The reasons, or the requisites for dependent failures are discussed in a rather general meaning. With such an underlying knowledge, a pipe system, which is usually comprised of a great number of pipe segments, dependent failure probability model is developed, and the effect of pipe segments failure dependency on the pipe system failure probability is presented. It is shown that component failure probability is normally a random variable, system failure probability depends on not only the mean values of the involved component failure probabilities, but also their standard deviations.