Evaluating properties of variable sampling interval control charts

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Abstract
Standard fixed sampling interval (FSI) control charts take samples from a process at fixed length sampling intervals for purposes of detecting changes in the peocess that may affect the quality of the output. Variable sampling interval (VSI) control charts vary the sampling interval as a function of what is observed from the process and can detect process changes faster than FSI control charts. Evaluation of properties of VSI control charts requires extensions of methods that have been developed for FSI control Control charts. A unified treatment of two widely used methods, the Markov chain method and the integral equation method. is given for VSI control charts.This unified treatment includes some results which are new in the FSI case. The new methods are used for the numerical evaluation of propertics of exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts.Some general optimality results for the choice fo the sampling intervals are also given.