A nonparametric CUSUM control chart for multiple stream processes based on a modified extended median test

Austin R. Brown, Kennesaw State University
Jay R. Schaffer, University Northern Colorado


In statistical process control applications, situations may arise in which several presumably identical processes or “streams” are desired to be simultaneously monitored. Such a monitoring scenario is commonly referred to as a “Multiple Stream Process (MSP).” Traditional MSP charting techniques rely on the assumption of normality, which may or may not be met in practice. Thus, a cumulative summation nonparametric MSP control charting technique, based on a modification of the classical extended median test was developed and is referred to as the “Nonparametric Extended Median Test Cumulative Summation (NEMT-CUSUM) chart.” Chart development, including calculation of control limits, is given. Through simulation, the NEMT-CUSUM is shown to perform consistently in the presence of normal and non-normal data. Moreover, it is shown to perform more optimally than parametric alternatives in certain circumstances. Results suggest the NEMT-CUSUM may be an attractive alternative to existing parametric MSP monitoring techniques in the case when distributional assumptions about the underlying monitored process cannot reasonably be made.