Robust parameter design using generalized linear mixed models

In robust parameter design, it is often the case that the quality characteristic is nonnormal. An example in semiconductor manufacturing is resistivity, which typically follows a gamma distribution. It is also common to have models that contain, in addition to fixed polynomial effects, a random effect representing an extraneous source of variation. In this article, we demonstrate the use of generalized linear mixed models (GLMM) for situations in which the response is nonnormal and in which the noise variable is a random effect. We discuss the analysis of the random effects as well as the fixed effects in a fitted model using GLMM techniques. A numerical example from semiconductor manufacturing is provided for illustration.