15.33 Consider Case Study 15.1 involving the injection molding data. Suppose mold temperature is difficult to control and thus it can be assumed that in the process it follows a normal distribution with mean 0 and variance σ2 z . Of concern is the variance of the shrinkage response in the process itself. In the analysis of Figure 15.7, it is clear that mold temperature, injection velocity, and the interaction between the two are the only important factors.

(a) Can the setting on velocity be used to create some type of control on the process variance in shrinkage which arises due to the inability to control temperature?

Explain.

(b) Using parameter estimates from Figure 15.7, give an estimate of the following models:

(i)mean shrinkage across the distribution of temperature;

(ii)shrinkage variance as a function of σ2 z .

(c) Use the estimated variance model to determine the level of velocity that minimizes the shrinkage variance.

(d) Use the mean shrinkage model to determine what value of velocity minimizes mean shrinkage.

(e) Are your results above consistent with your analysis from the interaction plot in Figure 15.6? Explain.