In the 33 factorial design of Problem 11-33 one of the responses is a standard deviation. Use

Question:

In the 33 factorial design of Problem 11-33 one of the responses is a standard deviation. Use the Box-Cox method to investigate the usefulness of transformations for this response. Would your answer change if we used the variance as the response?

Problem 11-33

An experiment has been run in a process that applies a coating material to a wafer. Each run in the experiment produced a wafer, and the coating thickness was measured several times at different locations on the wafer. Then the mean y₁ and standard deviation y₂ of the thickness measurement was obtained. The data [adapted from Box and Draper (1987)] are shown in the table below:

Mean Std. Dev. Run Speed Pressure Distance y2 1 -1.000 -1.000 -1.000 24.0 12.5 0.000 -1.000 -1.000 120.3 8.4 3 1.000 -1.000 -1.000 213.7 42.8 4 -1.000 0.000 -1.000 86.0 3.5 5 0.000 0.000 -1.000 136.6 80.4 1.000 0.000 -1.000 340.7 16.2 7 -1.000 1.000 -1.000 112.3 27.6 8 0.000