Highest Posterior Distribution (HPD) Control Chart for Individual Observation

Abstract

Highest Posterior Distribution (HPD) is one of the methods to determine the interval estimator of data having both symmetric and asymmetric distributions. On the symmetric distribution, the Lower Control Limit (LCL) and the Upper Control Limit (UCL) of Individual control chart will automatically have the equilibrium density value. However, the LCL and the UCL of Individual control chart for asymmetric distribution will never have the equilibrium density value. This research is aimed to propose HPD control chart based on the concept of equilibrium density. The simulation studies provide the control limits of Individual and HPD control charts for both symmetric and asymmetric distributions of data. The Average Run Length (ARL) of both Individual and HPD control charts are calculated by generating the data which follow normal distribution and some asymmetric distributions such as weibull, gamma, beta, and lognormal. The in-control ARL (ARL0) of Individual control chart for various asymmetric distributions violate the ARL0 target. Even for asymmetric distribution, the ARL0 of HPD control chart is convergent to certain value of ARL0 target. Hence, HPD control chart is appropriate to monitor both symmetric and asymmetric distribution of data.