Content –– Randomization, Randomization, Replication Replication
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An An Example Example •• •• •• •• •• ••
Hinged Hinged Box, Box, 100 100 ton ton Press Press Thickness Thickness is is .070 .070 in in Length Length is is response response Polypropylene Polypropylene Single Single Cavity Cavity Mold Mold Set Set Transfer Transfer Point Point and and Performed Performed Gate Gate Seal Seal Test Test •• Fix Fix Settings Settings (except (except mtemp mtemp and and hpress) hpress) 4/2/2009
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An An Example Example RUN
Mtemp
H Press
Length
1
70
5000
15
2
70
7000
19
3
90
5000
12
4
90
7000
17
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Pareto Pareto Chart Chart L e n g t h A v g D e l t a / 2
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Pareto Chart
4
3 2.25 2 -1.25 1 0.25 0
Hold press(B)
Mold temp(A) Factors
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Main Main Effects Effects Plot Plot 19
Main Effects
17.8 L e n g t h
16.6
15.4
14.2
13
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70(-) 90(+) Mold temp(A)
5000(-) 7000(+) Hold press(B) Factors
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Transfer Transfer Function Function •• The The equation equation (algebraic) (algebraic)
•• ••
ItIt comes comes from from MLR MLR Three Three important important assumptions assumptions
–– Two Two levels levels –– O.A. O.A. –– Variables Variables are are on on orthogonal orthogonal scale scale Software packages use MLR to generate transfer function
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MLR MLR Math Math yˆ = b0 + b1 x1 + b2 x2 + b12 x1 x2 + .........
β = [X X ] [X tY ] t
−1
b0 b 1 β = b2 b12 ...
y1 y 2 y3 Y = y4 . . yn
1.. − 1.. − 1.. − 1 1.. − 1.. + 1.. + 1 1.. + 1.. − 1.. + 1 X = 1 .. + 1 .. + 1 .. − 1
Note: the computer does the math, we just need to be able to interpret the output 4/2/2009
includes factors (assumes 4 run previous example), and interaction effect 29
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Contour Contour Plot Plot Contour Plot
7000 18.4
17.6
H 6600 o l d 6200
16.8 16
p r 5800 e s s 5400
15.2 14.4
13.6 12.8
5000
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70
74
78
82 Mold temp Length 30
86
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RSM RSM Plot Plot Response Surface
22 L e n g t h
19.6 17.2 14.8 12.4 10 5000
90 5400 5800 Hold press6200
86 82 78 6600
74 7000
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Mold temp
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Example Example Using Using DOE DOE Wisdom Wisdom click
Click on new
Name example 1 4/2/2009
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Example Example Using Using DOE DOE Wisdom Wisdom Click on add
Enter info on first factor 4/2/2009
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Example Example Using Using DOE DOE Wisdom Wisdom Click to add additional factors
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Example Example Using Using DOE DOE Wisdom Wisdom Add response
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Example Example Using Using DOE DOE Wisdom Wisdom Click when done
select 4/2/2009
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Example Example Using Using DOE DOE Wisdom Wisdom Select data window
Enter data
Click save when done 4/2/2009
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Example Example Using Using DOE DOE Wisdom Wisdom
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Example Example Using Using DOE DOE Wisdom Wisdom
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Example Example Using Using DOE DOE Wisdom Wisdom
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Experimental Experimental Objectives Objectives
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Where Where Can Can Molders Molders Use Use Designed Designed Experiments? Experiments? •• Problem Problem solving solving •• Tool Tool trials trials •• Establishment Establishment of of process process windows windows
2004
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Troubleshooting/screening Troubleshooting/screening
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Troubleshooting/screening Troubleshooting/screening FACTORS Mold Temp Barrel Temp Cure Time Back Press Inj Velocity Hold Press 4/2/2009
LOW 100 Low 40 50 1 200
HIGH 150 High 50 150 3.1 1100 44
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Troubleshooting/screening Troubleshooting/screening •• Response Response –– Appearance Appearance –– Decreasing Decreasing shape shape –– Rate Rate as as 1, 1, 2, 2, 33 (3 (3 is is best) best)
•• O.A. O.A. –– L8 L8 with with 55 repetitions repetitions
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Main Main Effects Effects Mold temp is big hitter, set at high for best appearance. Other factors appear to have little impact on appearance
5 4 a p p e a r
3 2 1 0 moldt
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barrelt
injvel ctime Factors
46
holdp
bckpre
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Modeling Modeling DJ DJ Example Example Toshiba ink cartridge
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DJ DJ Example Example FACTOR
LOW
Hold Pressure (psi) 5000
8500
Pack Speed (%)
15
30
Injection Vel. (%)
30
65
Mold Temp (deg.) 100 2004
HIGH
150 48
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Responses Responses For For DJ DJ RESPONSE LSL
NOM.
USL
SLOT1
31.90
31.95
32.0
SLOT2
56.68
56.83
56.98
SLOT3
38.62
38.72
38.8
SLOT4
33.60
33.65
33.70
SPLAY and FLOWLINES rated as Good, OK, Bad (3,2,1) 2004
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Runs Runs For For DJ DJ moldtemp injvel packspd holdpress 1 2 3 4 5 6 7 8 9 10 11 12 2004
100 100 100 100 100 100 100 150 150 150 150 150
30 30 65 30 65 65 30 65 30 65 30 30
15 30 15 30 25 15 15 30 15 15 30 15 50
4000 8000 8000 4000 8500 4000 4000 4000 8500 8500 8500 4000
Note: here are the trials, 4 cavity tool, did 5 shots per run. Response values are not shown, only some of the simple analysis (follows)
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Main Main Effects Effects Plot Plot Slot Slot 11 31.92
Main Effects
31.91 s 31.9 l o 31.89 t 1
31.88 31.87 31.86
100(-) 150(+) 30(-) 65(+) moldtemp(A) injvel(B)
15(-) 30(+) 4000(-)8500(+) packspd(C) packpress(D)
Factors 2004
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Main Main Effects Effects Plot Plot Slot Slot 22 56.82
Main Effects
56.81 s 56.8 l o 56.79 t 2
56.78 56.77 56.76
100(-) 150(+) 30(-) 65(+) 15(-) 30(+) 4000(-)8500(+) moldtemp(A) injvel(B) packspd(C) packpress(D) Factors
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Main Main Effects Effects Plot Plot Slot Slot 33 38.72
Main Effects
38.7 s l 38.68 o 38.66 t 3
38.64 38.62 38.6
100(-) 150(+) 30(-) 65(+) 15(-) 30(+) 4000(-)8500(+) moldtemp(A) injvel(B) packspd(C) packpress(D) Factors
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Main Main Effects Effects Plot Plot Slot Slot 44 33.63
Main Effects
33.62 s l o t 4
33.61 33.6 33.59 33.58 33.57
100(-) 150(+) 30(-) 65(+) moldtemp(A) injvel(B)
15(-) 30(+) 4000(-) 8500(+) packspd(C) packpress(D)
Factors 2004
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Main Main Effects Effects Plot Plot Splay Splay Main Effects
3.4 3.2 s p l a y
3 2.8 2.6 2.4 2.2
100(-) 150(+) moldtemp(A)
30(-) 65(+) injvel(B)
15(-) 30(+) 4000(-) 8500(+) packspd(C) packpress(D)
Factors 2004
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Main Main Effects Effects Plot Plot FLOWLINES FLOWLINES Main Effects
3 f l o w l i n e s
2
1
0
100(-) 150(+) moldtemp(A)
30(-) 65(+) injvel(B)
15(-) 30(+) 4000(-) 8500(+) packspd(C) packpress(D)
Factors 2004
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What What Is Is The The Best Best TradeTradeoff? off? Response Surface**packspd(C)=15.0000,packpress(D)=7920.00
Operate in this region D ( c o m p o s i t e )
0.4 0.3 0.2 0.1 0 30
150 37
140 44 injvel
130 51
120 58
110 65
2004
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moldtemp
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PICTURAL PICTURAL View View Of Of TradeTradeoff off (means) (means)
.
. Slot 1
.
Slot 2
. Slot 3
Slot 4
Note: slot 1 and slot 2 work the opposite of slots 3 and 4. If we attempt to increase slot 1 and slot 2, slots 3 and slots 4 decrease. Good time to find this out is during tool trial
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How How About About Variation? Variation? Monte Carlo Simulation can be used to predict variation about a process mean DOE Wisdom Analysis of Variance Dependent Variable: Number Runs(N): Multiple R: Squared Multiple R: Adjusted Squared Multiple R: Standard Error of Estimate: Variable Constant Mold Temp(A) Inj Vel(B) Pack Spd(C) Pack Prs(D) AB AC AD BC BD CD 2004
response 4 12 0.999807 0.999614 0.995757 0.000848528
Coefficient best setting 33.5985 0.00506435 150 -0.00941707 47 -0.00507645 15 -0.00436898 7920 0.00572135 0.00363698 -0.000393981 -0.00360833 -0.00193009 -0.00225509
How closely can the factors be controlled in production?
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Results Results of of Monte Monte Carlo Carlo Simulation Simulation
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ROBUST ROBUST DESIGN DESIGN Product Product Level Level •• What What itit Means Means –– Products Products Perform Perform Intended Intended Functions Functions at at Varying Varying Usage Usage Conditions Conditions –– Wide Wide Range Range Customer Customer Usage Usage –– Product Product Deterioration Deterioration –– Variation Variation in in Subsystems/Components Subsystems/Components
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Robustness Robustness At At The The Process Process Level Level •• •• •• •• •• ••
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Lot-to-Lot Lot-to-Lot Variation Variation in in Resin Resin Regrind Regrind Machine Machine Room Room Temperature Temperature Moisture Moisture Content Content Operator Operator
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Robust Robust Design Design (Cont.) (Cont.) •• Robust Robust Design Design Recognizes Recognizes That That Variability Variability Exists Exists and and is is the the Enemy Enemy of of High High Quality Quality Products Products and and Processes Processes •• Employs Employs DOE DOE as as aa Strategic Strategic Weapon Weapon •• Accomplished Accomplished by by Selecting Selecting the the Best Best Levels Levels for for Control Control Factors Factors so so That That Performance Performance Insensitive Insensitive to to Noise Noise Factors Factors
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Robust Robust Design Design (Examples) (Examples) •• Caramel Caramel Candy Candy Example Example
•• Industry Industry Examples Examples (HP (HP Ink Ink Cartridge…see Cartridge…see following following slides) slides)
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HP HPweld weldexample example
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HP HP Weld Weld Example, Example, The The Part Part Ink Cartridge
Energy director on base 4/2/2009
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Hp Hp Ireland Ireland
EDH is energy director height, MFI is melt flow index. They are both noise factor in this example 4/2/2009
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Robust Robust Design Design Example Example FACTORS
C/N
LOW
HIGH
APRESS
C
25
40
COL DIST
C
.004
.006
AMP
C
65
85
DWN SPD
C
2.6
4.0
MFI
N
LOW
HIGH
EDH
N
LOW
HIGH
•• HP HPIreland Ireland –– Review Reviewfactors, factors,levels, levels,responses, responses,Desirabilities Desirabilities –– Any Anyfactor factorsettings settingsminimize minimizevariation? variation? –– What Whatare areoptimal optimalsettings? settings? Desirability functions allow us to trade-
off multiple simultaneous responses (we will learn details later)
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The The Data Data Eight run inner OA Run
press 1 2 3 4 5 6 7 8
MFI EDH
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high high strength STD % 0.0067 0.00148 0.00941 0.00056 0.00906 0.0006 0.01129 0.0005 0.00703 0.00098 0.00941 0.00067 0.00911 0.00572 0.01136 0.00047
0 100 87 100 1 100 45 100
File “hp robust 1”
dist 25 25 25 25 40 40 40 40
amp 0.004 0.004 0.006 0.006 0.004 0.004 0.006 0.006
high low strength STD % 0.00707 0.00088 0.00985 0.00079 0.00932 0.00101 0.01152 0.00086 0.00703 0.00098 0.00991 0.00095 0.0085 0.00093 0.01177 0.0008
0 100 74 99 6 100 56 100
69
spd 65 85 65 85 65 85 65 85
2.6 4 4 2.6 4 2.6 2.6 4
low high strength STD % 0.00694 0.00116 0.00929 0.00044 0.00899 0.00068 0.01143 0.0004 0.00697 0.00096 0.00932 0.00065 0.00862 0.00052 0.01121 0.00068
0 100 80 100 4 100 59 100
low low strength STD % 0.00719 0.00111 0.00977 0.00088 0.00931 0.00112 0.01143 0.00077 0.00718 0.0011 0.00953 0.00098 0.00859 0.00078 0.01182 0.00079
0 98 74 100 7 93 53 100
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Robust Robust Design, Design, Strength Strength Main Effects
Average
0.012
0.011
s t r e n g t h
0.01
0.009
0.008
0.007
0.006 25(-) 40(+) press(A)
0.004(-) 0.006(+) dist(B)
65(-) 85(+) amp(C)
2.6(-) 4(+) spd(D)
Factors
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Robust Robust Design Design (Cont.) (Cont.) •• Students: Students: What What is is the the best best trade-off? trade-off? Mean (Weld Str) Stand Dev (Weld Str) % Good Welds D(composite) 0.0116059 0.00044375 122.25 1 95% CI: ± 0.000498452 ± 0.00193891 ± 39.7551 Constant 0.00924781 0.000975 66.75 Air Pressure(A) -3.78E-05 0.0001475 -2.75 Collapse Distance(B) 0.000960313 6.44E-05 16.1875 Amplitude(C) 0.00127219 -0.000275625 32.625 Down Speed(D) 8.78E-05 -0.0001725 3.9375
25 0.006 85 4
Here are the predicted optimal setting for factors
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RSM RSM Plot Plot Response Surface**Air Pressure(A)=25.0000,Down Speed(D)=4.00000
D ( 1 c o 0.8 m 0.6 p o 0.4 s i 0.2 t 0 e 0.004 )
85 81 77
0.005 Collapse Distance
73 69 0.006
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Amplitude
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Knowledge Knowledge Of Of The The Technology Technology To To Enhance Enhance Robustness Robustness •• Viscosity Viscosity vs. vs. Shear Shear Curves Curves •• Cavity Cavity Pressure Pressure Sensors Sensors
Cavity pressure changes are a major source of dimensional and appearance variation 4/2/2009
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Conventional Conventional Molding Molding •• ••
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Fill Fill and and Pack Pack are are Done Done on on First First Stage Stage Time Time is is Usually Usually Used Used to to Transfer Transfer From From Boost Boost to to Hold Hold
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Typical Typical Pressure Pressure Profile Profile
From “Plastic Part Design” by R.A. Malloy 4/2/2009
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Hydraulic Hydraulic Pressure Pressure Is Is Misleading Misleading Hydraulic Injection Pressure
Mold Cavity Pressure
Source: RJG, Inc. 4/2/2009
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TM Decoupled MOLDING Decoupled MOLDINGTM
DECOUPLED MOLDINGTM is a registered trademark of RJG, Inc. 4/2/2009
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Cavity Cavity Pressure Pressure Impact Impact
4/2/2009
Source: RJG, Inc. 78
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Cavity Cavity Control Control Impact Impact MOLDING GATE END EOF MOLD TECHNIQUE MOLD PRESS (s.d.) PRESS (s.d.) Traditional 514 860 Totally Decoupled
21.4
205
Source: RJG Associates, Decoupled Molding is a Trademark of RJG in Traverse City,
MI
4/2/2009
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Box Box And And Bubble Bubble Chart Chart •• •• •• •• ••
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Planning Planning Select Select an an Orthogonal Orthogonal Array Array Conduct Conduct Analysis Analysis Confirmation Confirmation
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Planning Planning •• •• •• •• •• ••
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Who Who Are Are the the Customers? Customers? How How Will Will Customers Customers Use Use Products? Products? What What are are the the Functions? Functions? Objectives? Objectives? Time Time Requirements Requirements Responses, Responses, Factors, Factors, Money Money
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Orthogonal Orthogonal Array Array •• AA Set Set of of Experimental Experimental Conditions Conditions (runs) (runs) Where Where the the Levels Levels of of Each Each Factors Factors are are Balanced Balanced Over Over the the Levels Levels of of the the Other Other Factors, Factors, Both Both Horizontally Horizontally and and Vertically Vertically •• AA Balanced Balanced Family Family of of Tests Tests Which Which Allows Allows For For Fast, Fast, Efficient, Efficient, Simple, Simple, and and Powerful Powerful Analysis Analysis •• Example-----Golf Example-----Golf 4/2/2009
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Orthogonal Orthogonal Vs Vs What? What? An An Example Example
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Factor Factor Assignments Assignments FACTOR
LEVELS
Carbon Black (C)
1.2, 2.1
Sulfur (S)
2, 2.5
Filler (F)
30, 33
Accelerator Type (A) Dupont, Allied Polymer Type (P) 4/2/2009
1, 2, 3, 4, 5 84
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Full Full Factorial Factorial Approach Approach •• Advantages Advantages
•• Disadvantages Disadvantages
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One-factor-at One-factor-at A A Time Time •• Advantages Advantages
•• Disadvantages Disadvantages
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Best Best Guess Guess Approach Approach •• Advantages Advantages
•• Disadvantages Disadvantages
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Experimentation Experimentation In In The The 00’s 00’s •• •• •• •• •• ••
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Full Full Factorials, Factorials, Taguchi Taguchi O.A.’s O.A.’s Fractional-Factorials Fractional-Factorials Plackett-Burman Plackett-Burman Hadamard Hadamard Matrices Matrices Box-Behnken, Box-Behnken, Central Central Composite Composite D-optimal D-optimal Designs Designs
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Module Module #2 #2 •• Goals Goals –– Understand Understand the the Steps Steps Required Required for for Success Success –– Set-up Set-up and and Analyze Analyze aa Simple Simple Design Design –– Learn Learn When When Analysis Analysis is is Unsuccessful Unsuccessful and and Grasp Grasp How How to to Recover Recover –– Apply Apply Desirability Desirability Functions Functions (using (using software). software).
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The The Box Box And And Bubble Bubble Details Details •• •• •• •• ••
Who Who is is the the customer? customer? How How will will product product be be used? used? Consider Consider applicability applicability of of functional functional analysis analysis What What is is the the objective? objective? What What are are the the detailed detailed questions questions to to be be answered? answered? When When can can we we start? start? When When do do we we need need an an answer? answer?
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The The Box Box And And Bubble Bubble Details Details (Cont) (Cont) •• Responses Responses –– Name, Name, how how measured?, measured?, MSA?, MSA?, shape, shape, critical critical values, values, weight weight
•• Factors Factors –– Name, Name, qualitative qualitative or or quantitative? quantitative? Range Range of of interest, interest, levels, levels, propensity propensity for for interactions interactions
•• Costs Costs –– Approximate Approximate cost cost per per run, run, time time per per run run 4/2/2009
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The The Box Box And And Bubble Bubble Details Details •• •• •• •• •• 4/2/2009
Select Select OA OA Determine Determine number number of of samples samples per per run, run, Discuss Discuss replication, replication, randomization, randomization, and and repetitions repetitions Conduct Conduct trials, trials, record record set set points points for for constant constant factors factors Analysis Analysis Confirm Confirm predictions predictions 92
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Four Four Types Types Of Of Factors Factors •• Effect Effect Location Location •• Effect Effect Variation Variation •• Effect Effect Both Both •• No No Effect Effect 4/2/2009
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Statistical Statistical Analysis Analysis Golf Golf Ball Ball Example Example
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Introduction Introduction To To Simple Simple Analysis Analysis Run
TEMP 1 2 3 4 5 6 7 8
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PIN 1 1 1 1 2 2 2 2
PACKT -20 -20 10 10 -20 -20 10 10
5 15 5 15 5 15 5 15
95
PACKP DURA. WT 600 45 900 47 900 64 600 69 900 49 600 49 600 69 900 74
44.8 45.3 45.3 44.8 45.4 44.9 44.9 45.4
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Main Main Effects Effects D U R A B I L I T Y
Main Effects
90 80 70 60 50 40 30
1(-) 2(+) TEMP(A)
-20(-) 10(+) PIN(B)
15(+) 600(-) 900(+) 5(-) PACKT(C) PACKP(D)
Factors 4/2/2009
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Main Main Effects Effects Main Effects
45.4 45.3 W E I G H T
45.2 45.1 45 44.9 44.8
2(+) 1(-) TEMP(A)
-20(-) 10(+) PIN(B)
15(+) 5(-) PACKT(C)
600(-) 900(+) PACKP(D)
Factors 4/2/2009
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Stats Stats Analysis Analysis Weight Weight DOE Wisdom Analysis of Variance Dependent Variable: WEIGHT Number Runs(N): 128 Multiple R: 0.963484 Squared Multiple R: 0.928301 Adjusted Squared Mu 0.925969 Standard Error of Esti 0.067707 Variable
Coefficient Std Error 95% CI
Tolerance T
Constant 45.1056 0.005985 ± 0.0118460 TEMP(A) 0.048281 0.005985 ± 0.011846 PIN(B) -0.0025 0.005985 ± 0.011846 PACKT(C) 0.007656 0.005985 ± 0.011846 4/2/2009 98 PACKP(D) 0.23375 0.005985 ± 0.011846
1 1 1 1
7537.012 8.068 -0.418 1.279 39.059
P(2 Tail) 0 0 0.677 0.203 Launsby Consulting 0
Stats Stats Analysis Analysis Durability Durability DOE Wisdom Analysis of Variance Dependent Variable: DURABILITY Number Runs(N): 128 Multiple R: 0.661862 Squared Multiple R: 0.438061 Adjusted Squared Mu 0.419787 Standard Error of Esti 12.5573 Variable Constant TEMP(A) PIN(B) PACKT(C) PACKP(D)
Source
Coefficient Std Error 58.4063 2 10.5938 1.375 0.0625
Sum of Sq DF
Regression 15119.63 Residual 19395.25
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1.10992 1.10992 1.10992 1.10992 1.10992
95% CI ± ± ± ± ±
Tolerance T
2.19701 2.19701 2.19701 2.19701 2.19701
4 123
3779.906 99 157.685
52.622 1.802 9.545 1.239 0.056
1 1 1 1
Mean SquaF Ratio 23.9713
P(2 Tail) 0 0.074 0 0.218 0.955
P 0 Launsby Consulting
Example Example Run
temp 1 2 3 4
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acid 1 1 2 2
time 0 1 0 1
time 67 66 17 26
time 79 71 22 26.5
100
time 71 81 18 25.5
time 73 67 19 27
time 69 68 17 28
time 65 73 17 27
70 61 17 26.6
Launsby Consulting
Example Example (Cont.) (Cont.) Main Effects
80 70 t i m e
60 50 40 30 20
4/2/2009
2(+) 1(-) temp(A)
0(-) 1(+) acid(B) Factors
101
-1(-)
1(+) AB
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Example Example (Cont.) (Cont.) Main Effects
6 5 S t i m e
4 3 2 1 0
4/2/2009
2(+) 1(-) temp(A)
1(+) 0(-) acid(B) Factors
102
1(+)
-1(-) AB
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Example Example (Cont.) (Cont.) t i m e l n
Pareto Chart
4 3 2 -1.4787
S D e l t a
1
-0.58861 -0.25787
0
temp(A)
AB Factors
acid(B)
R.O.T.: If absolute value of Ln S effect (Delta) is equal to or greater than 1.0, this is a strong reason to believe you have a factor which influences variation 4/2/2009
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Example Example #3 #3
QUESTION: How The Tabled Taguchi Designs Differ From Fractional-Factorials? 4/2/2009
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Example Example ## 44 •• Important Important terms terms –– Interaction Interaction Columns Columns –– Aliasing Aliasing –– Resolution Resolution
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Tabled Tabled Taguchi Taguchi Designs Designs See pages 52 thru 58 (Experimental Design for Injection Molding for L4, L8, L9, L16,…..)
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D-optimal D-optimal Designs Designs •• Advantages Advantages
•• Disadvantages Disadvantages
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How How Many Many Samples? Samples? R.O.T. R.O.T. Response Type
Pass/Fail
Np ′ ≥ 10
Visual (G,M,E)
10 to 20 Per Run
Quantitative
40 or More Per Experiment
Note: These are rules of thumb 4/2/2009
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How How Many Many Samples? Samples? •• Easy Easy to to provide provide if: if: –– You You have have an an estimate estimate of of the the standard standard deviation deviation for for response response being being studied studied –– Know Know what what is is aa practically practically significant significant difference difference
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Statistical Statistical Significance Significance •• People People talk talk aa great great deal deal about about statistical statistical significance; significance; yet yet spend spend almost almost no no time time regarding regarding practical practical significance significance •• Reality Reality –– Any Anyeffect effect(as (aslong longas asititisisnot notzero) zero)will willbe beshown shownas as statistically statisticallysignificant significantififenough enoughsamples samplesare areused used –– You Youcan canmathematically mathematicallyjustify justifyany anysample samplesize sizeby by tweaking tweakinginputs inputsto toformula formula
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Statistical/Practical Statistical/Practical Significance Significance
If the difference is not greater than 4, it is not of practical importance
Main Effects
20 19 b u m p h t
18
All are statistically significant
17 16 15 14 B(+)
A(-)
1(-)
(A)
2(+)
3(-)
(B)
2(-)
5(+) (C)
4(+) (D)
Factors
Variable Constant tech(A):A tech(A):B (B) (C) (D)
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Coefficient 17.0505 1.06016 -1.06016 0.689843 0.796313 -0.915697
Std Error 0.201485 0.209227 0.209227 0.209227 0.226216 0.249362
95% CI
Tolerance T
± 0.464627 ± 0.482480 ± 0.482480 ± 0.482480 ± 0.521657 ± 0.575030
0.888 0.888 0.908 0.875
111
P(2 Tail) 84.624 5.067 -5.067 3.297 3.52 -3.672
Need
0 0.001 0.001 0.011 0.008 0.006
Not a big deal
Consulting both before you get veryLaunsby excited
Sample Sample Size Size For For Mean Mean Shift Shift (one (one approach) approach) n=
16σ
2n = λ=
σ=
2
2
n = (tα + t β ) 2 σ 2 / λ2
Total number of samples in experiment
α = .02 β = .02
λ
2n ≥ 30
Minimum practical difference we wish to find as n ≈ (2 + 2) 2 σ 2 / λ2 significant Error standard deviation
λ=
Example: We decide to conduct an L8. We decide that 4 and estimate the error standard deviation as 4. The number of samples for the experiment is 32. We need to run the L8 4 times. 4/2/2009
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Confirmation Confirmation •• Recommended Recommended ## of of Tests Tests
•• Graphical Graphical Approach Approach
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Why Why You You May May Not Not Confirm Confirm •• •• •• •• •• •• •• •• 4/2/2009
Data Data Entry Entry Did Did Not Not Conduct Conduct Per Per Plan Plan Measurement Measurement System System Not Not Reliable Reliable Large Large Variation Variation in in the the Response Response Wrong Wrong About About Interactions Interactions Model Model is is Inadequate Inadequate Something Something Changed Changed (Viscosity) (Viscosity) “Computer “Computer On/Brain On/Brain Off” Off” 114
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Golf Golf Example Example Analysis Analysis Of Of Diameter Diameter •• Which Which Factors Factors Appear Appear to to be be Influencing Influencing the the Average? Average? •• Do Do Any Any Factors Factors Appear Appear to to be be Influencing Influencing the the Variation Variation in in the the Diameter? Diameter? •• How How Should Should We We Set Set the the Process Process to to Achieve Achieve aa Target Target Response Response of of 1.682? 1.682? Note: please use following graphs to answer above questions
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Main Main Effects Effects Diameter Diameter Main Effects
1.692 1.69 S I Z E
1.688 1.686 1.684 1.682 1.68
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2(+) 1(-) TEMP(A)
-20(-) 10(+) 5(-) 15(+) PIN(B) PACKT(C) Factors 116
600(-) 900(+) PACKP(D) Launsby Consulting
Variance Variance Analysis Analysis Diameter Diameter S I Z E l n
Pareto Chart
0.8 0.6
-0.54953
0.4 S D e l t a
4/2/2009
-0.28592 0.2 0.061876 0
PACKP(D)
PIN(B) TEMP(A) Factors 117
0.018528 PACKT(C)
Launsby Consulting
Stats Stats Analysis Analysis Diameter Diameter DOE Wisdom Analysis of Variance Dependent Variable: SIZE Number Runs(N): 128 Multiple R: 0.918717 Squared Multiple R: 0.844041 Adjusted Squared Mu 0.838969 Standard Error of Esti 0.001534 Variable
Coefficient Std Error
Constant 1.68614 TEMP(A) 0.000874 PIN(B) -0.00023 PACKT(C) 8.33E-05 PACKP(D) 0.003378
Source
0.000136 0.000136 0.000136 0.000136 0.000136
Sum of Sq DF
Regression 0.001566 4/2/2009 Residual 0.000289
95% CI ± ± ± ± ±
Tolerance T
0.000268335 0.000268 0.000268 0.000268 0.000268
4 123
0.000391 118 2.35E-06
12438.2 6.447 -1.709 0.614 24.916
1 1 1 1
Mean SquaF Ratio 166.417
P(2 Tail) 0 0 0.09 0.54 0
P 0 Launsby Consulting
Contour Contour Plot Plot Diameter Diameter 15 P A C K T
13 11
1.6824
9 7 5
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Contour Plot**TEMP(A)=1.00000,PIN(B)=10.0000
1.6832
1.684
1.6848
1.6856
1.6864
1.6872
1.688
816 600
660
720 PACKP SIZE 119
780
840
900
Launsby Consulting
Residual Residual Analysis Analysis •• What What is is it? it?
–– AA method method for for evaluating evaluating errors errors in in model model predictions predictions
•• What What are are the the benefits? benefits?
–– Check Check of of model model assumptions assumptions –– Evaluation Evaluation of of model model adequacy adequacy –– Increased Increased understanding understanding of of technology technology
•• What What patterns patterns should should emerge? emerge?
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Example Example •• “Epsoon” “Epsoon” (full-factorial, (full-factorial, single single cavity, cavity, 10 10 shots shots per per run) run) Factors
Levels
Mtemp
90, 130
Injection Velocity
60, 80 %
Pack Press
30, 60%
Responses Dimension “E” Total run out
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Dim Dim “E” “E”
13.06 d i m 13.05 e n s 13.04 i o n 13.03 E
13.02 13.01
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Main Effects
13.07
90(-)130(+)60(-)80(+)-1(-) 1(+) 30(-)60(+) -1(-) 1(+) -1(-) 1(+) -1(-) 1(+) mtemp(A) vel(B) -AB pack(C) -AC -BC ABC Factors
122
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TIR TIR
0.052
Main Effects
T 0.051 o t a 0.05 l r 0.049 u n 0.048 o u t 0.047 0.046
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123
90(-)130(+)60(-)80(+)-1(-) 1(+) 30(-)60(+) -1(-) 1(+) -1(-) 1(+) -1(-) 1(+) mtemp(A) vel(B) -AB pack(C) -AC -BC ABC Factors
Launsby Consulting
EPSOON EPSOON Dim Dim “E” “E” Student Student Residual Residual
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Dim Dim “E” “E” Student Student Residual Residual Plot Plot R e s i d u a l
S c a tte r
P lo t
8
d
6
i m
E
s t
4 2
u d
r
0
e s
-2 -4
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980 R u n
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O r d e r
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TIR TIR Student Student Residuals Residuals Residual Histogram
10 9
9
9 8
8 7 C o u n t
6
6
5 4
4
3 2 2
2 1 0
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4
1
2
3 2
2
1
0
0
-2.2 -2 -1.8-1.6-1.4-1.2 -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 T otal run out Studentized Residual
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TIR TIR Student Student Residuals Residuals R e s i d u a l
S c a tte r
P lo t
3 r u n
o u
2 1
t
s t
0
u d
-1
r e s l
-2 -3
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455 657585960616263646566 768697071727374757677 87980 R u n
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O r d e r
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Case Case Study Study “Hockey “Hockey Sticks” Sticks” Responses of Interest: Trim part for saddle bags of Length of the left motorcycle Length of the right Gap on left Gap on right Sinks on left Sinks on right Factors Studied: Mold Temperature (150 and 190) Injection Velocity (2 and 4 in/sec.) Hold Pressure (5000 and 14000 psi plastic)
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Case Case Study Study (cont.) (cont.) Two cavity tool for left and right part
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Case Case Study Study (cont.) (cont.) Relative Visc.
Speed 0.5
Decided to run DOE at 2 and 4 in/sec
18,720
20,000 1
10,070
15,000 10,000
4/2/2009
1.5
7,225
2
5,715
3
4,270
4
3,540
5
2,950
5,000 0 0.5 1 1.5 2 speed
130
3
4
Rel. Visc. 5
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Case Case Study Study (cont.) (cont.) Hold Time
Part Weight
2
Less than .088
3
.088
4
.089
5
.089
6
.089
7
.089
4/2/2009
A hold time of 6 seconds was selected. Appear to provide ample time for gate seal
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Case Case Study Study (cont.) (cont.) Run
4/2/2009
mold temperature
velocity
hold pressure
1
150
2
5000
2
150
2
14000
3
150
4
5000
4
150
4
14000
5
190
2
5000
6
190
2
14000
7
190
4
5000
8
190
4
14000
132
Conducted five shots per run
Launsby Consulting
Case Case Study Study (cont.) (cont.) Main Effects
0.4 l e n g t h
0.16 -0.08 -0.32
r i g h t
-0.56 -0.8
150(-) 190(+) mold temp(A)
l e f t
0.1 0 -0.1 -0.2 -0.3 -0.4
4/2/2009
5000(-) 14000(+) hold press(C)
Main Effects
0.2 l e n g t h
2(-) 4(+) velocity(B) Factors
150(-) 190(+) mold temp(A)
4(+) 2(-) velocity(B) Factors
14000(+) 5000(-) hold press(C)
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Case Case Study Study (cont.) (cont.) Main Effects
3.6 3.4
g a p
3.2
r i g h t
3 2.8 2.6 2.4
150(-) 190(+) mold temp(A)
4(+) 2(-) velocity(B) Factors
14000(+) 5000(-) hold press(C)
Main Effects
3.2 3 g a p l e f t
2.8 2.6 2.4 2.2 2
4/2/2009
150(-) 190(+) mold temp(A)
4(+) 2(-) velocity(B) Factors
14000(+) 5000(-) hold press(C)
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Case Case Study Study (cont.) (cont.) Main Effects
2.8 s i n k r i g h t
2.6 2.4 2.2 2 1.8 1.6
150(-) 190(+) mold temp(A)
2.4 s i n k
4(+) 2(-) velocity(B) MainFactors Effects
14000(+) 5000(-) hold press(C)
2.3 2.2
What could account for this difference?
2.1 l e f t
2 1.9 1.8
4/2/2009
Student question: does it make sense that these two responses display dramatically different main effects plots for Hold Press?
150(-) 190(+) mold temp(A)
4(+) 2(-) velocity(B) Factors
14000(+) 5000(-) hold press(C)
135
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Case Case Study Study (cont.) (cont.) DOE Wisdom Analysis of Variance Dependent Variable: length right Number Runs(N): 40 Multiple R: 0.977694 Squared Multiple R: 0.955885 Adjusted Squared Mu 0.946235 Standard Error of Esti 0.078724 Variable
Coefficient Std Error 95% CI
Constant mold temp velocity(B) hold press( AB AC BC ABC 4/2/2009
-0.1625 -0.083 0.006 0.3135 -0.0045 -0.03 0.029 0.0215
0.012447 0.012447 0.012447 0.012447 0.012447 0.012447 0.012447 0.012447
Tolerance T
± 0.0253545 ± 0.0253545 ± 0.0253545 ± 0.0253545 ± 0.0253545 ± 0.0253545 ± 0.0253545 ± 0.0253545 136
1 1 1 1 1 1 1
P(2 Tail) -13.055 -6.668 0.482 25.186 -0.362 -2.41 2.33 1.727
0 0 0.633 0 0.72 0.022 0.026 0.094 Launsby Consulting
Case Case Study Study (cont.) (cont.) DOE Wisdom Analysis of Variance Dependent Variable: length left Number Runs(N): 40 Multiple R: 0.95219 Squared Multiple R: 0.906665 Adjusted Squared Mu 0.886248 Standard Error of Esti 0.063236 Variable
Coefficient Std Error 95% CI
Constant mold temp velocity(B) hold press( AB AC BC ABC
4/2/2009
-0.13575 -0.03575 -0.00275 0.17175 -0.01175 -0.00325 0.01075 -0.00525
0.009998 0.009998 0.009998 0.009998 0.009998 0.009998 0.009998 0.009998
Tolerance T
± 0.0203662 ± 0.0203662 ± 0.0203662 ± 0.0203662 ± 0.0203662 ± 0.0203662 ± 0.0203662 ± 0.0203662
1 1 1 1 1 1 1
137
P(2 Tail) -13.577 -3.576 -0.275 17.178 -1.175 -0.325 1.075 -0.525
0 0.001 0.785 0 0.249 0.747 0.29 0.603
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Case Case Study Study (cont.) (cont.) DOE Wisdom Analysis of Variance Dependent Variable: gap right Number Runs(N): 40 Multiple R: 0.990342 Squared Multiple R: 0.980778 Adjusted Squared Mu 0.976573 Standard Error of Esti 0.085878 Variable
Coefficient Std Error 95% CI
Constant mold temp velocity(B) hold press( AB AC BC ABC
4/2/2009
2.9575 -0.2575 -0.0225 0.4825 -0.0175 0.0175 0.0225 0.0175
0.013579 0.013579 0.013579 0.013579 0.013579 0.013579 0.013579 0.013579
Tolerance T
± 0.0276584 ± 0.0276584 ± 0.0276584 ± 0.0276584 ± 0.0276584 ± 0.0276584 ± 0.0276584 ± 0.0276584
1 1 1 1 1 1 1
138
P(2 Tail) 217.808 -18.964 -1.657 35.534 -1.289 1.289 1.657 1.289
0 0 0.107 0 0.207 0.207 0.107 0.207
Launsby Consulting
Case Case Study Study (cont.) (cont.) DOE Wisdom Analysis of Variance Dependent Variable: gap left Number Runs(N): 40 Multiple R: 0.994618 Squared Multiple R: 0.989265 Adjusted Squared Mu 0.986916 Standard Error of Esti 0.053619 Variable
Coefficient Std Error 95% CI
Constant mold temp velocity(B) hold press( AB AC BC ABC 4/2/2009
2.5975 -0.0475 -0.0175 0.4575 -0.0025 -0.0075 0.0025 -0.0025
0.008478 0.008478 0.008478 0.008478 0.008478 0.008478 0.008478 0.008478
Tolerance T
± 0.0172689 ± 0.0172689 ± 0.0172689 ± 0.0172689 ± 0.0172689 ± 0.0172689 ± 0.0172689 ± 0.0172689
1 1 1 1 1 1 1 139
P(2 Tail) 306.384 -5.603 -2.064 53.964 -0.295 -0.885 0.295 -0.295
0 0 0.047 0 0.77 0.383 0.77 0.77 Launsby Consulting
Case Case Study Study (cont.) (cont.) DOE Wisdom Analysis of Variance Dependent Variable: sink right Number Runs(N): 40 Multiple R: 0.974639 Squared Multiple R: 0.949922 Adjusted Squared Mu 0.938967 Standard Error of Esti 0.158114 Variable
Coefficient Std Error 95% CI
Constant mold temp velocity(B) hold press( AB AC BC ABC 4/2/2009
2.275 -0.225 0.225 0.475 0.225 -0.025 0.025 0.025
0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025
Tolerance T
± 0.0509233 ± 0.050923 ± 0.050923 ± 0.050923 ± 0.050923 ± 0.050923 ± 0.050923 ± 0.050923
1 1 1 1 1 1 1 140
P(2 Tail) 91 -9 9 19 9 -1 1 1
0 0 0 0 0 0.325 0.325 0.325 Launsby Consulting
Case Case Study Study (cont.) (cont.) DOE Wisdom Analysis of Variance Dependent Variable: sink left Number Runs(N): 40 Multiple R: 0.725476 Squared Multiple R: 0.526316 Adjusted Squared Mu 0.422697 Standard Error of Esti 0.33541 Variable
Coefficient Std Error 95% CI
Constant mold temp velocity(B) hold press( AB AC BC ABC 4/2/2009
2.1 -0.15 0.05 0 -0.2 0.15 -0.05 0.1
0.053033 0.053033 0.053033 0.053033 0.053033 0.053033 0.053033 0.053033
Tolerance T
± 0.108025 ± 0.108025 ± 0.108025 ± 0.108025 ± 0.108025 ± 0.108025 ± 0.108025 ± 0.108025
1 1 1 1 1 1 1 141
P(2 Tail) 39.598 -2.828 0.943 0 -3.771 2.828 -0.943 1.886
0 0.008 0.353 1 0.001 0.008 0.353 0.068 Launsby Consulting
Case Case Study Study (cont.) (cont.) l e f t S t u d e n t i z e d R e s i d
4/2/2009
6
Residual Scatter Plot
4 2 0 -2 -4 -6
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334353637383940 Run Order
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Case Case Study Study (cont.) (cont.) Response Surface**velocity(B)=2.00000
1 D ( c 0.8 o m 0.6 p o 0.4 s i t 0.2 e 0 ) 190 182 174 mold temp 166 158 150
4/2/2009
5000
10400
8600
6800
12200
14000
hold press
143
Launsby Consulting
Case Case Study Study Best Best Set Set Points Points Mold temperature = 173 degrees Injection velocity = 2 inches/sec Hold pressure = 14000 psi. plastic (Note that this setting was not actually one of the eight trials conducted in the orthogonal array) From these settings the following values were predicted: Length right = .0965 +/- .1684 Length left = .0247 +/- .1352 Gap right = 3.404 +/- .183 Gap left = 3.063 +/- .115 Sink right = 2.43 +/- .34 Sink left = 2.11 +/- .717
4/2/2009
5 confirmation runs were conducted. All parts fell into above confidence Intervals 144
Launsby Consulting
Desirability Desirability Functions Functions •• •• ••
What What are are They? They? Why Why are are They They Needed? Needed? What What are are the the Steps Steps Required? Required? –– For For Each Each Response, Response, Determine Determine aa Shape Shape –– For For Each Each Response, Response, Determine Determine an an Importance Importance Weight Weight –– Analyze Analyze Composite Composite D D
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Composite Composite D D Example Example
4/2/2009
FACTOR
LOW
HIGH
A
1
2
B
1
2
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Composite Composite D D Example Example RESP
TYPE MIN.
NOM. MAX. WT.
Tensile Tent 1500 Hard.
Decr. 20
Elong. Inc.
4/2/2009
2000
500
147
2500
1
50
2
600
4
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Example Example
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Tensile Tensile Contour Contour Contour Plot
2 00 1950 1900 1.8 b
1850
1.6 1.4
1800
1750
1700
1650
1.6
1.8
1.2 1
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1
1.2
1.4 a Tensile 149
2
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Hardness Hardness Contour Contour Contour Plot
2 1.8 b
1.6
34
1.4 1.2 44 1 1
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32
36 42 1.2
40
38
1.4 a Hardness 150
1.6
1.8
2
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Elongation Elongation Contour Contour Contour Plot
2 1.8 b
510
520
560 530
1.6
540
1.2
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550
1.4
1
580 570
540 1
1.2
530 1.4 a Elongation 151
1.6
1.8
2
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Desirability Desirability Contour Contour Contour Plot
2 0.1 0.2 1.8 0.3 b
0.6 0.5
1.6 1.4
0.4
1.2 1
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1
1.2
1.4 a D(composite) 152
1.6
1.8
0 2
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Summary Summary •• Understand Understand the the Technology Technology of of Molding Molding •• Use Use the the Four Four Plastic Plastic Variables Variables as as the the Foundation Foundation for for DOE DOE •• Physics Physics First First •• 510 510 Rule Rule 4/2/2009
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