Bayesian Analysis of Split-Plot Experiments With Nonnormal Responses for Evaluating Nonstandard Performance Criteria

Abstract

Nonnormal responses are common in industrial experiments, and many experiments contain factors with levels that are difficult or costly to change, resulting in a split-plot randomization structure. For valid statistical inferences, it is important to account for the correlation induced by the restricted randomization. We demonstrate the usefulness of Bayesian methods for the analysis of split-plot experiments with nonnormal responses. Specifically, we illustrate the flexibility of Bayesian methods when one is interested in various functions of the response distribution, such as specific percentiles or exceedance probabilities. These summaries, beyond examining just the mean and variance, are straightforward with the Bayesian approach and do not require additional theoretical development. The discussion uses a split-plot film manufacturing example with gamma responses for illustration.

Keywords:  :

• Bayesian
• Generalized linear mixed model
• Hard-to-change factor
• Markov chain Monte Carlo
• Response surface method
• Restricted randomization