@article{Al-Essa2026, 
author = {Laila A. Al-Essa and Muhammad Imran and Farrukh Jamal},
title = {Applications of the novel extended Rayleigh distribution in statistical quality, censored data with application for engineering materials},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {14025-17074},
keywords = {acceptance sampling, Bayes estimation, Bell distribution, censored data, maximum likelihood estimation, statistical quality control},
url = {https://www.sciopen.com/article/10.3934/math.2026577},
doi = {10.3934/math.2026577},
abstract = {We introduce an extended three-parameter Rayleigh distribution using the genesis of a truncated discrete Bell distribution. The expressions for the    rth moment, Réyni entropy, and quantile function are presented. Moreover, a group acceptance sampling plan for a truncated life test using the median as a quality parameter is presented. Two estimation methods (classical and Bayesian) are used to estimate parameters. The practical relevance of the proposed model is demonstrated using two real-life datasets related to engineering materials. Bias and efficiency of the estimators are assessed through simulation. Additionally, we present a censored data application using data centered on the survival rates of kidney patients (   n  =  76, censored    =  23.7  %, event    =  76.3  %). However, the Kaplan–Meier survival curve supports the proposed exponentiated Bell Rayleigh distribution.}
}