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Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann–Whitney charts to monitor unknown shifts in the process location
Communications in Statistics - Simulation and Computation ( IF 0.9 ) Pub Date : 2020-08-28 , DOI: 10.1080/03610918.2020.1811331
K. Mabude 1 , J.-C. Malela-Majika 1 , P. Castagliola 2 , S. C. Shongwe 1
Affiliation  

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.



中文翻译:

无分布混合 GWMA-CUSUM 和 CUSUM-GWMA Mann-Whitney 图,用于监控过程位置的未知变化

摘要

Mann-Whitney (MW) 检验是用于比较两个总体的位置参数的最重要的非参数检验之一。与t检验不同,当正态性假设不成立时,可以使用 MW 检验。本文利用 MW U 统计量构建了两种高效的无分布监测方案,即混合一般加权移动平均累积和 (GWMA-CUSUM) MW U 方案(记为 U-MGC)及其逆版本,即CUSUM-GWMA MW U方案(记为U-MCG)。使用平均游程 ( ARL ) 和平均额外二次损失 ( AEQL )研究了所提出方案的性能) 值通过广泛的模拟。发现新提出的图表在小班次检测方面优于它们的竞争(现有和此处简要介绍的其他图表)无分布的 Shewhart、EWMA、CUSUM、混合 EWMA-CUSUM、混合 CUSUM-EWMA 和 GWMA MW U 图表很多情况。一个真实的例子被用来演示新方案的设计和实施。

更新日期:2020-08-28
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