A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals. Copyright

SUMMARYIn recent years, statistical process control for autocorrelated processes has received a great deal of attention. This is due in part to the improvements in measurement and data collection that allow processes to be sampled at higher frequency rates and, hence, data autocorrelation. A method for monitoring autocorrelated processes based on regression adjustment is presented in this paper. The performance of the residual-based control chart in terms of the average run length is compared to observation-based control charts via Monte Carlo simulations. In general, the observation-based control charts perform very poorly when data are correlated over time. Under the assumption that the model is correct, the residual-based control charts are superior for all cases considered here. This suggests using a residual-based control chart to detect the mean shift. This is recommended particularly for chemical processes where there are often cascade processes with several inputs but only a few outputs, and where many of the variables are highly autocorrelated.

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