Lecture 16 Today: Next day:

Two-Step Optimization Procedures Nominal the best problem: –Select the levels of the dispersion factors to minimize the dispersion –The select the levels of the adjustment factors to move the process on target Larger (Smaller) the better problem: –Select levels of location factors to optimize process mean –Select levels of dispersion factors that are not location factors to minimize dispersion Leaf Spring Example was a nominal the best problem

Response Modeling There may be several noise factors and control factors in the experiment The cross array approach identifies control factors to help adjust the dispersion and location models, but does not identify which noise factors interact with which control factors Cannot deduce the relationships between control and noise factors The response model approach explicitly model both control and noise factors in a single model (called the response model)

Response Modeling Steps: –Model response, y, as a function of both noise and control factors (I.e., compute regression model with main effects and interactions of both types of factors) –To adjust variance: make control by noise interaction plots for the significant control by noise interactions. The control factor setting that results in the flattest relationship gives the most robust setting. construct the variance model, and choose control factor settings that minimize the variance

Example: Leaf Spring Experiment (p. 438) fractional factorial design was performed: I=BCDE Experiment has 3 replicates

Example: Leaf Spring Experiment (p. 438) fractional factorial design was performed: I=BCDE

Example: Leaf Spring Experiment (p. 438)

Response Model:

Example: Leaf Spring Experiment (p. 438)

Variance Model:

Design Strategy for the Response Model