Investment in Series and Parallel Systems to Maximize Expected Life

A series (parallel) system consisting of n stochastically independent components is considered. The system works if, and only it, each component (at least one component) works. The failure time distribution of each component can be influenced by investment in that component. The optimization problem is to choose an investment allocation which maximizes expected system life. It is demonstrated that this nonseparable problem can be solved, in some cases, by solving a sequence of related separable problems. It is also shown that, under rather general conditions, a solution associated with the sequence of separable problems is a local maximum.