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Some memory-based control charts such as cumulative sum (CUSUM) control chart, exponentially weighted moving average (EWMA) control chart, and homogeneously weighted moving average (HWMA) control chart are used to monitor small-to-moderate shift in the process mean. An HWMA control chart is a memory-based enhanced version of an EWMA control chart because it detects smaller shifts earlier than an ordinary EWMA control chart. The use of auxiliary information-based HWMA statistic enhances the efficiency of a usual CUSUM control chart. This study intends to present an efficient version of usual CUSUM control chart by utilizing an auxiliary information-based HWMA statistic as input information into usual CUSUM control chart. Supremacy of the proposed control chart is established on the basis of average run length (ARL), percent decrease in ARL (PDARL), and Friedman rank test (FRT) by conducting a Monte Carlo simulation. A real-life application shows the implementation of the proposed control chart.
Anwer et al. (Sun,) studied this question.