Shewhart and EWMA Variable Sampling Interval Control Charts with Sampling at Fixed Times

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Abstract
Control charts used for process monitoring traditionally take samples from the process using a fixed sampling interval (FSI) between samples. In recent years variable sampling interval (VSI) control charts have been developed. A shorter sampling interval is used if the control statistic is close to but not outside the control limits. A longer sampling interval is used if the control statistic is not close to the control limits. VSI charts are able to detect most process changes substantially faster than FSI charts. One disadvantage to VSI charts as usually formulated is that the prediction of the times at which samples will be taken cannot be done for more than the next sample. This paper considers a modification of the VSI idea in which samples are always taken at specified, equally-spaced, fixed-time points with additional samples allowed between these fixed times when indicated by the process data. The location of these fixed times typically would be determined by administrative considerations or by the requirements of the process. This variable sampling interval with fixed times (VSIFT) feature is applied to the X̄ chart with and without the runs rule, to an S chart used with the X̄ chart, and to the exponentially weighted moving average chart. Simple methods are given for designing VSIFT charts for practical applications. For a given average sampling rate, VSIFT charts can be designed to give faster detection of process changes than the traditional FSI charts. Alternately, VSIFT charts can provide a required level of protection against process changes with a lower sampling cost than FSI charts.