8

8.3. Consider the plasma etch experiment described in Example 6.1. Suppose that only a one-half fraction of the design could be run. Set up the design and analyze, the data.

8.10. An article by J. J. Pignatiello Jr. and J. S. Ramberg in the Journal of Quality Technology (Vol. 17, 1985, pp. 198-206) describes the use of a replicated fractional factorial to investigate the effect of five factors on the free height of leaf springs used in an automotive application. The factors are A = furnace temperature. B = heating time. C = transfer time, D = hold down time, and E = quench oil temperature. The data are shown in Table P8.1

11 E Frec Height

+ +

- 7.78 8.15

+ i - 754 7.69

+ - 7;65 750 7- 1'3508 7.63 - + + 732 + + 7.56 7.18 : + 7.81

P. P. -1 V. 8 O., O, M  ;:t

7.81 7.75 7.88 8.06 77: 7.12 77: 7.56 7.44 7.62 7.25 7.59

(a) Write out the alias structure for this design. What is the resolution of this design?

(b) Analyze, the data. What factors influence the mean free height?

(c) Calculate the range and standard deviation of the free height for each run. Is there any indication that any of these factors affects variability in the free height?

(d) Analyze, the residuals from this experiment, and comment on your findings.

(e) Is this the best possible design for five factors in 16 runs? Specifically, can you find a fractional design for five factors in 16 runs with a higher resolution than this one?

8.13. Construct a 2^7-2 design by choosing two four-factor interactions as the independent generators. Write down the complete alias structure for this design. Outline the analysis of variance table. What is the resolution of this design?

8.18. Construct a 2_III ^5-2 design. Determine the effects that may be estimated if a full fold over of this design is performed.

8.45. Consider the following design: Run A C D E 1 I 2 i 3 -1 4 , 5 -1 6 , 7 -1 8 1 9 -1 0 , 1,, -1 2 113' 1 1,45 -1 16 1 -1 -1 , -1 -I 1 I -1 1 I - I -1 I I -1 -1 -1 -1 i 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 I I -1 63 , 1 36 - l 99 i 24 -1 66 54 -1 23 74 80 33 63 -1 44 96

(a) What is the generator for column E?

(b) If ABC is confounded with blocks, run 1 above goes in the ------block. Answer either + or -.

(c) What is the resolution of this design?

(d) (8 pts) Find the estimates of the main effects and their aliases.