Joint X and R Charts with Variable Sample Sizes and Sampling Intervals

Abstract

Recent studies have shown that the chart with variable sampling intervals (VSI) and/or with variable sample sizes(VSS) detects process shifts faster that the traditional chart. This article extends these studies for processes that are monitored by both, the and the R charts. A Markov chain model is used to determine the properties of the joint and R charts with variable sample sizes and sampling intervals (VSSI) scheme improves the joint and R control chart performance (in terms of the speed with which process mean and/or variance shifts are detected).