The alternative distribution of the non parametric extended median test CUSUM chart for multiple stream processes
Abstract
When monitoring a multiple stream process (MSP) where multiple processes which are assumed to be identical are being simultaneously monitored, but the assumption of normality cannot be reasonably be verified, the NEMT-CUSUM control chart has been proposed as a possible non parametric alternative. However, in the beginning stages of a monitoring program, it would be useful to the chart operator to know how effective the NEMT-CUSUM will be at detecting shifts away from target given. One way of assessing effectiveness is via statistical power, which is the probability of detecting a shift in some subset of streams at a particular point in time. The purpose of this study is to derive the alternative distribution of the NEMT-CUSUM plotting statistic such that statistical power can be estimated. Examples, practical implications, and future directions are given.