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A Bayesian Approach to the Analysis of Split-Plot Combined and Product Arrays and Optimization in Robust Parameter Design

Summary: 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 o↵er 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.

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  • Topics: Statistics
  • Keywords: Bayesian methods, Linear models, Markov chains, Monte Carlo methods, Prediction densities, Process optimization, Randomization tests, Response surface methodology (RSM), Robust design
  • Author: Robinson, Timothy J.; Pintar, Adam L.; Anderson-Cook, Christine M.; Hamada, Michael S.
  • Journal: Journal of Quality Technology