A comparison study of effectiveness and robustness of control charts for monitoring process mean

This article compares the effectiveness and robustness of nine typical control charts for monitoring the mean of a variable, including the most effective optimal and adaptive Sequential Probability Ratio Test (SPRT) charts. The nine charts are categorized into three types (the X¯ type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and fully adaptive (FA) version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and fully adaptive charts are designed optimally in order to minimize an index, Average Extra Quadratic Loss (AEQL), for the best overall performance. A Performance Comparison Index, PCI, is also proposed as the measure of the relative overall performance of the charts. This comparison study does not only compare the detection effectiveness of the charts, but also investigate their robustness in performance. Moreover, the probability distribution of the mean shift δ is studied explicitly as an influential factor in a factorial experiment. Apart from many other findings, the results of this study reveal that the SPRT chart is more effective than the CUSUM chart and X¯ chart by 58% and 126%, respectively, from an overall viewpoint. Moreover, it is found that the optimization design of charting parameters can increase the detection effectiveness by 29% on average, and the adaptive features can further enhance the detection power by 35%. Finally, a set of design tables are provided to facilitate the users to select a chart for their applications.

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