Optimal variable sampling interval control charts

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Abstract
The standard practice when using a control chart to detect changes in a process is to take samples from the process using fixed sampling intervals between samples. Recent work on the statistical properties of control charts which vary the sampling interval as a function of what is observed from the data has shown that this variable sampling interval feature can significantly improve the ability of a control chart to detect certain types of process changes. Reynolds and Arnold (1989) showed that if the length of the sampling interval must be chosen from the interval [l1,l2], where 01 2, the optimal one-sided Shewhart control chart uses only two interval lengths, the shortest possible interval l1 and the longest possible interval l2.Extensions of the results Reynolds and Arnold (1989) to two sided Shewhart charts and to chars which can be modeled as Markov chains are considered. It is shown that using only two sampling intervals is also optimal for these charts.