Reliability of the networks with random number of the units in each subnet

Abstract

Our work focuses on the reliability of networks for the serial-parallel type versus the parallel-serial type when the number of units in each subnet is a Power series distributed (PSD) random variable and the lifetimes of the units are independent, identically distributed random variables (i.i.d.r.v.). General formulas for calculating the survival/reliability functions of such networks were obtained. This formulas shows that solving the problem of identifying the best network in terms of its reliability does not matter the lifetime c.d.f. F(x) of each units in each subnetwork, the answer depending only of the number M and the probability distribution of the number of units in each of M subnetworks. Sufficient conditions have been formulated for the serial-parallel network to always be more reliable than the parallel-serial network. Some examples have been illustrated graphically.