WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 20, 2025
Derivative Closed-Form Formula for Average Run Length of Triple Moving Average Chart for Attribute Data
Authors: , , ,
Abstract: In statistical control chart mean change detection, the average run length is frequently used to compare control chart detection performance. In this research, the proof is presented of the formula for the average run length (ARL) of the triple moving average (TMA) control chart when the observed process values are attribute data such as Poisson and binomial distributions are used to detect several defects and defect proportion, respectively. The efficiency is measured by the average running length (ARL) when the process is under control (ARL=ARL0) and when the process is out of control (ARL=ARL1). The results showed that TMA control charts outperformed DMA, MA, and Shewhart control charts at a very minor magnitude of changes in mean levels, and as the mean change level increases, TMA control charts become more effective as the moving average width (k) decreases.
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Keywords: Minor change, Performance, Monitoring, Change, Moving Average, Explicit Form, Time-varying Control Chart
Pages: 135-150
DOI: 10.37394/23203.2025.20.16