Posterior Control Chart for Process Average under Conjugate Prior Distribution

Control charts for the process average play an important role in process control. In the presence of prior information, using Bayesian approach, one can construct posterior control chart for process average (X̅ posterior control chart). The control limits of the proposed chart are derived under the assumption that the process average has a conjugate prior distribution. Both cases – variance is known and variance is unknown – are discussed. When the variance is unknown, the control limits are constructed using Unbiased Estimator (UE) and Maximum Likelihood Estimator (MLE) of the variance. The power and Average Run Length (ARL) of the proposed chart are obtained. The newly constructed X̅ posterior control chart is compared with a few other X̅ charts described in the literature.