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Design_of_Experiments.ppt

This document provides an overview of design of experiments (DOE). It discusses key concepts like factors, responses, experimental design, and the four basic steps of DOE: plan, collect, analyze, and present. Examples are given to illustrate different types of experimental designs like full factorial designs, fractional factorial designs, and split lot designs. The document also discusses how to identify important factors, characterize relationships, and optimize responses through experimentation.

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2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.il Course Website: www.kpa.co.il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 2 Course Syllabus •Understanding Variability •Variability in Several Dimensions •Basic Models of Probability •Sampling for Estimation of Population Quantities •Parametric Statistical Inference •Computer Intensive Techniques •Multiple Linear Regression •Statistical Process Control •Design of Experiments
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 3 DOE Is a Problem-Solving Tool The color is too saturated... When you have a serious problem... … you need a good problem solving tool! We get banding when... The order wasn’t delivered on time...
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 4 • Which factors have the strongest effects? • Do any of the factors interact? • Which factor settings give the best results? DOE Helps Answer Key Questions The media jams when we print... Lubricant? Exit angle? Spring tension?
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 5 Process, Responses, and Factors -1 Factors Silver laydown, Finish time… Time, Catalyst… Transport speed, Capture lens... Responses Speed, Contrast Yield, Purity Image resolution, Banding Film Building Chemical Process Digital Imaging
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 6 Factors Compensation plan, Sales training Method of shipping, Order entry method Product positioning, Price Responses Sales revenue, Volume of new sales Shipping cost, Inventory level Trial purchase, Share of market Sales Supply Chain Product Develop. Process, Responses, and Factors -2
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 7 Screen: Which are the biggest factors? Characterize: What is the relationship between responses and factors? Optimize: What is the best setting of the factors? Verify: Are the results repeatable? Ask a Series of Questions Question Experiment(E) Q E Q E Q E (Q) Answer A A A
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 8 Cycle of Experimentation COLLECT Observe Code PLAN Questions Design Scope PRESENT Answer Questions Graphically Mathematically State Uncertainty Recommend ANALYZE Plot Plot Plot Model Conclude Four Basic Steps of DOE
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 9 A Serious Problem... I want my car to go fast … like that one!
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 10 What Factors Affect the Speed? Key Factor is: ___________________ Yes Air Holes No Slow Fast Shape
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 11 Key Factor is: _______________________________ Yes Air Holes No Slow Fast Slow Shape Effect of Air Holes
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 12 DOE Balanced Effects Key Factor is: _______________________________ Yes Air Holes No Slow Fast Slow Shape Slow
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 13 What factors affect flight time? What factors affect the quality of flight? The Helicopter Company
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 14 Length Width Factors Design Wing Wing Length Width 1 2.5 1.0 2 3.5 1.0 3 2.5 1.5 4 3.5 1.5 Response: Flight Time Your Experiment: Plan
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 15 Design # Repeat Test Wing Wing Flight Quality Flight Order Length Width Time of Flight 1 1 2 2 3 3 4 4 1 2 1 2 1 2 1 2 2.5 2.5 3.5 3.5 2.5 2.5 3.5 3.5 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 Your Experiment: Collect
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 16 Calculate averages for each design Wing Width 1.0 1.5 (1) (2) (3) (4) 2.5 3.5 Wing Length Avg. ___ Avg. ___ Avg. ___ Avg. ___ Your Experiment: Analyze
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 17 Your Experiment: Analyze Plot the data (one line for each Wing Width) Time 2.5 Wing Length 3.5
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 18 Your Experiment: Present Present  Answer the original question: Which factor most affects flight time?  Graphically  Numerically Recommendations:
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 19 What about Quality of Flight?  Is quality of flight related to flight time, or rotational speed, a combination, or something else entirely?  Does everyone think about this response in the same way?  What are the implications for analysis?
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 20 Health Imaging Customer Preference Study • Conventional thinking: Low noise a customer requirement • Some data suggested that high resolution (MTF) was larger driver • Experiment designed to identify key driver Which Is the Key Driver? MTF Hi Low Low Hi Noise 1 4 ? ?
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 21 X2 X1 “Homerun” X2 X1 “Shotgun” X2 X1 “Factorial” How Many Experiments? X2 X1 “1-at-a- time”
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 22 Typical Questions  Full factorial experiments can require many runs  The problem is greater if the response is nonlinear  Talk with an expert to decide how the experiment should be structured Full Factorial? Fractional Factorial? Linear Response? Curvature?
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 23 A A A A A B B B B B A B Is B better than A ?
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 24 - - - Split Lot Design A B A B A B A B A B A B
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 25 Factors and Levels Factors  Paste  Dielectric  Oven Levels -1 +1 -1 +1 -1 +1
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 26 Paste DielectOven Response -1 -1 -1 119 1 -1 -1 44 -1 1 -1 232 1 1 -1 135 -1 -1 1 11 1 -1 1 34 -1 1 1 45 1 1 1 80 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response 23 Full Factorial Design 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 27 Oven Dielect Paste 1 -1 1 -1 1 -1 130 110 90 70 50 Response Main Effects for Response 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response Main Effects Plot
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 28 1 -1 1 -1 Oven Dielect Paste 1 -1 1 -1 Interaction Plot for Response 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response Interaction Plots
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 29 C: Initial Gas Volume (m3) B: Piston Surface Area (m2) A: Piston Weight (Kg) D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m2) F: Ambient Temperature (0K) G: Gas Temperature (0K) 27 Full Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 30 0.6460 0.6500 0.6570 0.6540 0.6590 0.6570 0.6620 0.6580 1.2470 1.2350 1.2760 1.2480 1.3010 1.2880 1.2990 1.2840 0.1920 0.2150 0.2060 0.1880 0.2210 0.1990 0.1930 0.1920 0.3360 0.3850 0.3320 0.3220 0.3780 0.3550 0.3630 0.3530 0.6810 0.6780 0.6810 0.6820 0.6810 0.6820 0.6830 0.6800 1.4680 1.4590 1.4680 1.4790 1.4920 1.4720 1.4810 1.5040 0.4600 0.4690 0.4400 0.4250 0.4350 0.4120 0.4120 0.4460 0.9030 0.8280 0.9640 0.8360 0.8670 0.9380 0.9450 0.9730 0.4640 0.4610 0.4640 0.4600 0.4660 0.4670 0.4660 0.4650 0.9110 0.8950 0.8960 0.8970 0.9300 0.9220 0.9060 0.9260 0.1390 0.1310 0.1330 0.1480 0.1490 0.1690 0.1440 0.1490 0.2370 0.2340 0.2380 0.2400 0.2470 0.2260 0.2220 0.2720 0.4820 0.4810 0.4810 0.4810 0.4830 0.4820 0.4810 0.4830 1.0340 1.0360 1.0400 1.0270 1.0450 1.0570 1.0510 1.0370 0.3390 0.3200 0.3290 0.3170 0.2790 0.3180 0.3300 0.3200 0.6930 0.5790 0.6560 0.6780 0.6390 0.5880 0.6570 0.6500 G F E D C B A 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 Cube Plot - Means for Average 27 Full Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 31 G F E D C B A 0.8 0.7 0.6 0.5 0.4 Average Main Effects Plot - Means for Average A: Piston Weight (Kg) B: Piston Surface Area (m2) C: Initial Gas Volume (m3) D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m2) F: Ambient Temperature (0K) G: Gas Temperature (0K) 128 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 G F E D C B A 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 Interaction Plot for Average 27 Full Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 32 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 .001 .01 .05 .20 .50 .80 .95 .99 .999 P robability Eff_Avg Average: 0.0198583 Std Dev: 0.203497 N of data: 15 Anderson-Darling Normality Test A-Squared: 0.480 p-value: 0.199 Normal Probability Plot C_I niV ol A _Weight D_Spring B _Surfac CD 27 Full Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 33 Size of Full Factorial Designs
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 34 A B C AB AC BC ABC - - + + Fractional Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 35 135 34 45 119 Oven Dielect Paste 1 -1 1 -1 1 -1 Cube Plot - Means for Response Paste DielectOven Response -1 -1 -1 119 1 -1 -1 44 -1 1 -1 232 1 1 -1 135 -1 -1 1 11 1 -1 1 34 -1 1 1 45 1 1 1 80 23-1 Fractional Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 36 A B C D E F G 0.5 0.6 0.7 0.8 0.9 Average M ain Effects Plot - M eans for Average 2 ^(7 -3 ) = 1 6 16 A B C D E F G 0.5 0.6 0.7 0.8 0.9 Average M ain Effects Plot - M eans for Average 2^(7-2 ) = 3 2 32 A B C D E F G 0.40 0.52 0.64 0.76 0.88 Average M ain Effects Plot - M eans for Average 2 ^(7 -1 ) = 6 4 64
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 37 B_Surf C_IniVol D_Spring G_GasTem Average Std_Dev -1 -1 -1 -1 0.789 0.2104 1 -1 -1 -1 0.536 0.2691 -1 1 -1 -1 0.925 0.0174 1 1 -1 -1 0.504 0.2455 -1 -1 1 -1 0.486 0.1130 1 -1 1 -1 0.407 0.1667 -1 1 1 -1 0.528 0.1121 1 1 1 -1 0.446 0.1580 -1 -1 -1 1 0.420 0.1194 1 -1 -1 1 0.649 0.2503 -1 1 -1 1 0.520 0.2325 1 1 -1 1 0.335 0.0577 -1 -1 1 1 0.492 0.1366 1 -1 1 1 0.458 0.1186 -1 1 1 1 0.456 0.1464 1 1 1 1 0.424 0.1279 2 0 0 0 0.659 0.1476 -2 0 0 0 0.546 0.1945 0 2 0 0 0.602 0.1538 0 -2 0 0 0.517 0.1674 0 0 2 0 0.293 0.0874 0 0 -2 0 0.611 0.4334 0 0 0 2 0.422 0.2229 0 0 0 -2 0.623 0.2401 0 0 0 0 0.412 0.1285 0 0 0 0 0.456 0.1377 0 0 0 0 0.376 0.1105 0 0 0 0 0.483 0.2034 Central Composite Designs
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 38 0.3 -2 0.4 0.5 -2 0.6 -1 0.7 0.8 -1 0.9 0 1.0 0 1 1 2 2 0.4 -2 0.5 0.6 -2 -1 0.7 -1 0.8 0 0.9 0 1 1 2 2 Response Surfaces of Piston Performance 0.3 -2 0.4 -2 0.5 -1 0.6 -1 0 0.7 0 1 1 2 2 0.35 -2 0.45 0.55 0.65 -2 -1 0.75 0.85 -1 0.95 0 1.05 0 1 1 2 2 0.3 -2 0.4 0.5 -2 -1 0.6 0.7 -1 0.8 0 0.9 0 1 1 2 2 0.4 -2 0.5 0.6 -2 -1 0.7 0.8 -1 0 0.9 0 1 1 2 2
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 39 Case Study A: Manufacturing  Health Imaging Development Program  New mammography film (Kodak Min R-2000 film)  Emulsion making (cubes)  Factors: Ripener level, nucleation flow rate  Aims: Grain size 0.80 - 0.86 m Cubicity >60%  Goal: What is the operating window for getting the desired grain size and cubicity? A Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 40 Experimental Design 3 x 3 factorial design 30 18 6 0.388 69% 0.634 65% 0.754 60% 0.987 61% 0.821 47% 0.655 80% 1.259 48% Flow (cc/min) 13.2 39.6 66 Ripener (cc) A Case Study 0.543 76% 0.967 46%
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 41 0.50 0.60 0.70 0.80 0.86 0.90 1.00 1.10 1.20 Size Mapping the Effects: Grain Size FLOW (cc/min) RIPENER (cc) A Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 42 Cubicity 77% 72% 67% 62% 57% 52% 47% Mapping the Effects: Cubicity FLOW (cc/min) A Case Study RIPENER (cc)
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 43 Where Is the Overlap? FLOW (cc’s/min) RIPENER (cc’s) 77% 72% 67% 62% 57% 52% 47% 0.50 0.60 0.70 0.80 0.86 0.90 1.00 1.10 1.20 A Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 44 Case Study B: Business Units Consumer Imaging  New opportunity for branded photofinishing in the United States  Differentiation, pricing, segmentation all important considerations Question:How should a Kodak branded photofinishing option be priced? What share of choice can we expect? B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 45 Methodology  Mall intercept interviews with 100 consumers per cell who:  Have used at least three rolls of 35 mm film in the past year, and  Are responsible for deciding on photofinishing  Respondents complete “choice” exercises that simulate purchase decisions B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 46 CELL 1: Price Levels for Mass Merchant Store Processing: Overnight $3.49 $3.99 $4.99 Same Day $6.24 $6.99 $7.49 KODAK Premium Processing Bundle: Photofile $8.29 $9.29 $10.29 Price Levels B Case Study CELL 2: Price Levels for Drug/Food Store Processing: Overnight $4.49 $4.99 $5.99 Same Day $6.99 $7.99 $8.49 KODAK Premium Processing Bundle: Photofile $8.29 $9.29 $10.29
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 47 Choice Example 9 cards per person In-Store Overnight Processing $3.99 In-Store Same Day Processing $6.99 KODAK Premium Processing $9.29 Choice cards in study simulated Point of Sale (POS) B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 48 Results: Mass Merchant 57% 63% 63% 34% 23% 26% 10% 10% 14% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KPP Next Day KPP Same Day B Case Study Cell 1 - Mass Merchant (Same Day =$6.99 [median] and Next Day = $3.99 [median])
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 49 Cell 2 - Drug/Food (Same Day =$7.99 [median] and Next Day = $4.99 [median]) Results: Drug/Food 58% 67% 60% 35% 22% 26% 7% 14% 11% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 50 Cell 1 - Mass Merchant (Same Day =$6.24 [low] and Next Day = $3.49 [low]) Results: Mass Merchant 58% 63% 64% 29% 19% 22% 13% 14% 18% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 51 Cell 2 - Drug/Food (Same Day =$6.99 [low] and Next Day = $4.49 [low]) Results: Drug/Food 61% 69% 62% 31% 19% 22% 8% 16% 13% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 52 Model: Share of Choice Calculator INPUTS: Market: Mass Merchant Price for Same Day Processing: $6.99 Price for Next Day Processing: $3.99 Price for KODAK Premium Processing : $9.29 MODEL ESTIMATES: Share of Choice for KODAK Premium Processing : 26% Share of Choice for Same Day: 10% Share of Choice for Next Day: 63% B Case Study
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 53 a 25-1 Fractional Factorial Experiment 1. Purity by SE-HPLC 2. O.D.  Responses
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 54  Factors A. Freeze Temperature B. Thaw Temperature C. Volume D. Concentration E. Bulk
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 55  Levels FACTOR Low High A:FreezeTemp-196 -70 B:ThawRemp 5 23 C:Volume 1.8 200 D:Concprot 0.35 0.5 E:Bulk a b
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 56  Choosing the Experimental Array - 1 Fractional Factorial Design Factors: 5 Base Design: 5, 16 Runs: 32 Replicates: 2 Blocks: none Center p Design Generators: E = ABCD
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 57  Choosing the Experimental Array - 2 Design Generators: E = ABCD Alias Structure I + ABCDE A + BCDE, B + ACDE, C + ABDE, D + ABCE, E + ABCD AB + CDE, AC + BDE, AD + BCE, AE + BCD, BC + ADE BD + ACE, BE + ACD, CD + ABE, CE + ABD, DE + ABC
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 58 FreezeTemp ThawTemp Volume Concprot Bulk -196 5 1.8 0.35 b -70 5 1.8 0.35 a -196 23 1.8 0.35 a -70 23 1.8 0.35 b -196 5 200.0 0.35 a -70 5 200.0 0.35 b -196 23 200.0 0.35 b -70 23 200.0 0.35 a -196 5 1.8 0.50 a -70 5 1.8 0.50 b -196 23 1.8 0.50 b -70 23 1.8 0.50 a -196 5 200.0 0.50 b -70 5 200.0 0.50 a -196 23 200.0 0.50 a -70 23 200.0 0.50 b
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 59 -196 -70 0.35 0.50 FreezeTemp ThawTemp Volume Concprot Bulk 5 23 b a 1.8 200.0 2^(5-1) Fractional Factorial Design
2-Jun-23 (c) 2001, Ron S. Kenett, Ph.D. 60  Protocol of Experiment Two Independent samples for each run Each sample will be tested in duplicate a) Take the two bulks b) Dilute the two bulks at 0.5 and 0.35 mg/ml c) Take all the samples at the two freezing temperature conditions d) Take all the samples at the two thawing temperature conditions e) Start the analysis

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Design_of_Experiments.ppt

  • 1.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 1 Design of Experiments Instructor: Ron S. Kenett Email: ron@kpa.co.il Course Website: www.kpa.co.il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998
  • 2.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 2 Course Syllabus •Understanding Variability •Variability in Several Dimensions •Basic Models of Probability •Sampling for Estimation of Population Quantities •Parametric Statistical Inference •Computer Intensive Techniques •Multiple Linear Regression •Statistical Process Control •Design of Experiments
  • 3.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 3 DOE Is a Problem-Solving Tool The color is too saturated... When you have a serious problem... … you need a good problem solving tool! We get banding when... The order wasn’t delivered on time...
  • 4.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 4 • Which factors have the strongest effects? • Do any of the factors interact? • Which factor settings give the best results? DOE Helps Answer Key Questions The media jams when we print... Lubricant? Exit angle? Spring tension?
  • 5.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 5 Process, Responses, and Factors -1 Factors Silver laydown, Finish time… Time, Catalyst… Transport speed, Capture lens... Responses Speed, Contrast Yield, Purity Image resolution, Banding Film Building Chemical Process Digital Imaging
  • 6.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 6 Factors Compensation plan, Sales training Method of shipping, Order entry method Product positioning, Price Responses Sales revenue, Volume of new sales Shipping cost, Inventory level Trial purchase, Share of market Sales Supply Chain Product Develop. Process, Responses, and Factors -2
  • 7.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 7 Screen: Which are the biggest factors? Characterize: What is the relationship between responses and factors? Optimize: What is the best setting of the factors? Verify: Are the results repeatable? Ask a Series of Questions Question Experiment(E) Q E Q E Q E (Q) Answer A A A
  • 8.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 8 Cycle of Experimentation COLLECT Observe Code PLAN Questions Design Scope PRESENT Answer Questions Graphically Mathematically State Uncertainty Recommend ANALYZE Plot Plot Plot Model Conclude Four Basic Steps of DOE
  • 9.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 9 A Serious Problem... I want my car to go fast … like that one!
  • 10.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 10 What Factors Affect the Speed? Key Factor is: ___________________ Yes Air Holes No Slow Fast Shape
  • 11.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 11 Key Factor is: _______________________________ Yes Air Holes No Slow Fast Slow Shape Effect of Air Holes
  • 12.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 12 DOE Balanced Effects Key Factor is: _______________________________ Yes Air Holes No Slow Fast Slow Shape Slow
  • 13.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 13 What factors affect flight time? What factors affect the quality of flight? The Helicopter Company
  • 14.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 14 Length Width Factors Design Wing Wing Length Width 1 2.5 1.0 2 3.5 1.0 3 2.5 1.5 4 3.5 1.5 Response: Flight Time Your Experiment: Plan
  • 15.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 15 Design # Repeat Test Wing Wing Flight Quality Flight Order Length Width Time of Flight 1 1 2 2 3 3 4 4 1 2 1 2 1 2 1 2 2.5 2.5 3.5 3.5 2.5 2.5 3.5 3.5 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 Your Experiment: Collect
  • 16.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 16 Calculate averages for each design Wing Width 1.0 1.5 (1) (2) (3) (4) 2.5 3.5 Wing Length Avg. ___ Avg. ___ Avg. ___ Avg. ___ Your Experiment: Analyze
  • 17.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 17 Your Experiment: Analyze Plot the data (one line for each Wing Width) Time 2.5 Wing Length 3.5
  • 18.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 18 Your Experiment: Present Present  Answer the original question: Which factor most affects flight time?  Graphically  Numerically Recommendations:
  • 19.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 19 What about Quality of Flight?  Is quality of flight related to flight time, or rotational speed, a combination, or something else entirely?  Does everyone think about this response in the same way?  What are the implications for analysis?
  • 20.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 20 Health Imaging Customer Preference Study • Conventional thinking: Low noise a customer requirement • Some data suggested that high resolution (MTF) was larger driver • Experiment designed to identify key driver Which Is the Key Driver? MTF Hi Low Low Hi Noise 1 4 ? ?
  • 21.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 21 X2 X1 “Homerun” X2 X1 “Shotgun” X2 X1 “Factorial” How Many Experiments? X2 X1 “1-at-a- time”
  • 22.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 22 Typical Questions  Full factorial experiments can require many runs  The problem is greater if the response is nonlinear  Talk with an expert to decide how the experiment should be structured Full Factorial? Fractional Factorial? Linear Response? Curvature?
  • 23.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 23 A A A A A B B B B B A B Is B better than A ?
  • 24.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 24 - - - Split Lot Design A B A B A B A B A B A B
  • 25.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 25 Factors and Levels Factors  Paste  Dielectric  Oven Levels -1 +1 -1 +1 -1 +1
  • 26.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 26 Paste DielectOven Response -1 -1 -1 119 1 -1 -1 44 -1 1 -1 232 1 1 -1 135 -1 -1 1 11 1 -1 1 34 -1 1 1 45 1 1 1 80 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response 23 Full Factorial Design 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response
  • 27.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 27 Oven Dielect Paste 1 -1 1 -1 1 -1 130 110 90 70 50 Response Main Effects for Response 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response Main Effects Plot
  • 28.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 28 1 -1 1 -1 Oven Dielect Paste 1 -1 1 -1 Interaction Plot for Response 44 34 135 80 119 11 232 45 -1 1 Paste Dielect Oven -1 1 -1 1 Cube Plot - Means for Response Interaction Plots
  • 29.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 29 C: Initial Gas Volume (m3) B: Piston Surface Area (m2) A: Piston Weight (Kg) D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m2) F: Ambient Temperature (0K) G: Gas Temperature (0K) 27 Full Factorial Design
  • 30.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 30 0.6460 0.6500 0.6570 0.6540 0.6590 0.6570 0.6620 0.6580 1.2470 1.2350 1.2760 1.2480 1.3010 1.2880 1.2990 1.2840 0.1920 0.2150 0.2060 0.1880 0.2210 0.1990 0.1930 0.1920 0.3360 0.3850 0.3320 0.3220 0.3780 0.3550 0.3630 0.3530 0.6810 0.6780 0.6810 0.6820 0.6810 0.6820 0.6830 0.6800 1.4680 1.4590 1.4680 1.4790 1.4920 1.4720 1.4810 1.5040 0.4600 0.4690 0.4400 0.4250 0.4350 0.4120 0.4120 0.4460 0.9030 0.8280 0.9640 0.8360 0.8670 0.9380 0.9450 0.9730 0.4640 0.4610 0.4640 0.4600 0.4660 0.4670 0.4660 0.4650 0.9110 0.8950 0.8960 0.8970 0.9300 0.9220 0.9060 0.9260 0.1390 0.1310 0.1330 0.1480 0.1490 0.1690 0.1440 0.1490 0.2370 0.2340 0.2380 0.2400 0.2470 0.2260 0.2220 0.2720 0.4820 0.4810 0.4810 0.4810 0.4830 0.4820 0.4810 0.4830 1.0340 1.0360 1.0400 1.0270 1.0450 1.0570 1.0510 1.0370 0.3390 0.3200 0.3290 0.3170 0.2790 0.3180 0.3300 0.3200 0.6930 0.5790 0.6560 0.6780 0.6390 0.5880 0.6570 0.6500 G F E D C B A 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 Cube Plot - Means for Average 27 Full Factorial Design
  • 31.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 31 G F E D C B A 0.8 0.7 0.6 0.5 0.4 Average Main Effects Plot - Means for Average A: Piston Weight (Kg) B: Piston Surface Area (m2) C: Initial Gas Volume (m3) D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m2) F: Ambient Temperature (0K) G: Gas Temperature (0K) 128 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 G F E D C B A 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 Interaction Plot for Average 27 Full Factorial Design
  • 32.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 32 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 .001 .01 .05 .20 .50 .80 .95 .99 .999 P robability Eff_Avg Average: 0.0198583 Std Dev: 0.203497 N of data: 15 Anderson-Darling Normality Test A-Squared: 0.480 p-value: 0.199 Normal Probability Plot C_I niV ol A _Weight D_Spring B _Surfac CD 27 Full Factorial Design
  • 33.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 33 Size of Full Factorial Designs
  • 34.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 34 A B C AB AC BC ABC - - + + Fractional Factorial Design
  • 35.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 35 135 34 45 119 Oven Dielect Paste 1 -1 1 -1 1 -1 Cube Plot - Means for Response Paste DielectOven Response -1 -1 -1 119 1 -1 -1 44 -1 1 -1 232 1 1 -1 135 -1 -1 1 11 1 -1 1 34 -1 1 1 45 1 1 1 80 23-1 Fractional Factorial Design
  • 36.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 36 A B C D E F G 0.5 0.6 0.7 0.8 0.9 Average M ain Effects Plot - M eans for Average 2 ^(7 -3 ) = 1 6 16 A B C D E F G 0.5 0.6 0.7 0.8 0.9 Average M ain Effects Plot - M eans for Average 2^(7-2 ) = 3 2 32 A B C D E F G 0.40 0.52 0.64 0.76 0.88 Average M ain Effects Plot - M eans for Average 2 ^(7 -1 ) = 6 4 64
  • 37.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 37 B_Surf C_IniVol D_Spring G_GasTem Average Std_Dev -1 -1 -1 -1 0.789 0.2104 1 -1 -1 -1 0.536 0.2691 -1 1 -1 -1 0.925 0.0174 1 1 -1 -1 0.504 0.2455 -1 -1 1 -1 0.486 0.1130 1 -1 1 -1 0.407 0.1667 -1 1 1 -1 0.528 0.1121 1 1 1 -1 0.446 0.1580 -1 -1 -1 1 0.420 0.1194 1 -1 -1 1 0.649 0.2503 -1 1 -1 1 0.520 0.2325 1 1 -1 1 0.335 0.0577 -1 -1 1 1 0.492 0.1366 1 -1 1 1 0.458 0.1186 -1 1 1 1 0.456 0.1464 1 1 1 1 0.424 0.1279 2 0 0 0 0.659 0.1476 -2 0 0 0 0.546 0.1945 0 2 0 0 0.602 0.1538 0 -2 0 0 0.517 0.1674 0 0 2 0 0.293 0.0874 0 0 -2 0 0.611 0.4334 0 0 0 2 0.422 0.2229 0 0 0 -2 0.623 0.2401 0 0 0 0 0.412 0.1285 0 0 0 0 0.456 0.1377 0 0 0 0 0.376 0.1105 0 0 0 0 0.483 0.2034 Central Composite Designs
  • 38.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 38 0.3 -2 0.4 0.5 -2 0.6 -1 0.7 0.8 -1 0.9 0 1.0 0 1 1 2 2 0.4 -2 0.5 0.6 -2 -1 0.7 -1 0.8 0 0.9 0 1 1 2 2 Response Surfaces of Piston Performance 0.3 -2 0.4 -2 0.5 -1 0.6 -1 0 0.7 0 1 1 2 2 0.35 -2 0.45 0.55 0.65 -2 -1 0.75 0.85 -1 0.95 0 1.05 0 1 1 2 2 0.3 -2 0.4 0.5 -2 -1 0.6 0.7 -1 0.8 0 0.9 0 1 1 2 2 0.4 -2 0.5 0.6 -2 -1 0.7 0.8 -1 0 0.9 0 1 1 2 2
  • 39.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 39 Case Study A: Manufacturing  Health Imaging Development Program  New mammography film (Kodak Min R-2000 film)  Emulsion making (cubes)  Factors: Ripener level, nucleation flow rate  Aims: Grain size 0.80 - 0.86 m Cubicity >60%  Goal: What is the operating window for getting the desired grain size and cubicity? A Case Study
  • 40.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 40 Experimental Design 3 x 3 factorial design 30 18 6 0.388 69% 0.634 65% 0.754 60% 0.987 61% 0.821 47% 0.655 80% 1.259 48% Flow (cc/min) 13.2 39.6 66 Ripener (cc) A Case Study 0.543 76% 0.967 46%
  • 41.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 41 0.50 0.60 0.70 0.80 0.86 0.90 1.00 1.10 1.20 Size Mapping the Effects: Grain Size FLOW (cc/min) RIPENER (cc) A Case Study
  • 42.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 42 Cubicity 77% 72% 67% 62% 57% 52% 47% Mapping the Effects: Cubicity FLOW (cc/min) A Case Study RIPENER (cc)
  • 43.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 43 Where Is the Overlap? FLOW (cc’s/min) RIPENER (cc’s) 77% 72% 67% 62% 57% 52% 47% 0.50 0.60 0.70 0.80 0.86 0.90 1.00 1.10 1.20 A Case Study
  • 44.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 44 Case Study B: Business Units Consumer Imaging  New opportunity for branded photofinishing in the United States  Differentiation, pricing, segmentation all important considerations Question:How should a Kodak branded photofinishing option be priced? What share of choice can we expect? B Case Study
  • 45.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 45 Methodology  Mall intercept interviews with 100 consumers per cell who:  Have used at least three rolls of 35 mm film in the past year, and  Are responsible for deciding on photofinishing  Respondents complete “choice” exercises that simulate purchase decisions B Case Study
  • 46.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 46 CELL 1: Price Levels for Mass Merchant Store Processing: Overnight $3.49 $3.99 $4.99 Same Day $6.24 $6.99 $7.49 KODAK Premium Processing Bundle: Photofile $8.29 $9.29 $10.29 Price Levels B Case Study CELL 2: Price Levels for Drug/Food Store Processing: Overnight $4.49 $4.99 $5.99 Same Day $6.99 $7.99 $8.49 KODAK Premium Processing Bundle: Photofile $8.29 $9.29 $10.29
  • 47.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 47 Choice Example 9 cards per person In-Store Overnight Processing $3.99 In-Store Same Day Processing $6.99 KODAK Premium Processing $9.29 Choice cards in study simulated Point of Sale (POS) B Case Study
  • 48.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 48 Results: Mass Merchant 57% 63% 63% 34% 23% 26% 10% 10% 14% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KPP Next Day KPP Same Day B Case Study Cell 1 - Mass Merchant (Same Day =$6.99 [median] and Next Day = $3.99 [median])
  • 49.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 49 Cell 2 - Drug/Food (Same Day =$7.99 [median] and Next Day = $4.99 [median]) Results: Drug/Food 58% 67% 60% 35% 22% 26% 7% 14% 11% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study
  • 50.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 50 Cell 1 - Mass Merchant (Same Day =$6.24 [low] and Next Day = $3.49 [low]) Results: Mass Merchant 58% 63% 64% 29% 19% 22% 13% 14% 18% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study
  • 51.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 51 Cell 2 - Drug/Food (Same Day =$6.99 [low] and Next Day = $4.49 [low]) Results: Drug/Food 61% 69% 62% 31% 19% 22% 8% 16% 13% 0% 20% 40% 60% 80% 100% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study
  • 52.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 52 Model: Share of Choice Calculator INPUTS: Market: Mass Merchant Price for Same Day Processing: $6.99 Price for Next Day Processing: $3.99 Price for KODAK Premium Processing : $9.29 MODEL ESTIMATES: Share of Choice for KODAK Premium Processing : 26% Share of Choice for Same Day: 10% Share of Choice for Next Day: 63% B Case Study
  • 53.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 53 a 25-1 Fractional Factorial Experiment 1. Purity by SE-HPLC 2. O.D.  Responses
  • 54.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 54  Factors A. Freeze Temperature B. Thaw Temperature C. Volume D. Concentration E. Bulk
  • 55.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 55  Levels FACTOR Low High A:FreezeTemp-196 -70 B:ThawRemp 5 23 C:Volume 1.8 200 D:Concprot 0.35 0.5 E:Bulk a b
  • 56.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 56  Choosing the Experimental Array - 1 Fractional Factorial Design Factors: 5 Base Design: 5, 16 Runs: 32 Replicates: 2 Blocks: none Center p Design Generators: E = ABCD
  • 57.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 57  Choosing the Experimental Array - 2 Design Generators: E = ABCD Alias Structure I + ABCDE A + BCDE, B + ACDE, C + ABDE, D + ABCE, E + ABCD AB + CDE, AC + BDE, AD + BCE, AE + BCD, BC + ADE BD + ACE, BE + ACD, CD + ABE, CE + ABD, DE + ABC
  • 58.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 58 FreezeTemp ThawTemp Volume Concprot Bulk -196 5 1.8 0.35 b -70 5 1.8 0.35 a -196 23 1.8 0.35 a -70 23 1.8 0.35 b -196 5 200.0 0.35 a -70 5 200.0 0.35 b -196 23 200.0 0.35 b -70 23 200.0 0.35 a -196 5 1.8 0.50 a -70 5 1.8 0.50 b -196 23 1.8 0.50 b -70 23 1.8 0.50 a -196 5 200.0 0.50 b -70 5 200.0 0.50 a -196 23 200.0 0.50 a -70 23 200.0 0.50 b
  • 59.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 59 -196 -70 0.35 0.50 FreezeTemp ThawTemp Volume Concprot Bulk 5 23 b a 1.8 200.0 2^(5-1) Fractional Factorial Design
  • 60.
    2-Jun-23 (c) 2001, RonS. Kenett, Ph.D. 60  Protocol of Experiment Two Independent samples for each run Each sample will be tested in duplicate a) Take the two bulks b) Dilute the two bulks at 0.5 and 0.35 mg/ml c) Take all the samples at the two freezing temperature conditions d) Take all the samples at the two thawing temperature conditions e) Start the analysis