Effects of Correlated Sub-Samples in Statistical Process Control

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Abstract
This paper considers the effects of correlated data within subgroups that have been defined for the purposes of statistical process control. Such correlation may arise if the grouping is accomplished because of simplicity in data collection, such as multiple but similar measurements on a single product or multiple station machines. The effect of correlated measurements within the subgroup is shown to increase the Type I error rate for the X chart. Variance charts are shown not to be affected in the same fashion when equality of covariances of the measurements is assumed. Monte Carlo simulation is used to show similarity of the effects on the range chart when the number of measurements in the subgroup exceeds two. Several examples are given.

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