Lower confidence limit for reliability based on grouped data using a quantile-filling algorithm

The aim of this paper is to propose an approach to constructing lower confidence limits for a reliability function and investigate the effect of a sampling scheme on the performance of the proposed approach. This is accomplished by using a data-completion algorithm and certain Monte Carlo methods. The data-completion algorithm fills in censored observations with pseudo-complete data while the Monte Carlo methods simulate observations for complicated pivotal quantities. The Birnbaum–Saunders distribution, the lognormal distribution and the Weibull distribution are employed for illustrative purpose. The results of three cases of data-analysis are presented to validate the applicability and effectiveness of the proposed methods. The first case is illustrated through simulated data, and the last two cases are illustrated through two real-data sets.