Minimizing the mean damage for parallel-series systems with two failure modes

We address a non-convex optimization problem involving the minimization of the difference between two symmetric functions which are log convex. Specif ically we are interested in minimizing the mean system damage of a parallel -series system composed of a maximal number of identical units, each capabl e of failing in one of two ways. We characterize the solution of the problem, and develop an algorithm to so lve large scale versions of it. Numerical results are presented. It is shown that an optimal configuration with n available components may not use all n components.