Confidence interval estimation for reliability of a two parameter Weibull distribution under complete and censored samples

Estimating the reliability function of the two parameter Weibull distribution is a critical task in various fields, providing essential insights into product longevity and optimizing maintenance strategies. Due to its adaptable parameters namely scale parameter α and shape parameter β, the Weibull distribution models diverse failure behaviours, from early-life defects to wear-out periods. By evaluating reliability at key time phases namely early life (t < 0.1α), useful life (0.1α ≤ t ≤ α), and end-of-life (t > α), this estimation process supports quality control, operational forecasting, and end-of-life planning. Such reliability assessments help minimize operational disruptions, improve cost management, and support strategic planning across industries where dependability and lifecycle management are essential, such as in manufacturing, healthcare, and technology sectors. Although it holds practical significance, the estimation of confidence interval (CI) for the reliability function of two parameter Weibull distribution has been relatively underexplored in the literature. This paper presents a new approach for constructing CI for the reliability function of the Weibull distribution using the generalized variable (GV) technique, applicable to both complete samples and type II singly right-censored samples. The empirical evaluation of this method indicates that it provides coverage probabilities that are closely aligned with the nominal level, even when dealing with small uncensored samples (as small as 5) and censored samples where the proportion of censored observations can reach 70%. In comparison, traditional methods for the Weibull distribution tend to yield less reliable or widely varied coverage probabilities for complete samples. The findings are demonstrated through practical examples.