Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann–Whitney charts to monitor unknown shifts in the process location

Abstract

The Mann–Whitney (MW) test is one of the most important nonparametric tests used in the comparison of the location parameters of two populations. Unlike the t-test, the MW test can be used when the assumption of normality fails to hold. In this paper, the MW U statistic is used to construct two efficient distribution-free monitoring schemes, namely the mixed generally weighted moving average-cumulative sum (GWMA-CUSUM) MW U scheme (denoted as U-MGC) as well as its reversed version, i.e. the CUSUM-GWMA MW U scheme (denoted as U-MCG). The performances of the proposed schemes are investigated using the average run-length (ARL) and average extra quadratic loss (AEQL) values through extensive simulations. The newly proposed charts are found to be superior in small shifts detection than their competing (existing and others that are briefly introduced here) distribution-free Shewhart, EWMA, CUSUM, mixed EWMA-CUSUM, mixed CUSUM-EWMA and GWMA MW U charts in many situations. A real-life example is used to demonstrate the design and implementation of the new schemes.