Triple exponentially weighted moving average control charts without or with variable sampling interval for monitoring the coefficient of variation

Abstract

The coefficient of variation (CV) chart is widely used in the process where the standard deviation is proportional to the mean. In this work, two separate one-sided triple exponentially weighted moving average control charts are proposed to monitor the CV squared (denoted as TEWMA-${\gamma }^2$ chart). By adding the variable sampling interval (VSI) feature to the proposed -${\gamma }^2$charts, the VSI TEWMA-${\gamma }^2$ charts are further proposed to improve the performance of the TEWMA-${\gamma }^2$ charts. Through extensive Monte Carlo simulations, the zero-state and steady-state run length (RL) performances are presented. The comparisons with the existing CV charts, based on several run length metrics show the superiority of the proposed charts, especially for small shifts. Moreover, the overall measure, expected ARL (EARL), also shows the outperformance of the ${\gamma }^2$charts. In addition, based on the average time to signal (ATS) and adjusted ATS (AATS), it is shown that the VSI strategy makes the TEWMA-${\gamma }^2$ charts detect the shifts more quickly. An illustrative example from the sintering process is finally provided to display the application of the proposed charts.

KEYWORDS:

• One-sided TEWMA charts
• coefficient of variation
• variable sampling interval
• average run length
• average time to signal

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 71802110, 71872088, 72101123, 12201429, 72301130]; Key Research Base of Philosophy and Social Sciences in Jiangsu-Information Industry Integration Innovation and Emergency Management Research Center; The Excellent Innovation Teams of Philosophy and Social Science in Jiangsu Province [grant number 2017ZSTD022]; Postgraduate Research & Practice Innovation Program of Jiangsu Province [grant number KYCX21_0840]; NJUPT [grant number NY222176]; Doctoral Research Start-up Fund of Liaoning Province [grant number 2021-BS-142]; Research on Humanities and Social Sciences of the Ministry of Education [grant number 22YJC910009]; Research of economic and social development in Liaoning Province [grant number 20231s1ybkt-103].