Lower confidence limit for the availability of a parallel system with renewable components

A parallel system of n independent and renewable components with exponential up and down times is considered. A conservative lower confidence limit (LCL) on its availability in equilibrium is constructed by using the maximization method suggested by Gnedenko et al. (1969), The empirical coverage of the LCL is investigated by using the Monte Carlo simulation technique. The method uses the empirical percentage points of the sums of independent random variables distributed according to the F-distribution. A comparison is done with an alternative method of Zacks (1987) based on a large sample normal approximation. It is shown that the maximization method performs better than the large sample normal approximation.