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.