System reliability optimization with two-sided power distributed component failure times

Many systems connected in series are subject to failure earlier in their design life. The failure rate of such systems has been described by a two-sided power distribution, which enables modeling the entirety of the bathtub curve failure modes with a single distribution. We propose a time-dependent reliability optimization model for improving a system's reliability through the optimal allocation of redundant components whose failure distribution follows a two-sided power distribution. To solve the multi-criteria optimization model, we propose an algorithm that (i) identifies the scale tolerance at which a selected component will have a higher mean residual life, (ii) identifies the level of redundancy for enhancing system reliability, and (iii) identifies other optimal system characteristics, including minimized cost and minimized volume.