Economic design of a variable sampling rate EWMA chart

Abstract

A Variable Sampling Rate (VSR) control chart is a control chart whose sampling scheme is to vary the sampling interval and the sample size for the next sample depending on the current chart statistic. A VSR EWMA chart is an EWMA chart with the VSR sampling scheme. An economic model, which was developed for a VSR chart, is also applied here to evaluate the efficiency of the VSR EWMA chart. The properties of the VSR EWMA chart are obtained by using a Markov chain approach. The model contains cost parameters which allow the specification of the costs associated with sampling, false alarms and operating off target as well as search and repair. This economic model can be used to quantify the cost saving that can be obtained by using a VSR chart instead of a Fixed Sampling Rate (FSR) chart and can also be used to gain insight into the way that a VSR chart should be designed to achieve optimal economic performance. It is shown that with some design parameter combinations the economically optimal VSR chart has a lower false alarm rate than the FSR chart.