An efficient approach of designing distribution-free exponentially weighted moving average schemes with dynamic fast initial response for joint monitoring of location and scale

ABSTRACT

An EWMA scheme with the fast initial response (FIR) feature usually detects an initial out-of-control (OOC) situation much quicker compared to a standard EWMA scheme. Researches on EWMA schemes with the FIR feature primarily focussed on their OOC performance, ignoring the fact that the FIR feature may increase the number of false alarms at the early stage of monitoring. In this paper, we introduce the concept of an EWMA scheme with a dynamic FIR feature that restricts initial false alarms and also improves OOC performance. We discuss a data-dependent approach based on Kernel density estimation for the design parameters. We use the proposed concept in designing distribution-free FIR-based EWMA schemes for joint monitoring of location and scale. Simulation results demonstrate that our proposed procedure generally performs well under various continuous distributions. We illustrate the application of our proposed schemes using two sets of data arriving out of the manufacturing sector.

KEYWORDS:

• Exponentially weighted moving average
• false alarms
• fast initial response
• nonparametric
• simultaneous monitoring
• statistical process control

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62P30
• 62G99

Acknowledgements

Authors are grateful to the associate editor and two anonymous reviewers for their valuable comments that help us in improving the paper to a great extent.

Disclosure statement

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

Additional information

Funding

This work was supported by the Scientific Research Fund of Liaoning Provincial Education Department of China [grant number LSNQN201912]; the Natural Science Foundation of Liaoning Province [grant number 20180550973, 2020-MS-139]; the Liaoning BaiQianWan Talents Program; the Natural Science and Technology Foundation of Liaoning Province [grant number 2019ZD-0193]; the CAUC Science College Fundamental Research Funds for the Central Universities [grant number 3122017082] and the Informatization Special Project of the Ministry of Culture and Tourism [grant number xxhfzzx201904].