An Interval Estimate of System Availability

A confidence interval estimate for fixed sample size is obtained for the pointwise availability of one of the states in a system that switches at random between two states. The state definitions can be tailored to the problem at hand, provided only that the definitions are pointwise. The interval estimate is exact for all sample sizes, if the durations of both states follow exponential probability distributions. An asymptotic estimate is obtained where the state durations are either exponential or uniform (0, C), where c is unknown. Where the state durations follow other probability distributions, the interval estimate is dependent upon only the coefficient of variation of each state distribution. In these cases, interval estimation is dependent upon a priori estimates made of the two coefficients of variation. This dependence is, however, meaningful in the sense that errors in the a priori estimates are readily put in terms of errors in the interval estimate.