Optimizing Standby Reliability Systems Having Non-Decreasing Failure Rates

In this article we develop a bounding procedure which is applied in an algorithm for determining the number of back-up components to include in a series system. Operating only when original units fail, back-up components increase system reliability. They also add weight, take up space, and cost money. Maximizing the reliability of nuclear power plants, ships, aircraft, life support systems and electronic instruments leads to this class of resource allocation problem. Because the procedure requires only that the rate of failure of individual components remains constant or increases with time, the algorithm can accommodate a wide variety of failure probability distributions. In applications, the failure probability for various types of components might belong to different families and this can be readily handled by the algorithm presented.