One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

The one-sided and two-sided Shewhart w-of-w standard and improved runs-rules monitoring schemes to monitor the mean of normally distributed observations from independent and identically distributed (iid) samples are investigated from an overall performance perspective, i.e., the expected weighted run-length (EWRL), for every possible positive integer value of w. The main objective of this work is to use the Markov chain methodology to formulate a theoretical unified approach of designing and evaluating Shewhart w-of-w standard and improved runs-rules for one-sided and two-sided X- schemes in both the zero-state and steady-state modes. Consequently, the main findings of this paper are as follows: (i) the zero-state and steady-state ARL and initial probability vectors of some of the one-sided and two-sided Shewhart w-of-w standard and improved runs-rules schemes are theoretically similar in design; however, their empirical performances are different and (ii) unlike previous studies that use ARL only, we base our recommendations using the zero-state and steady-state EWRL metrics and we observe that the steady-state improved runs-rules schemes tend to yield better performance than the other considered competing schemes, separately, for one-sided and two-sided schemes. Finally, the zero-state and steady-state unified approach run-length equations derived here can easily be used to evaluate other monitoring schemes based on a variety of parametric and nonparametric distributions

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

International audienceThe 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

Distribution-free Phase II Mann–Whitney control charts with runs-rules

The addition of runs-rules has been recommended to improve the performance of classical, normal theory Shewhart-type control charts, for detecting small to moderate size shifts. In this paper, we consider adding both standard and improved runs-rules to enhance the performance of the distribution-free Phase II Shewhart-type chart based on the well-known Mann-Whitney statistic proposed by Chakraborti and Van de Wiel [1]. Standard runs-rules are typically of the form w-of-(w+v) with w > 1 and v 0 and the improved runs-rules scheme is a combination of the classical 1-of-1 runs-rule and the w-of-(w+v) runs-rules. The improved scheme improves the performance of the charts in detecting larger shifts while maintaining its performance in detecting small to moderate shifts. The in-control and out-of-control performance of the proposed runs-rules enhanced distribution-free charts are examined through extensive simulations. It is seen that the proposed charts have attractive performance compared to some competing charts, and are better in many cases. An illustrative example is provided, along with a summary and conclusions.The research of the third author was partly supported by a National Research Foundation grant (Reference: TTK14061168807,UID: 94102).http://link.springer.com/journal/1702017-09-30hb2016Statistic

An overview of synthetic‐type control charts: Techniques and methodology

In this paper, we provide an overview of a class of control charts called the synthetic charts. Synthetic charts are a combination of a traditional chart (such as a Shewhart, CUSUM, or EWMA chart) and a conforming run‐length (CRL) chart. These charts have been considered in order to maintain the simplicity and improve the performance of small and medium‐sized shift detection of the traditional Shewhart charts. We distinguish between different types of synthetic‐type charts currently available in the literature and highlight how each is designed and implemented in practice. More than 100 publications on univariate and multivariate synthetic‐type charts are reviewed here. We end with some concluding remarks and a list of some future research ideas.The South African Researchers Chair Initiative (SARCHI) Chair at the University of Pretoria.http://wileyonlinelibrary.com/journal/qre2020-11-01hj2020Science, Mathematics and Technology EducationStatistic