A Generalized Linear Modeling Approach to Robust Design

Abstract

This article presents an extension of the response surface approach to Taguchi's parameter design by accommodating generalized linear modeling. The approach of Myers, Khuri, and Vining is taken as a starting point, treating noise variables as fixed effects. It is, however, assumed that process variability is caused not only by the presence of noise factors but also by residual variation. Therefore, in addition to a model with a linear link function that relates the process mean to design and noise factors, a second model with a log-link function is proposed that relates the variance to a linear predictor in the design factors. The conditional response model, with noise factors taken as fixed, is fitted by iteratively reweighted least squares. Unconditionally, response surfaces for the process mean and process variance are produced through the use of a mean and variance operator on the conditional response model. As an illustration, data from an injection molding experiment are reanalyzed and residual dispersion effects, conditional on the noise factors, are modeled.

KEY WORDS:

• Design factors
• Dispersion effect
• Iteratively reweighted least squares
• Noise factors
• Parameter design
• Residual variation