Computer Appl of Stats Methods IEEN5321_600_202110 Homework 6 7(4) Consider the data from the first replicate of Problem 6

Computer Appl of Stats Methods IEEN5321_600_202110

Homework 6

7(4) Consider the data from the first replicate of Problem 6.1. Suppose that these observations could not all be run using the same bar stock. Set up a design to run these observations in two blocks of four observations each with ABC confounded. Analyze the data.

[6.1. An engineer is interested in the effects of cutting speed

(A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2³ factorial design are run. The results are as follows:

A B C Treatment Combination Replicate I II III (1) 22 31 25 32 43 29 — + b 35 34 50 + + ab 55 47 46 44 45 38 + ac 40 37 36 — + + be 60 50 54 + + + abC 39 41 47

7.8. Repeat Problem 7.7 assuming that four blocks are necessary. Suggest a reasonable confounding scheme.

[7.7. Using the data from the 2⁵ design in Problem 6.26, construct and analyze a design in two blocks with ABCDE confounded with blocks.]

[6.26. An experiment was run in a semiconductor fabrication plant in an effort to increase yield. Five factors, each at two levels, were studied. The factors (and levels) were A = aperture setting (small, large), B = exposure time (20%, below nominal, 20% above nominal), C = development time (30 and 45 s), D = mask dimension (small, large), and E = etch time (14.5 and 15.5 min). The unreplicated 2⁵ design shown below was run. ]

(1) = 7 d = 8 e = 8 de = 6 a = 9 ad = 10 ae = 12 ade = 10 b = 34 bd = 32 be = 35 bde = 30 ab = 55 abd = 50 abe = 52 abde = 53 c = 16 cd = 18 ce = 15 cde = 15 . = 20 acd = 21 ace = 22 acde = 20 be = 40 bcd = 44 bce = 45 bode = 41 abc = 60 abed = 61 abce = 65 abcde = 63

7.10 Consider the fill height deviation experiment in problem 6.20 Suppose that each replicate was run on a separate day. Analyze the data assuming that days are blocks.

[6.20. Consider a variation of the bottle filling experiment from Example 5.3 Suppose that the experiment is a 2³ factorial design with two replicates. The data are shown in Table P6.3]