Designing the Performance of EWMA Control Chart for Seasonal Moving Average Process with Exogenous Variables

The average run length (ARL) is deployed to measure control charts' effectiveness. This article provides a new exact analytical ARL solution for the exponentially weighted moving average (EWMA) control chart when the process is SMAX(Q,r)L. The explicit ARL solution for the SMAX(Q,r)L process wi...

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Bibliographic Details
Published in:IAENG international journal of applied mathematics 2023-06, Vol.53 (2), p.1-9
Main Author: Petcharat, Kanita
Format: Article
Language:English
Subjects:
Computing time
Control charts
Exact solutions
Existence theorems
Fixed points (mathematics)
Fredholm equations
Integral equations
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Summary:The average run length (ARL) is deployed to measure control charts' effectiveness. This article provides a new exact analytical ARL solution for the exponentially weighted moving average (EWMA) control chart when the process is SMAX(Q,r)L. The explicit ARL solution for the SMAX(Q,r)L process will be analyzed utilizing the Fredholm integral equation method. The fixed point theorem of Banach guarantees the solution's existence and uniqueness. In addition, ARL values are computed using numerical integral equations based on midpoint and Gaussian principles. The simulation's outcome revealed that the ARL values derived from the exact solution and numerical integral equation are identical. Regarding computational time, the result indicates that the exact analytical ARL solution outperforms the numerical integral equations. Therefore, the ARL values on EWMA control chart are evaluated using either the exact analytical ARL solution or the numerical integral equation.
ISSN:1992-9978
1992-9986