A Bayesian Approach for Interpreting Mean Shifts in Multivariate Quality Control

• Activity Number: 620
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Quality and Productivity
• Author(s): Matthias Hwai Yong Tan*+ and Jianjun Shi
• Companies: Georgia Institute of Technology and Georgia Institute of Technology
• Keywords: Multivariate Quality Control ; Interpretation of Out-of-Control Signal ; Mean Shifts ; Hierarchical Bayes ; Gibbs Sampling

Abstract

Multivariate quality characteristics are often monitored using a few statistics. However, it is difficult to determine the causes of an out-of-control signal based on a few summary statistics. Hence, if a control chart for the mean detects a change in the mean, the quality engineer needs to determine which means shifted and the directions of the shifts. This would greatly facilitate identification of causes and formulation of corrective actions. We propose a Bayesian approach that gives a direct answer to this question. For each mean, an indicator variable that indicates whether the mean shifted upwards, shifted downwards or remained unchanged is introduced. Prior distributions for the means and indicators capture prior knowledge about mean shifts and allow for asymmetry in upward and downward shifts. The mode of the posterior distribution of the vector of indicators or the mode of the marginal posterior distribution of each indicator gives the most likely scenario for each mean. Evaluation of the posterior probabilities of all possible values of the indicators is avoided by employing Gibbs sampling. This renders the computational cost more affordable for high-dimension problems.