An Improved Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

Abstract

Maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for detecting changes in both process mean and process variability. In this paper, we propose an improved MaxEWMA control charts based on ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS) schemes for simultaneous detection of both increases and decreases in the process mean and/or variability, named MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts. These MaxEWMA control charts are based on the best linear unbiased estimators of location and scale parameters obtained under ORSS and OIRSS methods. Extensive Monte Carlo simulations have been used to estimate the average run length and standard deviation of run length of the proposed MaxEWMA control charts. These control charts are compared with their counterparts based on simple random sampling (SRS), that is, MaxEWMA‐SRS and MaxGWMA‐SRS control charts. The proposed MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts are able to perform better than the MaxEWMA‐SRS and MaxGWMA‐SRS control charts for detecting shifts in the process mean and dispersion. An application to real data is provided to illustrate the implementation of the proposed MaxEWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.

A New Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Dispersion

“… and Haq et al . , respectively. It is worth mentioning that the MaxEWMA‐ODRSS control chart performs uniformly better than the control charts considered here, that is, all of the out‐of‐control ARLs and SDRLs of the MaxEWMA‐ODRSS control chart are uniformly less than those with the optimal MaxEWMA‐SRS, optimal MaxGWMA‐SRS and MaxEWMA‐ORSS control charts.…”

“…The values of ARLs and SDRLs of the MaxEWMA‐OIRSS control chart are taken from Haq et al . . It is clear that, even with imperfect rankings, the proposed MaxEWMA‐OIDRSS control chart turns out to be more sensitive than its counterparts when detecting all different shifts in the process mean and/or process dispersion.…”

“…Later on, Haq et al . suggested an improved MaxEWMA control charts based on ORSS and ordered imperfect RSS (OIRSS) schemes, named MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts, respectively, for monitoring changes in the process mean and process dispersion simultaneously.…”

Maximum Multivariate Exponentially Weighted Moving Average and Maximum Multivariate Cumulative Sum Control Charts for Simultaneous Monitoring of Mean and Variability of Multivariate Multiple Linear Regression Profiles

“…In recent years, joint monitoring of process mean and dispersion in both univariate and multivariate cases has been considered by some researchers. Simultaneous monitoring of the mean and variance in univariate process has been studied by Khoo et al [22], Zhang et al [23], Guh [24], Memar and Niaki [25], Teh et al [26], Sheu et al [27], Haq et al [28], and Prajapati and Singh [29]. The simultaneous monitoring of multivariate process mean vector and covariance matrix has also been addressed by several authors.…”

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

“…They showed that the RSS‐based mean charts are more powerful than the Shewhart mean chart based on SRS. For more details about the control charts based on different RSS schemes, refer to Abujiya and Muttlak, Abujiya et al , Abujiya et al , Al‐Omari and Haq, Mehmood, Haq, Haq et al , Haq et al , and the references cited therein.…”