1. 1 Chapter 3: Screening Designs 3.1 Fractional Factorial Designs 3.2 Blocking with Screening Designs

2. 2 Chapter 3: Screening Designs 3.1 Fractional Factorial Designs 3.2 Blocking with Screening Designs

3. Objectives Understand screening designs. Distinguish between important and significant factors using a fractional factorial design. Change the aliasing structure of a fractional factorial design. Generate and analyze a fractional factorial screening design. 3

4. Screening Designs 4 Catalyst and Concentration Concentration Pressure and Concentration Temperature Catalyst and Temperature Pressure Temperature and Pressure Pressure and Catalyst Pressure Temperature Temperature and Pressure Catalyst

5. Two-Level Full Factorial Designs 5

6. Two-Level Fractional Factorial Designs 6

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8. 3.01 Quiz Match the types of fractional factorial designs on the left with the number of necessary runs on the right. 1. 2 3-1 2. 2 6-2 3. 2 6-3 8 A. 4 runs B. 16 runs C. 8 runs

9. 3.01 Quiz – Correct Answer Match the types of fractional factorial designs on the left with the number of necessary runs on the right. 1. 2 3-1 2. 2 6-2 3. 2 6-3 1-A, 2-B, 3-C 9 A. 4 runs B. 16 runs C. 8 runs

10. Principles of Fractional Factorial Designs 1.The Pareto principle states that there might be a lot of factors, but very few are important. 2.The Sparsity of Effects principle states that usually the more important effects are main effects and low-order interactions. 3.The projection property states that every fractional factorial contains full factorials in fewer factors. 4.These designs can be used in sequential experimentation; that is, additional design points can be added to these designs to resolve difficulties or unanswered questions. 10

11. Two Factor, Two-Level Full Factorial Design TreatmentIABAB +1 +1 -1 +1+1+1 +1 -1+1 +1 11

12. Confounding or Aliasing Two effects are confounded (or aliased) if it is impossible to estimate each effect separately. In JMP, the aliasing structure can be defined by using the Change Generating Rules option. 12 In this example, the aliasing structure indicates that C is aliased with the AB interaction, or C = AB.

13. Fractional Factorial Example 13

14. Resolution Fractional factorial designs are classified according to their resolution. For resolution 3, main effects are not aliased with other main effects. However, some main effects are aliased with one or more two-factor interactions. For resolution 4, main effects are not aliased with either other main effects or two-factor interactions. However, two-factor interactions can be aliased with other two-factor interactions. For resolution 5, main effects and two-factor interactions are not aliased with other main effects or two-factor interactions. 14

15. Plackett-Burman Designs Plackett-Burman designs are an alternative to two-level fractional factorial designs for screening use run sizes that are a multiple of 4 rather than a power of 2 have main effects that are orthogonal and two-factor interactions that are only partially confounded are generally resolution 3 designs. 15

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17. 3.02 Multiple Choice Poll With which of the following types of screening designs are you most familiar? a.Full factorial designs b.Fractional factorial designs c.Plackett-Burman designs d.Other e.None of these 17

18. Important versus Significant Factors Screening studies test many potential effects for significance. You want to separate the vital few from the trivial many. Oftentimes screening tools are necessary to determine which effects are important in explaining variability in the response. 18

19. Screening Tools Scaled estimates Prediction profiler Half normal plot Pareto plot Interaction plot Screening platform 19

20. Factors of Interest 20

21. Two-Level Fractional Factorial Screening Design This demonstration illustrates the concepts discussed previously. 21

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24. 3.03 Quiz Match the tool on the left with its interpretation on the right. 24 1.Prediction Profiler 2.Scaled estimates 3.Pareto plot 4.Normal plot 5.Interaction plot A.deviations from the overall pattern indicate important effects B.a scale-invariant reference C.identifies if the effect of one factor depends on the level of another D.indicates an important effect with long bars E.changes the level of one variable at a time to see the effect on the response

25. 3.03 Quiz – Correct Answer Match the tool on the left with its interpretation on the right. 1-E, 2-B, 3-D, 4-A, 5-C 25 1.Prediction Profiler 2.Scaled estimates 3.Pareto plot 4.Normal plot 5.Interaction plot A.deviations from the overall pattern indicate important effects B.a scale-invariant reference C.identifies if the effect of one factor depends on the level of another D.indicates an important effect with long bars E.changes the level of one variable at a time to see the effect on the response

26. Exercise This exercise reinforces the concepts discussed previously. 26

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28. 3.04 Quiz In the exercise on etch rate, 3 factors, each at two levels, were examined in a full factorial design with 1 replicate. Such a design required 16 runs. The final model equation for etch rate is shown below. The model only contains two of the three factors. In future experiments, how many runs would be necessary to run a new full factorial design with 1 replicate? 28

29. 3.04 Quiz – Correct Answer In the exercise on etch rate, 3 factors, each at two levels, were examined in a full factorial design with 1 replicate. Such a design required 16 runs. The final model equation for etch rate is shown below. The model only contains two of the three factors. In future experiments, how many runs would be necessary to run a new full factorial design with 1 replicate? 8 runs; this is a 2^2 factorial design with one replicate, so the number of necessary runs is 4*2=8. 29

30. 30 Chapter 3: Screening Designs 3.1 Fractional Factorial Designs 3.2 Blocking with Screening Designs

31. Objectives Understand blocking in a screening experiment. Generate and analyze a screening design with blocking. 31

32. Blocking Blocks are groups of experimental units that are formed such that units within blocks are as homogeneous as possible. Blocking is a statistical technique designed to identify and control variation among groups of experimental units. Blocking is a restriction on randomization. 32

33. Two Factor, Two-Level Full Factorial Design TreatmentIABAB=Block +1 +1 -1 +1+1+1 +1 -1+1 +1 33

34. Three Factor, Two-Level Factorial Design TreatmentIABCAB=BlockAC=BlockBC=Block -1 -1 -1+1 +1 -1 -1 +1+1 +1 -1 +1 -1+1+1 +1 -1 +1 +1+1+1 +1 +1 -1 -1+1 +1 +1 -1 +1+1 +1+1 +1 +1 -1+1 +1 +1 +1 +1+1 34

35. Aliasing of Effects with a Blocking Factor 35

36. Filtration Rate 36 Temperature (continuous) Pressure (continuous) Catalyst (continuous) Concentration (continuous) 220-240 °C50-80 psi 10-15 pounds 10-12 %

37. Generating and Analyzing a Blocked Full Factorial Screening Design This demonstration illustrates the concepts discussed previously. 37

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39. Exercise This exercise reinforces the concepts discussed previously. 39

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41. 3.05 Quiz The Prediction Profiler output from Exercise 3 is below. Which factor is the most important? How did you determine that? 41

42. 3.05 Quiz – Correct Answer The Prediction Profiler output from Exercise 3 is below. Which factor is the most important? How did you determine that? The most important factor is Post Height; it has the steepest slope, meaning changes in Post Height result in a larger change in the response (Pull Strength) as compared to changes in the other factors. 42