Variable-sampling-interval control charts with sampling at fixed times

When control charts are used for process monitoring, the traditional practice is to take samples from the process by using a fixed sampling interval (FSI) between samples. Recently developed variable-sampling-interval (VSI) charts vary the sampling interval as a function of the process data to give faster detection of process changes. This paper considers a type of VSI control chart in which samples are always taken at specified equally spaced fixed time points, but additional samples are allowed between these fixed times when indicated by the data from the process. The location of the fixed times would typically be determined by administrative considerations such as testing schedules or by the desirability of sampling according to natural periods in the process. Markov process methods are given for analyzing the performance of these VSI with fixed times (VSIFT) charts. The VSIFT feature is considered for the (X) over bar-chart, the EWMA chart and the CUSUM chart. It is shown that VSIFT charts will detect most process shifts substantially faster than FSI charts. It is also shown that VSIFT charts are just as effective in detecting shifts as standard VSI charts that are not constrained to sample at the specified fixed times. In comparison with variable-sample-size (VSS) charts, the VSIFT charts are shown to be better at detecting large shifts but not as good at detecting small shifts.