Designing an Efficient Exponentially Weighted Moving Average Control Chart to Monitor the Mean of a Time-Series Process

Wilasinee  Peerajit

Authors

Wilasinee Peerajit Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

Keywords:

Average run length (ARL), integral equation, exponential white noise, long-memory fractionally integrated SMAX, exogenous variable

Abstract

This study covers the design of an efficient exponentially weighted moving average (EWMA) control chart for monitoring the mean of a time-series process characterized by long-memory dependence. Specifically, the study is focused on a fractionally integrated seasonal moving average process with an exogenous variable and exponential white noise. The structure of the proposed EWMA control chart is first formulated, followed by an evaluation of its performance based on the average run length (ARL) via a simulation study. An analytical expression for the ARL is derived through explicit formulas obtained by solving integral equations, while an approximated ARL is computed via a numerical integral equation approach. The existence and uniqueness of the analytical ARL solution are theoretically guaranteed using Banach’s fixed-point theorem. The simulation results reveal that both the analytical and approximated ARL methods produce comparable out-of-control ARL values, with similar accuracy. The simulation results reveal that both the analytical and approximate ARL methods produced comparable out-of-control ARL values, exhibiting similar accuracy in terms of detection performance. Nevertheless, the analytical approach based on explicit formulas demonstrated a clear computational advantage: achieving faster processing times while maintaining accuracy, as evidenced by a significantly lower average time-to-signal (ATS) criterion. These findings indicate that the explicit formula performs effectively for detecting shifts in process mean values. Therefore, this approach is recommended for practical applications. An illustrative example using real-world data further confirms the effectiveness and applicability of the proposed analytical ARL method in time-series process monitoring.

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