Random failure rates are usually assumed as constant values in reliability calculations. In this paper, this topic is investigated using stochastic models of uncertain phenomena like lightning, cold load pickup, and overloading, which result in random failures. An algorithm is developed to estimate the random failure rates in distribution networks during their lifetime. This algorithm stochastically generates the random failures as well as sustained failures as a result of equipment wear-out state due to the aging process and finally estimates the total number of temporary/sustained failures in a period of the network lifetime. The results of applying this algorithm to a real case study show that there is slight time-dependency between the random failure rate of the network and its lifetime.