One-sided Adaptive Truncated Exponentially Weighted Moving Average X¯ Schemes for Detecting Process Mean Shifts

ABSTRACT

One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) $\bar{X}$ scheme recommended in this paper is a control chart that combines a Shewhart $\bar{X}$ scheme and a new one-sided EWMA $\bar{X}$ scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The truncation method used in this paper helps to improve the sensitivity of the recommended scheme for detecting both small and large mean shifts simultaneously. To further improve the detection efficiency of the recommended scheme, we also suggest integrating a variable sampling interval (VSI) feature into the recommended scheme. Markov chain models are established to analyze the run length (RL) properties of the recommended scheme in both the zero-state and the steady-state cases. Comparison results show that the recommended one-sided ATEWMA $\bar{X}$ scheme works better than the conventional adaptive EWMA (AEWMA) $\bar{X}$ chart and the improved one-sided EWMA $\bar{X}$ chart in detecting a wide range of mean shifts. Finally, a numerical example is presented to illustrate the usage of the proposed one-sided ATEWMA $\bar{X}$ scheme for detecting process mean shifts.

KEYWORDS:

• Adaptive EWMA $\bar{X}$ control chart
• Markov chain model
• one-sided type scheme
• truncation method
• variable sampling interval

Disclosure statement

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

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant number: 71802110, 72101123); Humanity and Social Science Foundation of Ministry of Education of China (Grant number:19YJA630061); China Scholarship Council (Grant number: 202006840086); Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant number: KYCX21_0306); Key Research Base of Philosophy and Social Sciences in Jiangsu-Information Industry Integration Innovation and Emergency Management Research Center [None]; The Excellent Innovation Teams of Philosophy and Social Science in Jiangsu Province [2017ZSTD022];