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

Abstract

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 X -chart, classical EWMA, and CUSUM control charts. In this application, the proposed chart is found comprehensively better than not only Shewhart X-chart but also EWMA and CUSUM control charts. By comparing average run length, the proposed control chart is found always better than Shewhart 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.

An EWMA-DiD Control Chart to Capture Small Shifts in the Process Average Using Auxiliary Information

“…It is expected that the suggested chart performs better than the monitoring scheme proposed by Shabbir and Awan [2] in capturing small shifts in process. The advantage of applying this chart is that parameter and other sampling techniques are the same as the chart by [2]. As such, no additional information is required to apply EWMA-DiD except constant "λ".…”

“…In the literature of sampling techniques, Hanif et al [18], Hamad et al [19] and Awan and Shabbir [20] have developed new estimators by using auxiliary information. In quality control there are many cases where control charts have been improved by using correlated auxiliary variables; for example, Shabbir and Awan [2] proposed an efficient control chart to monitor process mean wherein charting statistic is based on two auxiliary variables. Abbassi and Riaz [21] have proposed a process control where they have used auxiliary information for Ranking as well as for estimation.…”

“…Based on the above discussion, the proposed control chart is a combination of two statistics; i.e., usual EWMA statistic and Y DiD statistic, as suggested by Shabbir and Awan [2]. It is expected that the suggested chart performs better than the monitoring scheme proposed by Shabbir and Awan [2] in capturing small shifts in process.…”

“…In this article, an EWMA-DiD control chart has been proposed to monitor small shifts in process average. This chart is based on an estimator suggested by Shabbir and Awan [2]. In recent research, several charts have been suggested wherein two monitoring techniques have been merged to improve the performance of the chart.…”

“…As such, no additional information is required to apply EWMA-DiD except constant "λ". Assuming "λ = 1" the proposed chart performs the same as the control chart suggested by [2].…”