A Special Variable Sample Size and Sampling Interval Chart

Abstract

Among the variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) charts that use two values of each adaptive parameter, a VSI chart is the best chart to detect large shifts in the process mean while a VSSI chart is the best one to detect small shifts. Neither of the two is uniformly superior to the other for detecting a shift of any magnitude over a wide range. We propose a special VSSI (SVSSI) chart whose statistical performance very closely matches that of such VSI and VSSI charts for detecting large and small shifts, respectively. The three charts perform almost similarly for detecting moderate shifts. An SVSSI chart uses two sampling intervals and three sample sizes. A reasonable procedure is described to obtain its optimal design. Guidelines are provided to choose a design that is fairly close to the optimal one. Besides this, we introduce a new measure of statistical performance of a control chart which unifies the two measures in the existing literature that measure the average shift detection time of a chart with different approaches.