A multi-objective discrete reliability optimization problem for dissimilar-unit standby systems

A new methodology for the reliability optimization of a k dissimilar-unit nonrepairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes arranged in a series–parallel configuration. We also propose an approximate technique to extend the model to the general types of nonconstant hazard functions. To evaluate the system reliability, we apply the shortest path technique in stochastic networks. The purchase cost of each component is assumed to be an increasing function of its expected lifetime. There are multiple component choices with different distribution parameters available for replacement with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system to minimize the initial purchase cost of the system, maximize the system mean time to failure, minimize the system variance of time to failure, and also maximize the system reliability at the mission time. The goal attainment method is used to solve a discrete time approximation of the original problem.