Estimating the cumulative downtime distribution of highly reliable components

Compound Bernoulli processes are motivated as satisfactory approximations to alternating renewal processes that model the availability of highly reliable components. The cumulative downtime distribution derived from a compound Bernoulli process is more tractable and can easily be estimated from data using maximum likelihood techniques. The special case of exponential repair times is examined in detail and a uniformly minimum variance unbiased estimator for the cumulative downtime distribution is derived and compared to the maximum likelihood estimator and a nonparametric estimator in terms of mean-squared error.