Statistical monitoring of a process with autocorrlated output and observable autocorrelated measurement error.

Our objective in this work is to monitor a production process yielding output that is correlated and contaminated with autocorrelated measurement error. Often, the elimination of the causes of the autocorrelation of the measurement error and the reduction of the measurement error to a negligible level is not feasible because of regulatory restrictions, technological limitations, or the expense of requisite modifications. In this process, reference material is measured to verify the performance of the measurement process, before the product material is measured. We propose the use of a transfer function to account for measurement error in the product measurements. We obtain the base production signal and use a modified version of the common cause (CC) chart and the special cause control (SCC) chart, originally proposed by Roberts and Alwan (1988), to monitor the base production process. We incorporate control limits in the CC chart as suggested by Alwan (1991) and Montgomery and Mastrangelo (1991) and add MR-chart to the original SCC chart. The common cause control (CCC) chart and SCC charts comprise a flexible monitoring scheme capable of detecting not only changes in the process mean, but also shifts in the mean and the variance of the random shocks that generate the base process.