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

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.

KEYWORDS:

• Average run length
• expected average run length
• Markov-chain
• multivariate coefficient of variation
• run rules

Acknowledgments

This work was supported by the Fundamental Research Grant Scheme (FRGS), Grant Number FP080-2018A and the Universiti Sains Malaysia under Short Term Grants, Grant Number 304/PKOMP/6315170.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Universiti Sains Malaysia, Short Term Grants [grant number 304/PKOMP/6315170]; Fundamental Research Grant Scheme, Malaysia [grant number FP080-2018A].