An SPRT control chart with variable sampling intervals

The sequential probability ratio test (SPRT) chart is a very effective control chart. It is much faster to detect mean shifts compared with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{X} $$\end{document} and CUSUM charts, even their VSSI (variable sample sizes and sampling intervals) versions. This article proposes an SPRT scheme, called the VSI SPRT chart, which uses the variable sampling intervals (VSI) scheme to further increase the effectiveness of the SPRT chart for detecting process mean shifts. This VSI SPRT chart employs a long sampling interval d1 when the process is likely to be in control and adopts a short sampling interval d2 when the process seems close to an out-of-control condition. The results of the case studies show that the adaptive feature has the potential to further increase the overall detection effectiveness of the SPRT chart compared with the fixed sampling interval SPRT chart and, therefore, to reduce the manufacturing costs. This new chart is particularly effective when mean shift is moderate.