An extended nonparametric homogeneously weighted moving average sign control chart

Abstract

Parametric (or traditional) control charts are based on the assumption that the quality characteristic of interest follows a specific distribution. However, in many applications, there is a lack of knowledge about the underlying distribution. To this end, nonparametric (or distribution‐free) control charts have been developed in recent years. In this article, a nonparametric double homogeneously weighted moving average (DHWMA) control chart based on the sign statistic is proposed for monitoring the location parameter of an unknown and continuous distribution. The performance of the proposed chart is measured through the run‐length distribution and its associated characteristics by performing Monte Carlo simulations. The DHWMA sign chart is compared with other nonparametric sign charts, such as the homogeneously weighted moving average, generally weighted moving average (GWMA), double GWMA, and triple exponentially weighted moving average sign charts, as well as the traditional DHWMA chart. The results indicate that the proposed chart performs just as well as and in some cases better than its competitors, especially for small shifts. Finally, two examples are provided to show the application and implementation of the proposed chart.

Homogeneously Weighted Moving Average Control Charts: Overview, Controversies, and New Directions

“…Malela-Majika et al [35] corrected the variance used in the HHWMA X chart design proposed by [51]. For more details regarding the parametric DHWMA and HWMA charts for monitoring the location parameter, readers are referred to Alevizakos et al [22,23,56,65].…”

“…Riaz et al [53] proposed the DHWMA SN chart, which is a reparameterisation of the HWMA SN chart. At the same time, Alevizakos et al [23] mimicked the DEWMA SN chart and proposed the DHWMA SN chart for monitoring shifts in the location parameter. Compared to the HWMA, GWMA, double GWMA (DGWMA), triple exponentially weighted moving average (TWMA) SN charts, and classical DHWMA, it was found that the DHWMA SN chart performs better than the competing charts in many cases, especially for small shifts in the process parameter.…”