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.

Constructing a Sensitive Control Chart to Monitor Process Mean using Optimal Filter: Time-Frequency Analysis Approach

“…The more quickly a control chart detects shifts, the better its performance. The Average Run Length (ARL) is usually used to assess the control charts in the time domain [36]. When the process is in-control, ARL is shown by 0 ARL and for out-of-control conditions, it is shown by 1 ARL .…”

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

“…Sunthornwat et al [21] found the explicit formula and the optimal parameters to evaluate the ARL for a long-memory ARFIMA process on the EWMA chart. Recently, Supharakonsakun et al [22] presented the exact solution of the ARL on the modified EWMA chart for the MA(1) process. Saghir et al [23] proposed a modified EWMA chart that deduce the existing chart from its special cases.…”

Exact Run Length Evaluation on Extended EWMA Control Chart for Autoregressive Process

“…After that, Peerajit et al [17] studied the NIE method of ARL on CUSUM chart. Supharakonsakun et al [18] evaluated the ARL by NIE method on modified EWMA and compared efficiency with EWMA control chart. Sunthornwat et al [19] derived explicit formulas of ARL on CUSUM chart for seasonal and non-seasonal moving average processes with exogenous variables and evaluated against the NIE method.…”