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

• Activity Number: 552
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Adam Pintar*+ and Timothy Robinson and Christine Anderson-Cook and Michael S Hamada
• Companies: National Institute of Standards and Technology and University of Wyoming and Los Alamos National Laboratory and Los Alamos National Laboratory
• Keywords: Bayesian Predictive Density ; Generalized Linear Mixed Models ; Hard-to-Change Factor ; Markov Chain Monte Carlo ; Process Optimization ; Response Surface

Abstract

Experiments for robust parameter design studies often require a split-plot randomization structure. For example, experiments with one or more hard-to-change factors would suggest a randomization restriction. Further, the most natural optimization criteria may not be the mean and variance and the response of interest is not always appropriately modeled by the normal distribution. A non-negative response might call the normal distribution into question. In this talk, an algorithm for finding optimal parameter settings when the response is non-normal and a split-plot randomization structure is present is described. The algorithm uses the Bayesian paradigm of inference because it naturally accommodates non-normal responses, a split-plot randomization structure, and non-standard optimization criteria. To illustrate, an experiment aimed at manufacturing high quality film is considered, where the goal is to find control factor settings, the mixture proportions of the film, which lead to a large proportion of high quality film across the anticipated manufacturing ranges of three environmental variables.