# Quality and Reliability Engineering International

## An Efficient Shewhart‐Type Control Chart to Monitor Moderate Size Shifts in the Process Mean in Phase II

### Journal Article

According to Shewhart, control charts are not very sensitive to small and moderate size process shifts that is why those are less likely to be effective in Phase II. So to monitor small or moderate size process shifts in Phase II, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are considered as alternate of Shewhart control charts. In this paper, a Shewhart‐type control chart is proposed by using difference‐in‐difference estimator in order to detect moderate size shifts in process mean in Phase II. The performance of the proposed control chart is studied for known and unknown cases separately through a detailed simulation study. For the unknown case, instead of using reference samples of small sizes, large size reference sample(s) is used as we can see in some of nonparametric control chart articles. In an illustrative example, the proposed control charts are constructed for both known and unknown cases along with Shewhart $\overline{X}$‐chart, classical EWMA, and CUSUM control charts. In this application, the proposed chart is found comprehensively better than not only Shewhart $\overline{X}$‐chart but also EWMA and CUSUM control charts. By comparing average run length, the proposed control chart is found always better than Shewhart $\overline{X}$‐chart and in general better than classical EWMA and CUSUM control charts when we have relatively higher values of correlation coefficients and detection of the moderate shifts in the process mean is concerned. Copyright © 2015 John Wiley & Sons, Ltd.

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