A nonparametric double generally weighted moving average signed‐rank control chart for monitoring process location

Abstract

Most control charts have been developed based on the actual distribution of the quality characteristic of interest. However, in many applications, there is a lack of knowledge about the process distribution. Therefore, in recent years, nonparametric (or distribution-free) control charts have been introduced for monitoring the process location or scale parameter. In this article, a nonparametric double generally weighted moving average control chart based on the signed-rank statistic (referred as DGWMA-SR chart) is proposed for monitoring the location parameter. We provide the exact approach to compute the run-length distribution, and through an extensive simulation study, we compare the performance of the proposed chart with existing nonparametric charts, such as the exponentially weighted moving average signed-rank (EWMA-SR), the generally weighted moving average signed-rank (GWMA-SR), the double exponentially weighted moving average signed-rank (DEWMA-SR), and the double generally weighted moving average sign (DGWMA-SN) charts, as well as the parametric DGWMA-X chart for subgroup averages. The simulation results show that the DGWMA-SR chart (with suitable parameters) is more sensitive than the other competing charts for small shifts in the location parameter and performs as well as the other nonparametric charts for larger shifts. Finally, two examples are given to illustrate the application of the proposed chart.

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

“…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. The run length-based attribution characteristics of the resulting scheme are studied in detail, while several numerical comparisons revealed its superiority against other competitors, especially for slight changes.…”

Generally weighted moving average monitoring schemes: Overview and perspectives

“…Phanyaem 77 briefly discussed the DGWMA sign scheme with repetitive sampling and showed that it is more sensitive than the corresponding DEWMA sign scheme in many situations. Alevizakos et al 78 proposed the DGWMA signed‐rank scheme to monitor the location shifts of unknown but continuous and symmetric distributions. Apart from showing that it outperforms its competitors in many situations, they also showed that the DGWMA signed‐rank scheme is not IC robust for nonsymmetric distributions.…”

A nonparametric triple exponentially weighted moving average sign control chart

“…developed a nonparametric DEWMA chart based on the signed‐rank statistic to improve the performance of the EWMA signed‐rank chart. Other works for nonparametric control charts are those of Chakraborti et al., 20 Bakir, 21 Chakraborti and Eryilmaz, 22 Li et al., 23 Zou and Tsung, 24 Yang et al., 25 Abbasi et al., 26 Abid et al., 27 Triantafyllou, 28 Tang et al., 29 Triantafyllou, 30 Alevizakos et al, 31 Triantafyllou and Panayiotou, 32,33 and Mukherjee and Marozzi 34 . In all previous works, it is assumed that the process location parameter is known.…”