Optimal operating policies of X-bar control chart for non-normal variables with generalised Pareto in-control times

Abstract

In designing the control charts, the choice of control chart parameters like sample size and sampling interval are most important. To determine the optimal design parameters, it is required to consider the model for statistical economic design of control charts with suitable probability distribution for quality characteristic and process in-control times, which are random in nature. In this paper, we consider the economic statistical design of X-bar control chart for non-normal quality characteristic. Here, it is assumed that the sample average of the quality characteristic X-bar has a Johnson distribution and the process in-control times follow generalised Pareto distribution. With suitable cost considerations and modifying the Lorenzen and Vance (1986) cost model, the expected cost per unit time is derived. The optimal sample size and the time interval between samples are obtained by minimising the expected cost per unit time. The sensitivity of the design with respect to the parameters and costs is also studied. This model is much useful for reducing the production cost and to improve product quality in places like, glassware industries, chemicals and films industries, etc.