Optimal reliability allocation with discrete cost-reliability data for components

This paper addresses the optimal allocation of reliability among components that are to be assembled into a system. While it is a generally accepted notion that a component's cost is an increasing function of its reliability, most research to date adopts exponentially increasing, closed-form functions to relate cost and reliability. However, in practice such functions are often unknown or difficult to construct, and it is often more reasonable to describe cost-reliability relationships via discrete data sets. We consider such situations, where each component is available at several reliability levels with corresponding costs. The design optimization problem results in a nonlinear integer program. Because every system configuration has an equivalent representation as either a series connection of parallel subsystems or a parallel connection of series subsystems, we provide formulations, linear relaxations, and algorithms for these two.