The limit of sum of Markov Bernoulli variables in system reliability evaluation

For 2-state maintainable and repairable systems modeled by nonstationary Markov chains, a limiting compound Poisson distribution is derived for the sum of Markov Bernoulli random variables. The result is useful for estimating the distribution of the sum of negative-margin hours in a boundary-crossing scenario involving any physical system with interarrival times of system failures that are negative-exponentially distributed, where the positive- and negative-margin states denote desirable and undesirable operating conditions. three test cases from the IEE Reliability Test system are analyzed. The mean and variance/mean ratio are generated for each case. The results of compound Poisson distribution estimation for the sum of Markov Bernoulli random variables with varying probabilities can be used to solve the problem of estimating the distribution of the popular reliability index (cumulated loss-of-load hours) in large electric power generation systems where the hourly load demand varies