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

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