Approximately Optimum Confidence Bounds on Series- and Parallel-system Reliability for Systems with Binomial Subsystem Data

A method is derived for obtaining either randomized or nonrandomized lower confidence bounds on the reliability of independent series or parallel systems when subsystem data are binomially distributed. Both types of confidence bounds agree with published values of optimum confidence bounds to within about a unit in the second significant figure. In using the method derived for obtaining nonrandomized confidence bounds there is no difficulty with the number of subsystems in the system or of a requirement of equal sample sizes, as with the standard method of obtaining the optimum bounds. Existence of subsystems for which no failures are observed also presents no difficulty, in contrast to the maximum-likelihood and likelihood-ratio approximations. Numerical comparisons are made between optimum confidence bounds and those based on other approximating methods.