Abstract:
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Multivariate control charts can be used to monitor the means of two or more correlated variables of a process. We consider processes where the target values of the means, variances, and covariances are estimated from the data. During monitoring, small random samples are collected at equal time intervals. Since estimates based on small samples are unreliable, the estimates of variances and covariances are updated with each new sample. In order to increase the sensitivity of the charts to detect small shifts from the target, past sample information is retained for each variable using an exponentially weighted moving average statistic (EWMA). Three multivariate, EWMA control charts are compared in this paper, each based on the componentwise sample average, sign, and signed rank statistics, respectively. The properties of the charts are evaluated using simulation. We study the advantages and disadvantages of each chart for various cases. Finally, we give recommendations on how to apply these charts in practice.
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