Control charts for autocorrelated processes under parameter estimation
Garza Venegas, Jorge Arturo
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Statistical Processes Monitoring is a collection of statistical-based methodologies and methods for monitoring the quality of manufactured products or services. Within these tools, control charts are powerful ones to assist practitioners on the detection of departures from in-control situations as long as the assumptions made on their design are fulfilled; otherwise, their power might decrease. For instance, control charts performance has been shown to be negatively affected when using estimated parameters (in which case the Average Run Length, ARL, becomes a random variable) or when dealing with autocorrelated data. Given that, this research is focused on the effect of parameter estimation on the performance of the X-bar and the modified S^2 control charts for monitoring the mean and the variance, respectively, of autocorrelated processes under parameter estimation. The average of the ARL and its standard deviation are considered as performance measures as they take into account the sampling variability of the ARL. Furthermore, a bootstrapping methodology is applied to adjust control limits in order to have a guaranteed conditional in-control performance with a certain probability and the effect on the out-of-control ARL is also studied.