We introduce an extended three-parameter Rayleigh distribution using the genesis of a truncated discrete Bell distribution. The expressions for the $r$th 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 $=23.7\mathrm{\%}$, event $=76.3\mathrm{\%}$). However, the Kaplan–Meier survival curve supports the proposed exponentiated Bell Rayleigh distribution.