Monitoring Processes That Wander Using Integrated Moving Average Models

Often the least appropriate assumption in traditional control-charting technology is that process data constitute a random sample. In reality most process data are correlated—either temporally, spatially, or due to nested sources of variation. One approach to monitoring temporally correlated data uses a control chart on the forecast errors from a time series model of the process with, possibly, a transfer-function term to model compensatory adjustments. If the time series term is an integrated moving average, then a sudden level shift in the process results in a patterned shift in the mean of forecast errors. Initially the mean shifts by the same amount as the process level, but then it decays geometrically back to 0 corresponding to the ability of the forecast to “recover” from the upset. We study four monitoring schemes—umulative sums (CUSUM's), exponentially weighted moving averages, Shewhart individuals charts, and a likelihood ratio scheme. Comparisons of signaling probabilities and average run lengt...