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

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 (NPHWMA RSS ) 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 NPHWMA RSS control chart. The proposed NPHWMA RSS 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 NPHWMA RSS 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.

Reassessment of performance evaluation of EWMA control chart for exponential process

“…The primary goal of this research is to determine IC and OC RL using L sigma limits under the assumption of the Monte Carlo simulation method. Many researchers Abid et al., 22 Noor‐ul‐Amin et al., 23 Aslam and Anwar, 24 Abbasi et al., 12 Rasheed et al., 25 Zhang et al., 26 Almanjahie et al., 27 and Arslan et al 19 . used L sigma limits under Monte Carlo simulation for the performance evaluation of EWMA charts in various setup.…”

Introduction to the Special Issue on New Trends in Statistical Computing and Data Science

“…In the third paper entitled "Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process" by Almanjahie et al [3], the authors suggested a nonparametric homogeneously weighted moving average for detecting shifts in the process location of a continuous and symmetric distribution based on the Wilcoxon signed-rank test with ranked set sampling control chart.…”