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Design of Experiments

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. Course Syllabus. Understanding Variability Variability in Several Dimensions

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Design of Experiments

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  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 (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 (c) 2001, Ron S. Kenett, Ph.D.

  3. DOE Is a Problem-Solving Tool We get banding when... The color is too saturated... The order wasn’t delivered on time... When you have a serious problem... … you need a good problem solving tool! (c) 2001, Ron S. Kenett, Ph.D.

  4. DOE Helps Answer Key Questions Lubricant? The media jams when we print... Spring tension? Exit angle? • Which factors have the strongest effects? • Do any of the factors interact? • Which factor settings give the best results? (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 FilmBuilding ChemicalProcess Digital Imaging (c) 2001, Ron S. Kenett, Ph.D.

  6. Process, Responses, and Factors -2 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. (c) 2001, Ron S. Kenett, Ph.D.

  7. Ask a Series of Questions Question Experiment(E) Q E Q E Q E (Q) Answer A A A 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? (c) 2001, Ron S. Kenett, Ph.D.

  8. Four Basic Steps of DOE COLLECT Observe Code ANALYZE Plot Plot Plot Model Conclude PLAN Questions Design Scope PRESENT Answer Questions Graphically Mathematically State Uncertainty Recommend Cycle of Experimentation (c) 2001, Ron S. Kenett, Ph.D.

  9. A Serious Problem... I want my car to go fast … like that one! (c) 2001, Ron S. Kenett, Ph.D.

  10. What Factors Affect the Speed? Yes Air Holes Fast No Slow Shape Key Factor is: ___________________ (c) 2001, Ron S. Kenett, Ph.D.

  11. Effect of Air Holes Yes Slow Fast Air Holes No Slow Shape Key Factor is: _______________________________ (c) 2001, Ron S. Kenett, Ph.D.

  12. DOE Balanced Effects Yes Slow Fast Air Holes No Slow Slow Shape Key Factor is: _______________________________ (c) 2001, Ron S. Kenett, Ph.D.

  13. The Helicopter Company What factors affect flight time? What factors affect the quality of flight? (c) 2001, Ron S. Kenett, Ph.D.

  14. Your Experiment: Plan Factors Length 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 Width (c) 2001, Ron S. Kenett, Ph.D.

  15. Your Experiment: Collect 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 (c) 2001, Ron S. Kenett, Ph.D.

  16. Your Experiment: Analyze Wing Width 1.5 1.0 (1) (3) 2.5 Avg. ___ Avg. ___ Wing Length (4) (2) 3.5 Avg. ___ Avg. ___ Calculate averages for each design (c) 2001, Ron S. Kenett, Ph.D.

  17. Your Experiment: Analyze Plot the data (one line for each Wing Width) Time 2.5 3.5 Wing Length (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: (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? (c) 2001, Ron S. Kenett, Ph.D.

  20. Which Is the Key Driver? MTF 1 ? Hi ? 4 Low Low Hi Noise • Health Imaging Customer Preference Study • Conventional thinking: Low noise a customer requirement • Some data suggested thathigh resolution (MTF) was larger driver • Experiment designed to identify key driver (c) 2001, Ron S. Kenett, Ph.D.

  21. How Many Experiments? X2 X2 X1 X1 “Homerun” “1-at-a-time” X2 X2 X1 X1 “Shotgun” “Factorial” (c) 2001, Ron S. Kenett, Ph.D.

  22. 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 Typical Questions Linear Response? ? FractionalFactorial? Full Factorial? Curvature? (c) 2001, Ron S. Kenett, Ph.D.

  23. A A A A A A B B B B B B Is B better than A ? (c) 2001, Ron S. Kenett, Ph.D.

  24. A A A A A A B B B B B B Split Lot Design (c) 2001, Ron S. Kenett, Ph.D.

  25. Factors Paste Dielectric Oven Levels -1 +1 -1 +1 -1 +1 Factors and Levels (c) 2001, Ron S. Kenett, Ph.D.

  26. 23Full Factorial Design Paste Dielect Oven 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 (c) 2001, Ron S. Kenett, Ph.D.

  27. Main Effects Plot (c) 2001, Ron S. Kenett, Ph.D.

  28. Interaction Plots (c) 2001, Ron S. Kenett, Ph.D.

  29. A: Piston Weight (Kg) B: Piston Surface Area (m2) C: Initial Gas Volume (m3) 27Full Factorial Design D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m2) F: Ambient Temperature (0K) G: Gas Temperature (0K) (c) 2001, Ron S. Kenett, Ph.D.

  30. 27Full Factorial Design (c) 2001, Ron S. Kenett, Ph.D.

  31. E: Atmospheric Pressure (N/m2) C: Initial Gas Volume (m3) F: Ambient Temperature (0K) G: Gas Temperature (0K) A: Piston Weight (Kg) B: Piston Surface Area (m2) D: Spring Coefficient (N/m) 27Full Factorial Design 128 (c) 2001, Ron S. Kenett, Ph.D.

  32. 27Full Factorial Design (c) 2001, Ron S. Kenett, Ph.D.

  33. Size of Full Factorial Designs (c) 2001, Ron S. Kenett, Ph.D.

  34. Fractional Factorial Design A B C AB AC BC ABC - + + - (c) 2001, Ron S. Kenett, Ph.D.

  35. 23-1Fractional Factorial Design Paste Dielect Oven 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 (c) 2001, Ron S. Kenett, Ph.D.

  36. 32 64 16 (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 (c) 2001, Ron S. Kenett, Ph.D.

  38. Response Surfaces of Piston Performance (c) 2001, Ron S. Kenett, Ph.D.

  39. Case Study A: Manufacturing A Case Study • 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? (c) 2001, Ron S. Kenett, Ph.D.

  40. Experimental Design A Case Study 3 x 3 factorial design 0.388 69% 0.634 65% 0.821 47% 30 18 6 Flow (cc/min) 0.543 76% 0.754 60% 0.967 46% 0.655 80% 0.987 61% 1.259 48% 66 39.6 13.2 Ripener (cc) (c) 2001, Ron S. Kenett, Ph.D.

  41. Mapping the Effects: Grain Size A Case Study Size 0.50 0.60 0.70 0.80 0.86 0.90 FLOW (cc/min) 1.00 1.10 1.20 RIPENER (cc) (c) 2001, Ron S. Kenett, Ph.D.

  42. Mapping the Effects: Cubicity A Case Study Cubicity 67% 62% 72% 57% FLOW (cc/min) 52% 77% 47% RIPENER (cc) (c) 2001, Ron S. Kenett, Ph.D.

  43. Where Is the Overlap? A Case Study 0.50 0.60 0.70 0.80 0.86 67% 0.90 62% 72% 57% FLOW (cc’s/min) 1.00 52% 77% 1.10 47% 1.20 RIPENER (cc’s) (c) 2001, Ron S. Kenett, Ph.D.

  44. Case Study B: Business Units B Case Study 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? (c) 2001, Ron S. Kenett, Ph.D.

  45. Methodology B Case Study • 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 (c) 2001, Ron S. Kenett, Ph.D.

  46. Price Levels B Case Study 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 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 (c) 2001, Ron S. Kenett, Ph.D.

  47. Choice Example B Case Study 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) (c) 2001, Ron S. Kenett, Ph.D.

  48. Results: Mass Merchant 100% 80% 63% 63% 57% 60% 40% 34% 26% 23% 20% 14% 10% 10% 0% $8.29 $9.29 $10.29 Next Day KPP Same Day B Case Study Cell 1 - Mass Merchant (Same Day =$6.99 [median] and Next Day = $3.99 [median]) Price of KPP (c) 2001, Ron S. Kenett, Ph.D.

  49. Results: Drug/Food 100% 80% 67% 60% 58% 60% 40% 35% 26% 22% 20% 14% 11% 0% 7% $8.29 $9.29 $10.29 Price of KODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study Cell 2 - Drug/Food (Same Day =$7.99 [median] and Next Day = $4.99 [median]) (c) 2001, Ron S. Kenett, Ph.D.

  50. Results: Mass Merchant 100% 80% 63% 64% 58% 60% 40% 29% 22% 19% 20% 18% 14% 13% 0% $8.29 $9.29 $10.29 Price ofKODAK Premium Processing Next Day KODAK Premium Processing Same Day B Case Study Cell 1 - Mass Merchant (Same Day =$6.24 [low] and Next Day = $3.49 [low]) (c) 2001, Ron S. Kenett, Ph.D.

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