A Nonparametric Repetitive Sampling DEWMA Control Chart Based on Linear Prediction

Abstract

Distribution-free control charts can be useful in statistical process control (SPC) when only limited or no information about the distribution of the data of the process is available. In this paper, a linear prediction related double exponentially weighted moving average (DEWMA) sign control chart using a repetitive sampling scheme (RSNPDEBLP) has been considered for a binomially distributed process variable to improve the efficiency of detecting small drifts in its place of small changes. The proposed RSNPDEBLP control chart is assessed in average run length (ARL) for the various values of sample sizes. The efficiency of the proposed RSNPDEBLP control chart is compared with the existing EWMA and DEWMA sign control charts using single sampling and repetitive sampling schemes in terms of ARLs. When there are small changes in the process after the stabilization period, the proposed control chart is used to control small trends rather than small shifts.

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

“…Note that parameter k simply expresses how many times the standard deviation of the monitoring statistic wriggles into the decision interval of the resulting chart. Shafqat et al (2020) introduced a linear prediction related double EWMA sign control scheme utilizing the repetitive sampling plan. The resulting control scheme is suitable for monitoring binomially distributed data and seems to be efficient in tracking down plausible small changes of the underlying process.…”

“…Following a similar argumentation as the one provided by Brown and Meyer (1961), Shafqat et al (2020) constructed a double EWMA control chart for delivering linear predictions of the form…”

“…the control coefficients k1 and k2 take on values depending on the other design parameters of the scheme as well as its required in-or out-of-control level of attribution. The nonparametric chart proposed by Shafqat et al (2020) declares that the process is in-control if Wu et al (2020) established nonparametric control chart for joint monitoring the time interval T between successive occurrences of an event E and its magnitude X. The authors also established a "continuousify" technique combined with a common Markov chain technique in order to investigate the run length distribution and its characteristics.…”

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

“…Improving the performance of the EWMA‐type control charts during start‐up period has never been addressed for the nonparametric SPM context. For some recent contributions to nonparametric charts, refer, for instance, to Mukherjee et al., 13 Triantafyllou, 14 Chong et al., 15,16 and Shafqat et al 17 . Next though, a literature review of some related parametric research works is discussed and thereafter, the objective of this paper is outlined.…”

A New Nonparametric Tukey MA-EWMA Control Charts for Detecting Mean Shifts

“…It was found that the efficiency of the proposed control chart was better than that of the EWMA and TCC at all change levels. Besides, many authors developed and designed nonparametric control chart in several situations including, for instance, Abbas et al [19], Riaz et al [20], Shafqat et al [21], Chakraborti and Graham [22], and Mabude et al [23].…”