A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data

The Maximus, bootstrap, and Bayes methods can be useful in calculating lower s-confidence limits on system reliability using binomial component test data. The bootstrap and Bayes methods use Monte Carlo simulation, while the Maximus method is closed-form. The Bayes method is based on noninformative component prior distributions. The three methods are compared by means of Monte Carlo simulation using 20 simple through moderately complex examples. The simulation was generally restricted to the region of high reliability components. Sample coverages and average interval lengths are both used as performance measures. In addition to insights regarding the adequacy and desirability of each method, the comparison reveals the following regions of superior performance: 1. The Maximus method is generally superior for: a) moderate to large series systems of reliable components with small quantities of test data per component, and b) small series systems of repeated components. 2. The bootstrap method is generally superior for highly reliable and redundant systems. 3. The Bayes method is generally superior for: a) moderate to large series systems of reliable components with moderate to large numbers of component tests, and b) small series systems of reliable non-repeated components.