The SPRT control chart for the process mean with samples starting at fixed times

Abstract In contrast to traditional fixed sampling interval (FSI) control charts, variable sampling interval (VSI) charts vary the sampling interval as a function of the process data, thus detecting many process changes substantially faster than their FSI counterparts. However, an administrative complication in the practical implementation of VSI charts is that future sampling times are unpredictable. This paper develops a control chart for monitoring the process mean that is based on applying a sequential probability ratio test (SPRT) to the observations at each sampling point. It is assumed that the time required to take each individual observation is too long to be neglected, and that the possible times for starting an SPRT are equally spaced and determined (fixed) by administrative or process requirements. This chart is called the SPRT fixed-times (SPRTFT) chart because the SPRTs are started at the specified fixed times. Exact expressions in terms of integral equations are developed for the performance measures of the SPRTFT chart. A simple design method for the SPRTFT chart is developed based on corrected diffusion approximations to its statistical properties. Comparisons are made between the performancy of the SPRTFT chart and the FSI and VSI X and cumulative sum (CUSUM) charts, including VSI versions of the X and CUSUM charts constrained to sample also at fixed times. Compared to these charts, the SPRTFT control chart is shown to be highly efficient and have significant administrative advantages.