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14-1 Introduction

14-1 Introduction. An experiment is a test or series of tests. The design of an experiment plays a major role in the eventual solution of the problem. In a factorial experimental design , experimental trials (or runs) are performed at all combinations of the factor levels.

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14-1 Introduction

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  1. 14-1 Introduction • An experiment is a test or series of tests. • The design of an experiment plays a major role in the eventual solution of the problem. • In a factorial experimental design, experimental trials (or runs) are performed at all combinations of the factor levels. • The analysis of variance (ANOVA) will be used as one of the primary tools for statistical data analysis.

  2. 14-2 Factorial Experiments Definition

  3. 14-2 Factorial Experiments Figure 14-3Factorial Experiment, no interaction.

  4. 14-2 Factorial Experiments Figure 14-4Factorial Experiment, with interaction.

  5. 14-2 Factorial Experiments Figure 14-5Three-dimensional surface plot of the data from Table 14-1, showing main effects of the two factors A and B.

  6. 14-2 Factorial Experiments Figure 14-6Three-dimensional surface plot of the data from Table 14-2, showing main effects of the A and B interaction.

  7. 14-2 Factorial Experiments Figure 14-7Yield versus reaction time with temperature constant at 155º F.

  8. 14-2 Factorial Experiments Figure 14-8Yield versus temperature with reaction time constant at 1.7 hours.

  9. 14-2 Factorial Experiments Figure 14-9Optimization experiment using the one-factor-at-a-time method.

  10. 14-3 Two-Factor Factorial Experiments

  11. 14-3 Two-Factor Factorial Experiments The observations may be described by the linear statistical model:

  12. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model

  13. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model

  14. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model

  15. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model To test H0: i = 0 use the ratio To test H0: j = 0 use the ratio To test H0: ()ij = 0 use the ratio

  16. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Definition

  17. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model

  18. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1

  19. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1

  20. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1

  21. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1

  22. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1

  23. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1

  24. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Example 14-1 Figure 14-10Graph of average adhesion force versus primer types for both application methods.

  25. 14-3 Two-Factor Factorial Experiments 14-3.1 Statistical Analysis of the Fixed-Effects Model Minitab Output for Example 14-1

  26. 14-3 Two-Factor Factorial Experiments 14-3.2 Model Adequacy Checking

  27. 14-3 Two-Factor Factorial Experiments 14-3.2 Model Adequacy Checking Figure 14-11Normal probability plot of the residuals from Example 14-1

  28. 14-3 Two-Factor Factorial Experiments 14-3.2 Model Adequacy Checking Figure 14-12Plot of residuals versus primer type.

  29. 14-3 Two-Factor Factorial Experiments 14-3.2 Model Adequacy Checking Figure 14-13Plot of residuals versus application method.

  30. 14-3 Two-Factor Factorial Experiments 14-3.2 Model Adequacy Checking Figure 14-14Plot of residuals versus predicted values.

  31. 14-4 General Factorial Experiments Model for athree-factor factorial experiment

  32. 14-4 General Factorial Experiments Example 14-2

  33. Example 14-2

  34. 14-4 General Factorial Experiments Example 14-2

  35. 14-5 2k Factorial Designs 14-5.1 22 Design Figure 14-15The 22 factorial design.

  36. 14-5 2k Factorial Designs 14-5.1 22 Design The main effect of a factor A is estimated by

  37. 14-5 2k Factorial Designs 14-5.1 22 Design The main effect of a factor B is estimated by

  38. 14-5 2k Factorial Designs 14-5.1 22 Design The AB interaction effect is estimated by

  39. 14-5 2k Factorial Designs 14-5.1 22 Design The quantities in brackets in Equations 14-11, 14-12, and 14-13 are called contrasts. For example, the A contrast is ContrastA = a + ab – b – (1)

  40. 14-5 2k Factorial Designs 14-5.1 22 Design Contrasts are used in calculating both the effect estimates and the sums of squares for A, B, and the AB interaction. The sums of squares formulas are

  41. 14-5 2k Factorial Designs Example 14-3

  42. 14-5 2k Factorial Designs Example 14-3

  43. 14-5 2k Factorial Designs Example 14-3

  44. 14-5 2k Factorial Designs Residual Analysis Figure 14-16Normal probability plot of residuals for the epitaxial process experiment.

  45. 14-5 2k Factorial Designs Residual Analysis Figure 14-17Plot of residuals versus deposition time.

  46. 14-5 2k Factorial Designs Residual Analysis Figure 14-18Plot of residuals versus arsenic flow rate.

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