A nonparametric triple exponentially weighted moving average sign control chart

Abstract

Nonparametric control charts are used in process monitoring when there is insufficient information about the form of the underlying distribution. In this article, we propose a triple exponentially weighted moving average (TEWMA) control chart based on the sign statistic for monitoring the location parameter of an unknown continuous distribution. The run‐length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. We also compare its statistical performance with existing nonparametric sign charts, such as the cumulative sum (CUSUM), exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double exponentially weighted moving average (DEWMA) sign charts as well as the parametric TEWMA‐trueX¯ chart. The results show that the TEWMA sign chart is superior to its competitors, especially for small shifts. Moreover, two examples are given to demonstrate the application of the new scheme.

Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature

“…Also, the FIR features discussed here can be incorporated in the TEWMA schemes recently proposed in Chatterjee et al 47 . and Alevizakos et al 48 …”

Nonparametric EWMA-Type Control Charts for Monitoring Industrial Processes: An Overview

“…It is forthright that the resulting nonparametric sign scheme generates an alarm if the charting statistic is located out of the region determined by the corresponding control limits. According to the extensive numerical results provided by Alevizakos et al (2020b), the proposed double GWMA monitoring scheme seems to be more efficient than its competitors for slight changes in the location parameter, while its attribution is similar to the other nonparametric charts for bigger changes. Alevizakos et al (2020a) proposed a triple EWMA control scheme which utilizes the sign statistic for monitoring the location parameter of the underlying process.…”

“…It is forthright that the proposed distribution-free scheme generates an out-of-control alarm if the charting statistic is located out of the region determined by the corresponding control limits. According to the extensive numerical results provided by Alevizakos et al (2020b), the proposed double GWMA control scheme seems to be more efficient than its competitors for slight changes in the location parameter, while its attribution seems to be almost similar compared to the other nonparametric charts for bigger changes.…”

“…Moreover, Aslam et al (2020) argued that the resulting control scheme is an attractive alternative for practitioners, especially when the aim is to track down slight to middling changes in the process. Alevizakos et al (2020b) established a nonparametric double GWMA control scheme based on the signed-rank statistic for monitoring the location parameter of the underlying process. The run length distribution of the resulting chart is investigated in some detail, while plenty numerical calculations have been accomplished based on proper Monte Carlo simulation procedures.…”

“…In their framework, a new fast initial response feature is also activated in order to make the resulting chart more efficient. Following a similar argumentation as the one established by Alevizakos et al (2020b), Letshedi et al (2021) constructed their triple EWMA scheme based on the following monitoring statistic:…”