A Modified Double Monte Carlo Technique to Approximate Reliability Confidence Limits of Systems with Components Characterized by the Weibull Distribution

摘要

A modified Double Monte Carlo technique is developed for determination of lower confidence limits of system reliability based on component test data. It is assumed that the components test data consists of failure times, which are distributed according to a known two-parameter Weibull probability distribution. These failure times are randomly generated using the true shape and scale parameters of the distribution. Maximum-likelihood estimators are twice obtained for the shape and scale parameters and then substituted into the reliability equation to obtain an estimator for the component reliability. A given number of these estimators are obtained and used to form an empirical distribution of reliabilities for each component. A given number of samples from this distribution are used to calculate various system reliabilities. Since the true system reliability is known, it can be determined if a given confidence interval contain the true number, hence giving you a method of validating any confidence interval. (Author)