Control Charts for the Variance and Coefficient of Variation Based on Their Predictive Distribution

Abstract

Abstract This article develops a control chart for the variance of a normal distribution and, equivalently, the coefficient of variation of a log-normal distribution. A Bayesian approach is used to incorporate parameter uncertainty, and the control limits are obtained from the predictive distribution for the variance. We evaluate this control chart by examining its performance for various values of the process variance. Keywords: Bayesian analysisCoefficient of variationControl chartLog-normal distributionNormal distributionPredictive distributionRun lengthVarianceMathematics Subject Classification: 62F1562P30 Acknowledgment The author thanks two referees for helpful comments, and Professor Douglas M. Hawkins for making the data used in Sec. 3 available.