Open Access

ARTICLE

Exact Run Length Evaluation on a Two-Sided Modified Exponentially Weighted Moving Average Chart for Monitoring Process Mean

by Piyatida Phanthuna, Yupaporn Areepong^*, Saowanit Sukparungsee

Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

* Corresponding Author: Yupaporn Areepong. Email:

Computer Modeling in Engineering & Sciences 2021, 127(1), 23-41. https://doi.org/10.32604/cmes.2021.013810

Received 22 August 2020; Accepted 09 December 2020; Issue published 30 March 2021

Abstract

A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts such that this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for the performance evaluation on control charts. This paper proposes the explicit formula for evaluating the average run length on a two-sided modified exponentially weighted moving average chart under the observations of a first-order autoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparison of the explicit formula and the numerical integral technique is carried out using the absolute relative change for checking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL of the explicit formula and the numerical integral equation method are hardly different, but this explicit formula is much faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classical EWMA and the modified EWMA control charts are compared and the results show that the latter is better for small and intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the health field as COVID-19 data in Thailand and Singapore.

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