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Chapter
73 = —0.2? Use the same pooled estimate of a2 that was used in the analysis of variance. 14.29 Using the estimates of the variance components in Exercise 14.25, evaluate the power when we test the variance component due to filters to be zero. 14.30 A defense contractor is interested in studying an inspection process to detect failure or fatigue of transformer parts. Three levels of inspections are used by three randomly chosen inspectors, Five lots are used for each combination in the study. The factor levels are given in the data. The response is in failures per 1000 pieces. Inspection Level Full Reduced Military Military Inspector Inspection Specification Commercial A 6.15 5.52 7.50 7.42 7.08 6.17 5.85 5.89 5.48 5.48 5.65 5.30 5.98 5.35 5.02 B 7.58 6.52 7.68 5.86 6.17 6.20 6.54 5.64 5.44 5.75 5.28 5.38 5.12 5.68 4.87 7.70 6.82 6.19 6.21 5.66 7.19 c 6.42 5.39 5.36 5.90 5.85 5.35 5.35 6.12 5.01 (a) Write an appropriate model, with assumptions. (b) Use analysis of variance to test the appropriate hypothesis for inspector, inspection level, and interaction. 14.31 A manufacturer of latex house paint (brand A) would like to show that their paint is more robust to the material being painted than their two closest competitors. The response is the time, in years, until chipping occurs. The study involves the three brands of paint and three randomly chosen materials. Two pieces of material are used for each combination. Brand of Paint A B Material C A 5.50 5.15 4.75 4.60 5.10 5.20 B 5.60 5.55 5.50 5.60 5.40 5.50 C 5.40 5.48 5.05 4.95 4.50 4.55 (a) What is this type of model called? (b) Analyze the data, using the appropriate model. (c) Did the manufacturer of brand A support its claim with the data?
14
Factorial Experiments (Two or More Factors)
14.32 A plant manager would like to show that the yield of a woven fabric in his plant does not depend on machine operator or time of day and is consistently high. Four randomly selected operators and three randomly selected hours of the day are chosen for the study. The yield is measured in yards produced per minute. Samples are taken on 3 randomly chosen days. The data follow: Operator 2 3 4 1 9.8 9.8 10.0 9.5 10.1 10.3 9.7 9.8 9.6 9.7 10.2 10.0 2 10.2 10.1 10.2 10.3 9.9 9.8 9.8 10.1 9.7 9.7 9.5 9.9 9.9 10.0 10.5 10.4 10.2 10.2 10.3 10.1 9.8 10.2 9.3 9.7 (a) Write the appropriate model. (b) Evaluate the variance components for operator and time. (c) Draw conclusions. Time 1
14.33 A process engineer wants to determine if the power setting on the machines used to fill certain types of cereal boxes results in a significant effect on the actual weight of the product. The study consists of 3 randomly chosen types of cereal manufactured by the company and 3 fixed power settings. Weight is measured for 4 different randomly selected boxes of cereal at each combination. The desired weight is 400 grams. The data are presented here. Power Setting Low
Cereal T y p e 2 3 395 390 392 392 402 405 401 400 394 401 399 399 Current 396 399 390 392 404 403 400 402 395 502 400 399 High 410 408 404 406 415 412 408 407 401 400 413 415 (a) Give the appropriate model, and list the assumption being made. (b) Is there a significant effect due to the power setting? (c) Is there a significant variance component due to cereal type? 1