Estimation of mean and variance response surfaces in robust parameter design

Abstract

The means and variances of noise variables are typically assumed known in the literature on design and analysis of robust design experiments. However, these parameters are often unknown in practice and estimated with process data. Thus, variability in the data is a source of error in the robust design of a system. This thesis proposes a methodology that integrates planning of a combined array experiment with planning of sample sizes for estimation of means and variances of the noise variables. We study the effects of variability in process data on the estimated mean and variance models. The variances of the models are derived. Mathematical programs for finding sample sizes and mixed resolution designs that minimize the average variances are formulated. Issues in the practical application of these programs are addressed. Finally, graphical plots are introduced to allow comparison of the performances of alternative combinations of sample sizes and designs.