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Messina, Montgomery, Keats & Runger

Montgomery, Keats, Runger, and Messina (1994) for further discussion of MacGregor's work. In this study, we investigate how MacGregor's rules operate when additional assignable causes occur. We show that applying SPC to the control actions can result in rapid detection of these assignable causes, and if the assignable cause is eliminated, considerable reduction in output variation can be obtained. Finally, we compare these results on the control actions with those obtained on the deviation from target in the earlier paper to develop robust control schemes for the control engineer to employ in practice.

Method of Analysis

An example will show how SPC and EPC can be integrated for the control actions described in Equation (3) after which the results of a comprehensive simulation study are presented. The details of the Computer program that was employed to generate this chart and the following simulation results is discussed in Messina (1992). Figurę 1 shows the control actions (denoted as uJ for a realization of the process for 500 observations. In this study, the parameter values of the control actions are <J> = 0.95 and 0 = 0.4. At time t = 251, a sustained shift in the process of 10 units was introduced. The plot of the data in Figurę 1 clearly shows that the data form a pattem representative of correlated data. An ARIMA time series model can be used to describe this data. An ARIMA (0,1,1) model fits this data reasonably well. Muth (1960) shows that an optimal forecast is provided by the EWMA with weighting parameter X. In this case, the appropriate value of X is found to be 0.90.

Next we want to determine what type of SPC control schemes can be employed with these control actions which are correlated. Maragah and Woodall (1991) examined the effect of correlation on a Shewhart control chart. Their results show that depending on the type of autocorrelation, the Shewhart chart signals too freąuently or too infreąuently. Alwan (1992) also examines the effects of autocorrelation on the Shewhart control chart. The results of this study, indicate that mild cases of autocorrelation, which are often difficult to notice without formal time-series machineiy can dramatically deteriorate the ability of the standard control chart to correctly sift the effects of special from common causes. Harris and Ross (1991) examine the effects of autocorrelated data for the CUSUM and EWMA control chart procedures in terms of the average run length (ARL). The results of this study shows that the average number of observations reąuired to trigger an indication when no shift has actually occurred in the process is very sensitive to the presence of autocorrelation. In summary, the presence of autocorrelation severely