Comparative analysis of availability for a redundant repairable system

We consider the steady-state availability, denoted A, of a repairable system consisted of one operating unit and one spare. This paper we are interested in computational comparisons of confidence intervals for A   based on four feasible and efficient approaches. The natural estimator A^ of A, defined as the ratio of the sample mean lifetime of the operating unit to the sum of the sample mean lifetime of the operating unit and the sample mean downtime of system, is strongly consistent and asymptotically normal. The interval estimations for A   are constructed through four bootstrap approaches; standard bootstrap confidence interval, percentile bootstrap confidence interval, bias-corrected percentile bootstrap confidence interval as well as bias-corrected and accelerated confidence interval. Finally, by calculating the coverage percentage and the average length of intervals, some numerical simulation comparisons are conducted in order to illustrate the performances of A^ on various interval estimations.