Monitoring the coefficient of variation using a variable sample size EWMA chart

摘要

Control charts for monitoring the coefficient of variation (CV) have been receiving a lot of attention in the literature, with numerous more powerful and robust CV charts being proposed. CV charts are attracting attention due to their usefulness in monitoring processes with an inconsistent mean and a standard deviation which changes with the mean. These processes could not be monitored by conventional mean and/or standard deviation-type charts. One of the strategies to improve the performance of CV charts is by incorporating adaptive features, i.e. by varying the chart's parameters according to past sample information. Hence, this paper proposes a variable sample size (VSS) Exponentially Weighted Moving Average (EWMA) chart to monitor the CV squared (gamma(2)), which is not available in the literature. The proposed chart allows different sample sizes to be adopted in the EWMA chart according to prior sample information. This paper shows the derivation of formulae to compute the average run length (ARL), average sample size (ASS) and expected average run length (EARL). Subsequently, an optimization algorithm to optimize the performance of the proposed chart is developed. Tables of optimal charting parameters are also provided. Next, the performance of the proposed chart is compared with five existing CV charts in the literature. The comparison shows that the proposed chart outperforms the five existing CV charts in almost all scenarios. Finally, this paper shows the implementation of the VSS EWMA-gamma(2) chart on an actual industrial example.