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 zero corresponding to the ability of the forecast to “recover” from the upset. We study 4 monitoring schemes: cumulative sums (CUSUMs), exponentially weighted moving averages, Shewhart individuals charts, and a likelihood ratio scheme. Comparisons of signaling probabilities and average run lengths show that CUSUMs can be designed to perform at least as good as, and often better than any of the other schemes. Shewhart individuals charts often perform much worse than the others. Graphical aids are provided for designing CUSUMs in this context.