1. Engineering Statistics Design of Engineering Experiments

2. Learning objectives After careful study of this chapter, you should be able to do the following: Design and conduct engineering experiments involving several factors using the factorial design approach. Know how to analyze and interpret main effects and interactions. Understand how the ANOVA is used to analyze the data from these experiments. Know how to use the two level series of factorial designs.

3. Introduction Experiment - a test or series of tests. Designs of experiment plays a major role in the eventual solution of the problem that initially motivated the experiment. In this chapter, we focus on experiments that include 2 or more factors. In factorial experimental designs, experimental trials (or run) are performed at all combinations of factor level.

4. Some potential areas of factorial design application includes :

5. Factorial experiments When several factors are of interest in an experiment, a factorial experimental design should be used. Thus if there are two factors A and B, with a levels of factor A and b levels of factor B, then each replicates contains all ab treatment combinations.

7. Two factor interactions plot

8. Three-dimensional surface plot

9. 2 k Factorial Design 2 = level (e.g. two value of T, P or t; two operators; low and high level etc.) k = factors A complete replicate of such a design requires 2 x 2 x ……x 2 = 2 k observations, and is called 2 k factorial design. 2 k design- useful in the early stage of experimental work.

10. 2 2 Factorial Design The simplest type of 2 k design Two factors A and B, each at two levels. + and – sign for level is called geometric notation

11.  The effects of interest in the 2 2 design are the main effects, A and B and the two factor interaction AB.

13. EXAMPLE 1 (i)

14. (ii) Assess the importance of effect

16. Standard error of effects

17. (From Example 1)

18. Recall: t ratio = effect estimate /estimated standard error  t ratio is used to judge whether the effect is significantly different from zero.  The significant effect is the important effect in experiment

19. Regression model & Residual Analysis Since the only active variable is deposition time (x 1 ), thus the regression model is

22. 2 3 factorial design Has 2 3 = 8 runs or treatment combinations.

28. EXAMPLE 2

29. (i)

30. (ii)

31. Regression model & Residual analysis

32. (Table From Example 2)