On dynamic probabilistic models in network reliability

Abstract

Our work addresses the issue of the reliability of serial-parallel networks versus the reliability of parallel-serial networks based on dynamic probabilistic models. Thus, calculation formulas for the lifetime cumulative distribution functions of these systems was deduced, as well as their survival/reliability functions. These formulas allow us to launch two new classes of lifetime distributions called: Min(Max-PSD)-PSD and Max(Min-PSD)-PSD distributions. The research framework is a general one, in the sense that it is based on the assumption that the number of network units, but also the number of subnetworks can be random variables belonging to the Power Series Distributions class. The theoretical results was illustrated by graphical examples.