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

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.