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Traditional statistical process control charts assume that observations are independent and normally distributed about some mean. We investigate the robustness of traditional charts to data correlation when the correlation can be described by an ARMA(1,1) model. We compare the performance of the Shewhart chart and the Exponentially Weighted Moving Average (EWMA) chart to the performance of the Special-Cause Control (SCC) chart and the Common-Cause Control (CCC) chart proposed by Alwan and Roberts (1988), which are designed to account for data correlation. We also explore the possibility of putting limits on the CCC chart, in order to predict quality abnormalities. The measure of performance used is the average run length (ARL). The results show that the ability of the EWMA chart to detect shifts in the process mean is quite robust to data correlation, while the corresponding individuals Shewhart chart rarely detects such shifts more quickly than the other charts. The SCC and CCC charts are shown to be preferred in most cases when a shift in the process mean exceeds 2 standard deviations. The experimental results can aid practitioners in deciding which chart would be most effective at detecting specified shifts in the process mean given the nature of their particular correlated environments. Two methodologies are utilized to explain the relative performance of the SPC charts compared: the dynamic step response function, and response surface methodology. Such methods not only facilitate a discussion of our results, but also make it possible to predict the relative performance of the charts when the process can be described by a model which is more complex than the ARMA(1,1) model.
Wardell et al. (Sat,) studied this question.