A Simultaneous Control Chart for Mean and Variance Based on Bayesian Predictive Density

Monitoring process mean and variance simultaneously in a single control chart simplifies the process monitoring. If in addition، a simultaneous control chart is capable of recognizing the source of contamination، this capability leads to additional simplicity. These are the reasons why simultaneous control charts have attracted many researchers and manufacturers. Recently، in the statistical process control literature some control charts have been introduced which are based on the idea of Bayesian predictive density. This type of control charts، not only brings into account the uncertainty concerning the estimation of unknown parameters، but also do not need extensive simulations for computation of control limits. These control charts have been introduced for mean and variance in both univariate and multivariate situations. Up to now، no simultaneous control chart has been introduced based on Bayesian predictive density. In this paper، using the idea of Bayesian predictive density، we introduce a new simultaneous control chart for monitoring univariate mean and variance. We illustrate the important capabilities of this new chart through simulated data. This new chart is applicable when parameters are unknown. In other words، it brings into account the uncertainty concerning the unknown parameters. This chart is able to recognize the source of contamination and is sensitive to small changes in the mean and variance. In this chart the control limits، needless of simulation، can simply be obtained from normal table.