Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann–Whitney charts to monitor unknown shifts in the process location. Issue 11 (2nd November 2022)

• Record Type: Journal Article
• Authors: Mabude, K.; Malela-Majika, J.-C.; Castagliola, P.; Shongwe, S. C.
• Is Part Of: Communications in statistics. Volume 51:Issue 11(2022)
• Page Start: 6667
• Page End: 6690
• Publication Date: 2022-11-02
• Subjects: Asymptotic control limits -- Distribution-free -- Exact control limits -- Mann–Whitney U statistic -- Mixed CUSUM-GWMA scheme -- Mixed GWMA-CUSUM scheme -- Phase I -- Phase II; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2020.1811331
• Languages: English
• ISSNs: 0361-0918

Abstract

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.