Accuracy of Univariate, Bivariate, and a `Modified Double Monte Carlo' Technique for Finding Lower Confidence Limits of System Reliability

The purpose of this paper is to compare the accuracy of two asymptotic (univariate and bivariate) techniques and a modified double Monte Carlo technique to obtain system reliability s-confidence limits from component test data modeled by the 2-parameter Weibull distribution. The bivariate technique assumes that the maximum likelihood estimators of the component shape and scale parameter have their asymptotic bivariate normal distribution. The univariate technique assumes that the component reliability estimates have their asymptotic s-normal distribution. A variation of the univariate technique using the beta distribution as the distribution of the component reliability estimates is also examined. The analysis reveals that: 1. The bivariate technique is generally superior to the other asymptotic techniques for the four system-configurations examined. 2. The accuracy of each technique increases as the component test-data sample-size increases, as anticipated. 3. For low system-reliability all four techniques are close in their performance. 4. The s-confidence intervals are in general s-biased (upward), that is the actual s-confidence levels are lower than desired. 5. When sample size reaches 30, the bivariate and modified double Monte Carlo techniques are comparable for three of four systems studied. 6. As sample-size for component test-data increases, the accuracy of the double Monte Carlo method increases more rapidly than other methods and it can be used in a much wider variety of situations.