On the α-risks for shewhart control charts

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Abstract
The performance of the usual Shewhart control charts for monitoring process means and variation can be greatly affected by nonnormal data or subgroups that are correlated. Define the αk-risk for a Shewhart chart to be the probability that at least one “out-of-control” subgroup occurs in k subgroups when the control limits are calculated from the k subgroups. Simulation results show that the αk-risks can be quite large even for a process with normally distributed, independent subgroups. When the data are nonnormal, it is shown that the αk-risk increases dramatically. A method is also developed for simulating an “in-control” process with correlated subgroups from an autoregressive model. Simulations with this model indicate marked changes in the αk-risks for the Shewhart charts utilizing this type of correlated process data. Therefore, in practice a process should be investigated thoroughly regarding whether or not it is generating normal, independent data before out-of-control points on the control charts are interpreted to be due to some real assignable cause.

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