Repetitive Sampling Control Chart for Gamma Distribution in  Uncertain Environments

Zainalabideen Al-Husseini; Khudhayr A. Rashedi; Muhammad Aslam

Authors

Zainalabideen Al-Husseini Department of Accounting, College of Adminstrative Sciences, Al-Mustaqbal University, 51001, Babylon, Iraq
Khudhayr A. Rashedi Department of Mathematics, College of Science, University of Ha’il, Hail, Saudi Arabia
Muhammad Aslam Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia;

Keywords:

Control chart, shift; simulation; imprecise data; industrial process

Abstract

This paper introduces an innovative control chart customized for the gamma
distribution, specifically crafted to handle uncertain conditions through repetitive sampling. The
control chart's coefficients, along with the probabilities of remaining in control or detecting a shift,
and the average run lengths, were derived by assuming the symmetrical behavior typical of the
normal distribution, using the neutrosophic interval method. The performance of this chart was
evaluated by assessing average run lengths under various uncertain process conditions. The chart's
efficacy in identifying both minor and major process shifts was investigated. This study also
provides a comparison between the newly proposed chart and existing ones. To demonstrate its
practical utility, an example from the healthcare sector is provided. Both simulation results and
this practical example confirm that the new control chart is effective in swiftly identifying
deviations in processes, making it a valuable tool for managing uncertainty.

DOI:10.5281/zenodo.14119402