A bayesian approach to the analysis of split-plot combined and product arrays and optimization in robust parameter design. - Robinson, Timothy J. (Journal of Quality Technology)
Many robust parameter design (RPD) studies involve a split-plot randomization structure and it is essential to account for the induced correlation structure to obtain valid inferences in the analysis. Bayesian methods are appealing for these studies because they naturally accommodate a general class of models, can account for parameter uncertainty in process optimization, and offer the necessary flexibility when one is interested in nonstandard performance criteria e.g., the probability that a new response exceeds some threshold value. In this paper, we present a Bayesian approach to process optimization for a general class of RPD models, including both normal and non-normal responses, in the split-plot context using an empirical approximation of the posterior distribution for an objective function of interest. Two examples from the literature, one involving a crossed array and the other a combined array, are used for illustration.