Reliability analysis of transmission lines with common mode failures when repair times are arbitrarily distributed

The authors present the evaluation of the probability and frequency of failure for a system of two parallel redundant transmission lines with common mode failure. The component down times are assumed to follow an overdispersed Gamma distribution. The two system models are presented based, respectively, on the parallel device of stages on the use of supplementary variables. The results are checked by Monte Carlo simulations. The merits of the supplementary variable model are pointed out and the relevance of the form of the distribution as well as the necessity of a careful statistical analysis of the actual failure data is addressed. It is shown that, for a Gamma distribution with shape parameter less than unity, the form of the down-time distribution can have an orders-of-magnitude effect on the probability of failure