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Open AccessArticle

Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables

1
Industrial Technology Program, Faculty of Science and Technology, Pathumwan Institute of Technology, Bangkok 10330, Thailand
2
Department of Applied Statistics, Faculty of Applied Science King Mongkut’s University of Technology, Bangkok 10800, Thailand
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 173; https://doi.org/10.3390/sym12010173
Received: 19 November 2019 / Revised: 24 December 2019 / Accepted: 8 January 2020 / Published: 16 January 2020
The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters—which are the reference value ( a ) and control limit ( h )—for designing a CUSUM chart with a minimum out-of-control ARL is presented. In addition, the explicit formulas for the CUSUM control chart were applied with the practical data of a stock price from the stock exchange of Thailand, and the resulting performance efficiency is compared with an exponentially weighted moving average (EWMA) control chart. This comparison showed that the CUSUM control chart efficiently detected a small shift size in the process, whereas the EWMA control chart was more efficient for moderate to large shift sizes. View Full-Text
Keywords: CUSUM control chart; moving average process with exogenous variable; average run length; explicit formula; numerical integral equation CUSUM control chart; moving average process with exogenous variable; average run length; explicit formula; numerical integral equation
MDPI and ACS Style

Sunthornwat, R.; Areepong, Y. Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables. Symmetry 2020, 12, 173.

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