Confidence limits on the inherent availability of equipment

The inherent availability, is an important performance index for a repairable system, and is usually estimated from the times-between-failures and the times-to-restore data. The formula for calculating a point estimate of the inherent availability from collected data is well known. But the quality of the calculated inherent availability is suspect because of small data sample sizes. The solution is to use the confidence limits on the inherent availability at a given confidence level, in addition to the point estimator. However, there is no easy way to compute the confidence limits on the calculated availability. Actually, no adequate approach to compute the confidence interval for the inherent availability, based on sample data, is available. In this paper, the uncertainties of small random samples are taken into account. The estimated mean times between failures, mean times to restore and the estimated inherent availability are treated as random variables. When the distributions of both times-between-failures and times-to-restore are exponential, the exact confidence limits on the inherent availability are derived. Based on reasonable assumptions, a nonparametric method of determining the approximate confidence limits on the inherent availability from data are proposed, without assuming any times-between-failures and times-to-restore distributions. Numerical examples are provided to demonstrate the validity of the proposed solution, which are compared with the results obtained from Monte Carlo simulations. It turns out that the proposed method yields satisfactory accuracy for engineering applications.