The efficiency of run rules schemes for the multivariate coefficient of variation: a Markov chain approach

XinYing Chew · Khai Wah Khaw · Wai Chung Yeong

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

Control charts are one of the important tools to monitor quality. The coefficient of variation (CV) is a common measure of dispersion in many real-life applications. Recently, CV control charts are proposed to monitor processes which do not have a constant mean and a standard deviation which changes with the mean. These processes cannot be monitored by standard control charts which monitor the mean and/or standard deviation. This research proposes the monitoring of the multivariate coefficient of variation (MCV) by means of run rules (RR MCV) control charts, which is not available in the existing literature. The design of these charts is obtained using a Markov-chain approach. The proposed charts are simple to implement. The performance of the RR MCV and Shewhart MCV (SH MCV) charts are compared in terms of the average run length (ARL) and the expected average run length (EARL). An example is illustrated based on a real dataset. The findings revealed that the performance of the proposed charts surpasses the SH MCV chart for detecting small and moderate MCV shifts.

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References

1992Introduction to Statistical Quality Control 1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1987An Introduction to Statistical Quality Control.1987Exact Results for Shewhart Control Charts With Supplementary Runs Rules 1955CONTROL CHARTS WITH WARNING LINES 2013The Coefficient of Variation as an Index of Measurement Reliability 2011Monitoring the Coefficient of Variation Using EWMA Charts 2007A Control Chart for the Coefficient of Variation

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2021One-sided variable sampling interval EWMA control charts for monitoring the multivariate coefficient of variation in the presence of measurement errors 2020A combined mixed- s -skip sampling strategy to reduce the effect of autocorrelation on the X scheme with and without measurement errors 2022Proposed nonparametric runs rules Lepage and synthetic Lepage schemes 2020Multivariate coefficient of variation charts with measurement errors 2024Enhanced distribution-free Cucconi schemes based on runs: An application to the surveillance of daily average customer service time

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