Detection of Multiple Change Points from Clustering Individual Observations

In the preliminary analysis, also called Stage 1 analysis or retrospective analysis, of statistical process control, one may confront multiple shifts and/or outliers, especially with a large number of observations. This paper addresses the analysis of individual observations, and shows that the X-chart and CUSUM chart may fail to detect the presence of any shifts or outliers when multiple shifts and/or outliers are present. A new method is introduced which is effective in detecting single or multiple shifts and/or outliers. The algorithm and an effective stopping rule that controls the false detection rate are described. Suggestions are given for reducing masking and for diagnosing the number of shifts or outliers present.

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