Open Access

ARTICLE

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Ibrahim M. Almanjahie^1,2, Zahid Rasheed^3,4,*, Majid Khan⁵, Syed Masroor Anwar⁶, Ammara Nawaz Cheema⁷
1 Department of Mathematics, College of Science, King Khalid University, Abha, 62529, Saudi Arabia
2 Statistical Research and Studies Support Unit, King Khalid University, Abha, 62529, Saudi Arabia
3 School of Mathematics and Statistics, Xi’an Jiaotong University China, Xi’an, 710049, China
4 Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh, 12500, Pakistan
5 Government Post Graduate College, Haripur, 22620, Pakistan
6 Department of Statistics, University of Azad Jammu and Kashmir, Muzaffarabad, 13100, Pakistan
7 Department of Mathematics, Air University, Islamabad, 44000, Pakistan
* Corresponding Author: Zahid Rasheed. Email:
(This article belongs to this Special Issue: New Trends in Statistical Computing and Data Science)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2091-2118. https://doi.org/10.32604/cmes.2023.022201

Received 26 February 2022; Accepted 15 July 2022; Issue published 23 November 2022

Abstract

Nonparametric (distribution-free) control charts have been introduced in recent years when quality characteristics do not follow a specific distribution. When the sample selection is prohibitively expensive, we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts. In this study, we proposed a nonparametric homogeneously weighted moving average based on the Wilcoxon signed-rank test with ranked set sampling () control chart for detecting shifts in the process location of a continuous and symmetric distribution. Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed control chart. The proposed control chart’s performance is compared to that of parametric and nonparametric control charts. These control charts include the exponentially weighted moving average (EWMA) control chart, Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart, the nonparametric EWMA sign control chart, Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart, and the homogeneously weighted moving average control charts. The findings show that the proposed control chart performs better than its competitors, particularly for the small shifts. Finally, an example is presented to demonstrate how the proposed scheme can be implemented practically.

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Keywords

Nonparametric control charts; run-length; ranked set sampling; Wilcoxon signed-rank

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