Distributionally Robust Design for Redundancy Allocation

In this paper, we consider a redundancy allocation problem for a series parallel system with uncertain component lifetimes that minimizes system costs while safeguarding system reliability over a given threshold level. We consider mixed redundancy strategies of cold standby and active redundancy with multiple types of components. We address lifetime uncertainty in the framework of distributionally robust optimization. In particular, we assume the probability distributions of the component lifetimes are not exactly known with only limited distributional information (e.g., mean, dispersion, and support) being available. We protect the worst-case system reliability constraint over all the possible component lifetime distributions that are consistent with the given distributional characteristics. The proposed modeling framework enjoys computationally attractive structures. The evaluation of the worst-case system reliability in our redundancy allocation problem can be transformed into a linear program, and the resulting overall redundancy allocation optimization problem can be cast as a mixed integer linear program that does not induce any additional integer variables (other than original allocation variables). In addition, the extreme joint distribution of component lifetimes can be efficiently recovered by solving a linear program. Our modeling framework can also be extended to incorporate the startup failures and common-cause failures for cold standbys and active parallels, respectively, to cater to more computationally complex settings. Finally, the computational experiments positively demonstrate the performance of the proposed approach in protecting system reliability.