The exact solution of the average run length on a modified EWMA control chart for the first-order moving-average process

Abstract

Statistical process control methods are widely used in several fields for monitoring and detecting process problems.One of them is the control chart which is powerful and effective for monitoring many types of processes, and its capability is usually measured using the average run length (ARL).In this article, we investigate explicit formulas for both the one-and the two-sided ARL on a modified exponentially weighted moving-average (EWMA) control chart for a first-order moving-average process with exponential white noise.The accuracy of the solution obtained with the modified EWMA control chart was compared to the numerical integral equation method and extended to a comparative performance with the standard EWMA control chart.The results show that the ARL obtained by the explicit formulas and the numerical integral equation method are in close agreement.The performance comparison shows that the modified EWMA control chart is dramatically more sensitive than the standard EWMA control chart for almost all of the studied exponential smoothing parameters and magnitudes of shift size.To demonstrate its capability, the proposed approach was applied to Thailand/US monthly foreign exchange rates data, yielding in good performance.

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