9.23. An article by W. D. Baten in the 1956 volume of Industrial Quality Control described an experiment to study the effect of three factors on the lengths of steel bars. Each bar was subjected to one of two heat treatment processes and was cut on one of four machines at one of three times during the day (8 A.M., 11 A.M., or 3 P.M.). The coded length data are as follows:

(a) Analyze the data from this experiment, assuming that the four observations in each cell are replicates.

(b) Analyze the residuals from this experiment. Is there any indication that there is an outlier in one cell? If you find an outlier, remove it and repeat the analysis from part (a). What are your conclusions?

(c) Suppose that the observations in the cells are the lengths (coded) of bars processed together in heat treatment and then cut sequentially (that is, in order)
on the four machines. Analyze the data to determine the effects of the three factors on mean length.

(d) Calculate the log variance of the observations in each cell. Analyze this response. What conclusions can you draw?

(e) Suppose the time at which a bar is cut really cannot be controlled during routine production. Analyze the average length and the log variance of the length for each of the 12 bars cut at each machine/heat treatment process combination. What conclusions can you draw?
9.7 Problems 447

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Heat Time Treat- of ment Day Process 1 2 Machine 3 4 1 6 9 7 1 3 5 95 1 0 24 8 A.M. 2 4 6 6 5 -1 0 0 1 3 4 0 1 6 38 7 3 12 67457 19. 6 3 4 5 5 4 2 7 9 10 1 -1 4 8 1 0 11 9 11 A.M. 2 3 16 4 2 094 1 -2 1 59 24 1 3 -1 1 6 3 10 11 -1 2 10 5 6 6 4 6 1 4 88 3 P.M. 2 6 087 0 -2 4 3 3 7 10 0 4 -4 70