A Univariate Monte Carlo Technique to Approximate Reliability Confidence Limits of Systems with Components Characterized by the Weibull Distribution.
Abstract
A univariate Monte Carlo technique is developed for the determination of lower confidence limits of system reliability based on component test data. It is assumed that the component 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 found for the shape and scale parameters and then substituted into the reliability equation to obtain the maximum-likelihood estimator for the component reliability. The estimated bias in this estimator is subtracted to yield an approximately unbiased estimator of the component reliability. Using the empirical variance of the reliability estimate and assuming a normal distribution, a Monte Carlo simulation is run for four hypothetical systems consisting of as many as five components. The simulation is repeated 600 times. Since the true reliability is known, on each run it can be determined if the desired confidence intervals contain the true system reliability. The result is an absolute measure of the effectiveness of the univariate technique.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1979
- Accession Number
- ADA113998
Entities
People
- Randall Blanton Putz
Organizations
- Air Force Institute of Technology