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2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Course Website:

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Presentation on theme: "2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Course Website:"— Presentation transcript:

1 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.1 Design of Experiments Instructor: Ron S. Kenett Course Website: Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998

2 2-Jan-14 (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

3 2-Jan-14 (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...

4 2-Jan-14 (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?

5 2-Jan-14 (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

6 2-Jan-14 (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

7 2-Jan-14 (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 QuestionExperiment(E)QEQEQE (Q) AnswerAAA

8 2-Jan-14 (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 Model Conclude Four Basic Steps of DOE

9 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.9 A Serious Problem... I want my car to go fast … like that one!

10 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.10 What Factors Affect the Speed? Key Factor is: ___________________ Yes Air Holes No Slow Fast Shape

11 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.11 Key Factor is: _______________________________ Yes Air Holes No Slow FastSlow Shape Effect of Air Holes

12 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.12 DOE Balanced Effects Key Factor is: _______________________________ Yes Air Holes No Slow FastSlow Shape Slow

13 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.13 What factors affect flight time? What factors affect the quality of flight? The Helicopter Company

14 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.14 Length Width Factors DesignWingWing LengthWidth Response: Flight Time Your Experiment: Plan

15 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.15 Design #RepeatTestWingWingFlightQuality FlightOrderLengthWidthTimeof Flight Your Experiment: Collect

16 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.16 Calculate averages for each design Wing Width (1) (2) (3) (4) Wing Length Avg. ___ Your Experiment: Analyze

17 2-Jan-14 (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

18 2-Jan-14 (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:

19 2-Jan-14 (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?

20 2-Jan-14 (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 Hi Noise 1 4 ? ?

21 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.21 X2X2 X1X1 Homerun X2X2 X1X1 Shotgun X2X2 X1X1 Factorial How Many Experiments? X2X2 X1X1 1-at-a- time

22 2-Jan-14 (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?

23 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.23 AAAAABBBBBAB Is B better than A ?

24 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.24 Split Lot Design A B A B A B A B A B A B

25 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.25 Factors and Levels Factors Paste Dielectric Oven Levels -1+1

26 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.26 PasteDielectOvenResponse Full Factorial Design

27 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.27 Main Effects Plot

28 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.28 Interaction Plots

29 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.29 C: Initial Gas Volume (m 3 ) B: Piston Surface Area (m 2 ) A: Piston Weight (Kg) D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m 2 ) F: Ambient Temperature ( 0 K) G: Gas Temperature ( 0 K) 2 7 Full Factorial Design

30 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D Full Factorial Design

31 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.31 A: Piston Weight (Kg) B: Piston Surface Area (m 2 ) C: Initial Gas Volume (m 3 ) D: Spring Coefficient (N/m) E: Atmospheric Pressure (N/m 2 ) F: Ambient Temperature ( 0 K) G: Gas Temperature ( 0 K) Full Factorial Design

32 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D Full Factorial Design

33 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.33 Size of Full Factorial Designs

34 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.34 A B C AB AC BC ABC Fractional Factorial Design

35 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.35 PasteDielectOvenResponse Fractional Factorial Design

36 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D

37 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.37 B_SurfC_IniVolD_SpringG_GasTemAverageStd_Dev Central Composite Designs

38 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.38 Response Surfaces of Piston Performance

39 2-Jan-14 (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 Cubicity >60% Goal: What is the operating window for getting the desired grain size and cubicity? A Case Study

40 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.40 Experimental Design 3 x 3 factorial design % % % % % % % Flow (cc/min) Ripener (cc) A Case Study % %

41 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D Size Mapping the Effects: Grain Size FLOW (cc/min) RIPENER (cc) A Case Study

42 2-Jan-14 (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)

43 2-Jan-14 (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% A Case Study

44 2-Jan-14 (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

45 2-Jan-14 (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

46 2-Jan-14 (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

47 2-Jan-14 (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

48 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.48 Results: Mass Merchant 57% 63% 34% 23% 26% 10% 14% 0% 20% 40% 60% 80% 100% $8.29$9.29$10.29 Price of KPP Next DayKPPSame Day B Case Study Cell 1 - Mass Merchant (Same Day =$6.99 [median] and Next Day = $3.99 [median])

49 2-Jan-14 (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

50 2-Jan-14 (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

51 2-Jan-14 (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

52 2-Jan-14 (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

53 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.53 a Fractional Factorial Experiment 1. Purity by SE-HPLC 2. O.D. Responses

54 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.54 Factors A. Freeze Temperature B. Thaw Temperature C. Volume D. Concentration E. Bulk

55 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.55 Levels FACTORLowHigh A:FreezeTemp B:ThawRemp523 C:Volume D:Concprot E:Bulkab

56 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.56 Choosing the Experimental Array - 1 Fractional Factorial Design Factors: 5 Base Design: 5, 16 Resolution: V Runs: 32 Replicates: 2 Fraction: 1/2 Blocks: none Center pts (total): 0 Design Generators: E = ABCD

57 2-Jan-14 (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

58 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.58 FreezeTempThawTempVolumeConcprotBulk b a a b a b b a a b b a b a a b

59 2-Jan-14 (c) 2001, Ron S. Kenett, Ph.D.59

60 2-Jan-14 (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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