Distribution‐free composite Shewhart‐GWMA Mann‐Whitney charts for monitoring the process location

Abstract

The Mann‐Whitney (MW) statistic is one of the most recommended two‐sample statistical tests when the assumption of normality fails to hold due to its robustness and fascinating properties especially when small sample sizes are involved. In order to improve the sensitivity of the generally weighted moving average (GWMA) monitoring scheme toward the detection of large shifts, in this paper, a new distribution‐free phase II composite Shewhart‐GWMA (CSG) scheme is proposed using the MW U statistic. The performance of the proposed scheme is investigated using the average run‐length (ARL) and average extra quadratic loss (AEQL) values through extensive simulations. The performance of this newly proposed monitoring scheme is found to be superior when compared to numerous memory‐type MW schemes (some existing and others introduced in this paper) in many situations. An illustrative example is given to demonstrate the implementation of the CSG MW U scheme using real‐life data.

Weibull-Exponential Distribution and Its Application in Monitoring Industrial Process

“…e effectiveness of the FSI scheme over the VSI (variable sampling interval) scheme was justified through a numerical study. For further achievements to the statistical process monitoring literature on the Shewhart-CUSUM and Shewhart-EWMA, for instance, Aslam et al [37] improved the GWMA (generally weighted moving average) monitoring scheme for the detection of large shift in the process. For this purpose, they proposed the phase-II composite Shewhart-GWMA scheme using the Mann-Whitney U statistic.…”

A novel single composite Shewhart‐EWMA control chart for monitoring the process mean

“…Their setback is that, due to their inertia, they are relatively slow in detecting large shifts in the process. After the introduction of the Shewhart, EWMA and CUSUM schemes, many authors have developed more advanced and enhanced monitoring schemes; see for instance, Daudin, 5 Mosquera and Aparisi, 6 Abbas et al., 7 Abbasi et al., 8 Shamma and Shamma, 9 Lucas and Saccucci, 10 Abujiya et al., 11,12 Zaman et al., 13 Ali and Haq, 14,15 Mabude et al 16 . and Huang et al 17 …”

“…4 Their setback is that, due to their inertia, they are relatively slow in detecting large shifts in the process. After the introduction of the Shewhart, EWMA and CUSUM schemes, many authors have developed more advanced and enhanced monitoring schemes; see for instance, Daudin, 5 Mosquera and Aparisi, 6 Abbas et al, 7 Abbasi et al, 8 Shamma and Shamma, 9 Lucas and Saccucci, 10 Abujiya et al, 11,12 Zaman et al, 13 Ali and Haq, 14,15 Mabude et al 16 and Huang et al 17 An efficient monitoring scheme is expected to detect small to large shifts as quickly as possible. One of the possible techniques to enhance the sensitivity of a monitoring scheme towards small to large shifts is the combination of memoryless and memory-type schemes such as the composite Shewhart-EWMA and Shewhart-CUSUM monitoring schemes (see, for example, Lucas, 18 Klein, 19 Capizzi and Masarotto, 20 Shamsuzzaman et al 21 and Freitas et al, 22 just to cite a few).…”