Redundancy optimization of static series-parallel reliability models under uncertainty

This paper extends the classical model of Ushakov on redundancy optimization of series-parallel static coherent reliability systems with uncertainty in system parameters. Our objective function represents the total capacity of a series-parallel static system, while the decision parameters are the nominal capacity and the availability of the elements. We obtain explicit expressions (both analytic and via efficient simulation) for the constraint of the program, viz, for the Cdf of the system total capacity, and then show that the extended program is convex mixed-integer. Depending on whether the objective function and the associated constraints are analytically available or not, we suggest using deterministic and stochastic (simulation) optimization approaches, respectively. The last case is associated with likelihood ratios (change of probability measure). A genetic algorithm for finding the optimal redundancy is developed, and supporting numerical results are presented.