Least-Cost Allocations of Reliability Investment

This paper presents two complementary techniques for determining optimal allocation of reliability investment in a multi-stage system. The first is a step-wise dynamic programming algorithm, which has proved to be a simple and direct means for obtaining the exact solution to the basic problem of least-cost allocation of redundancy. The second technique is an explicit solution to the investment allocation problem if the unreliability of each stage decreases exponentially (and continuously) as its cost increases. This solution is based on an inequality, which for reasonably reliable systems justifies minimizing the sum of the stage unreliabilities instead of the system unreliability.