EWMA control charts with variable sample sizes and variable sampling intervals

Abstract

Traditional control charts for process monitoring are based on taking samples of fixed size from the process using a fixed sampling interval. Variable Sample Size (VSS) and Variable Sampling Interval (VSI) control charts vary the sampling rate from the process as a function of the data from the process. VSS and VSI control charts sample at a higher rate when there is evidence of a change in the process, and are thus able to detect process changes faster than traditional control charts. This paper considers general VSS and VSI control charts and develops integral equation and Markov chain methods for finding the statistical properties of these charts. EWMA charts with the VSS and/or the VSI features are studied in detail, and different ways of defining the EWMA control statistic are investigated. It is shown that using either the VSS or VSI feature in an EWMA control chart substantially improves the ability to detect all but very large shifts in the process mean. The VSI feature usually gives more improvement in detection ability than the VSS feature, and using both features together sometimes gives more improvement than using either one separately. Guidelines are given for choosing the possible sample sizes and the possible sampling intervals for these charts. EWMA charts with the VSS and/or VSI feature are compared to CUSUM charts and Shewhart X¯ charts with the VSS and/or VSI features.