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

Abstract

The exponentially weighted moving average (EWMA) control chart is a memory‐type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small‐to‐moderate shifts. This paper proposes a new distribution‐free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank‐sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real‐life illustration is provided to show the application and implementation of the new chart.

The use of fast initial response features on the homogeneously weighted moving average chart with estimated parameters under the effect of measurement errors

“…39 Initial response features considered here are a power transformation adjustment factor (denoted as FIR adj ) such that when the effect of FIR has completely disappeared, the FIR adj equals 1. According to Steiner, 21 Haq et al, 24 and Letshedi et al, 25 the BFIR, MFIR, and IMFIR features are respectively given by…”

“…The aforementioned researches and others concluded that FIR features shrink the time‐varying control limits of the CUSUM, EWMA, and GWMA schemes, and therefore, improve their performances in detecting start‐up problems. More recently, Letshedi et al 25 proposed the use of a new improved MFIR feature (denoted as IMFIR) to improve the performance of a single, double and triple EWMA schemes based on the nonparametric Wilcoxon rank‐sum statistic. The IMFIR feature is shown to be more effective than the MFIR and BFIR features in detecting location shifts in a nonparametric setup.…”

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

“…Finally, Letshedi et al (2021) proposed a new distribution-free triple EWMA control chart based on the Wilcoxon rank-sum statistic to improve the ability for tracking down plausible changes in location parameter of the underlying distribution. In their framework, a new fast initial response feature is also activated in order to make the resulting chart more efficient.…”

“…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:…”

Robust Distribution-Free Hybrid Exponentially Weighted Moving Average Schemes Based on Simple Random Sampling and Ranked Set Sampling Techniques

“…A well-known nonparametric test is based on the Wilcoxon rank-sum (W) statistic [29]. In the SPM context, control charts based on the W statistic have been studied by Li et al [30], Malela-Majika and Rapoo [31], Mukherjee et al [32], Chong et al [33], Mabude et al [34], Tercero-Gomez et al [35], Triantafyllou [36], and Letshedi et al [37]. Most of the latter articles were studied under the assumption of simple random sampling (SRS) technique.…”