Approximate Confidence Limits for Complex Systems with Exponential Component Lives

Abstract

The asymptotic distribution of the log-likelihood ratio is shown to provide a method of determining approximate confidence bounds for the reliability function of any coherent system when each component has an exponential life with unknown failure rate and component performance data are provided in the form: number of failures (minimum of one) and total operating time. Thus the method applies under all general types of censoring. This extends the results of the authors, Ann. Math. Statist. (1968), on confidence limits for coherent structures with binomial data on the component's reliability. Methods similar to those previously utilized are combined with some special properties of the exponential distribution to obtain the results.