A New Modified EWMA Control Chart for Monitoring Processes Involving Autocorrelated Data

Abstract

Control charts are one of the tools in statistical process control widely used for monitoring, measuring, controlling, improving the quality, and detecting problems in processes in various fields. The average run length (ARL) can be used to determine the efficacy of a control chart. In this study, we develop a new modified exponentially weighted moving average (EWMA) control chart and derive explicit formulas for both one and the two-sided ARLs for a p-order autoregressive (AR(p)) process with exponential white noise on the new modified EWMA control chart. The accuracy of the explicit formulas was compared to that of the well-known numerical integral equation (NIE) method. Although both methods were highly consistent with an absolute percentage difference of less than 0.00001%, the ARL using the explicit formulas method could be computed much more quickly. Moreover, the performance of the explicit formulas for the ARL on the new modified EWMA control chart was better than on the modified and standard EWMA control charts based on the relative mean index (RMI). In addition, to illustrate the applicability of using the proposed explicit formulas for the ARL on the new modified EWMA control chart in practice, the explicit formulas for the ARL were also applied to a process with real data from the energy and agricultural fields.

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