Redundancy allocation to maximize a lower percentile of the system time-to-failure distribution

An algorithm is presented which solves the redundancy-allocation problem when the objective is to maximize a lower percentile of the system time-to-failure distribution. The algorithm uses a genetic algorithm to search the prospective solution-space and a bisection search as a function evaluator. Previously, the problem has most often been formulated to maximize system reliability. For many engineering-design problems, this new formulation is more appropriate because there is often no clearly defined mission time on which to base component and system reliability. Additionally, most system designers and users are risk-averse, and maximization of a lower percentile of the system time-to-failure distribution is a more conservative (less risky) strategy compared to maximization of the mean or median time-to-failure. Results from over 60 examples clearly indicate that the preferred system design is sensitive to the user's perceived risk. We infer from these results that engineering-design decisions need to consider risk explicitly, and use of mean time-to-failure as a singular measure of product integrity is insufficient. Similarly, the use of system reliability as the principal performance measure is unwise unless mission time is clearly defined.