Reliability Allocation for Networks and Systems

The work here is motivated by a problem in engineering design, namely, the allocation of reliability to the subsystems of a system, or to the nodes of a network. Allocation problems in reliability have been considered before, but the focus has been on allocating redundancy rather than reliability. Attempts at the latter topic suffer from a drawback, namely, that component interdependencies have not been considered. Here we overcome this drawback, and then provide a foundation for addressing a class of optimization problems in reliability. This boils down to finding the fixed points of a function in a unit square. For this we use results from probability on the crossing properties of star-ordered distributions. We illustrate our approach by considering series, parallel, and bridge-structured networks. In the latter two cases, we are able to show that an optimal allocation of reliability could lead to system collapsibility, i.e., a simplification of the system's architecture. For the case of series systems with dependent life lengths, we observe the result that independence when incorrectly assumed could result in an overallocation of reliability.