Control Charts for the Mean and Variance based on Changepoint Methodology

Abstract

This article develops a control chart for the mean and variance of a normal distribution based on changepoint methodology. A Bayesian approach is used to incorporate parameter uncertainty. The resulting control chart plots the probabilities of “no change” as samples become available at the monitoring stage. Average run length considerations are used to set the control limits. Simulations are used to compare the proposed chart with a more traditional Shewhart-type combined control chart for the mean and variance.

Keywords:

• Bayesian analysis
• Changepoint model
• Control chart
• Estimated parameters
• Mean
• Normal distribution
• Predictive distribution
• Run length
• Variance

Mathematics Subject Classification:

• 62F15
• 62H99
• 62P30

Acknowledgment

The author wishes to thank two anonymous reviewers for their very useful comments and suggestions.