Exact Confidence Intervals for the Hazard Rate of a Series Reliability System

Abstract

An objective Bayesian method for the determination of upper confidence limits for the hazard rate of an exponential serial reliability system is described. The method is applicable when time-to-failure or failure-in-time data of components are available. Gamma distributions serve as posterior distributions for the hazard rate of the individual hazard rates of the components. A posterior distribution for the system hazard rate is derived by the sum of all components’ hazard rate distributions. Results of an extensive simulation study are presented. The outcome provides strong evidence that coverage probability of this model is always at least as big as the nominal level, regardless of the chosen confidence level or system configuration. In this sense, the proposed method provides conservative but reasonable estimates for the upper limit of the hazard rate. We conclude that this method provides a favorable way for interval estimation of the FIT rate for a serial system, when component data are available. In application, the stated confidence level has an objective and comprehensible interpretation by providing statistical validity. This is of practical importance for the plausibility of a sensitive reliability measure like the FIT rate.