Optimal system reliability for a mixed series and parallel structure

AbstractThe paper considers a generalization of the optimal redundancy problem. We consider any mixed series and parallel network consisting of N modules. The ith module has a reliability cost function of ri(di) where di is the investment in module i. The reliability investment functions are not required to be concave or continuous in the dynamic programming model. The objective is to maximize the system reliability subject to cost, weight, or volume constraints. The paper differs from others in that we permit modules in logical parallel to be of different designs, and investment in a module does not necessarily imply that redundant components will be used. Many previous models have been restricted to the parallel series situation which is a special case of this model.A dynamic programming model is presented for the problem. The application of the generalized decomposition operator is used to develop a set of recursive relations for any mixed series and parallel system of modules. An example and comments on generalizations are included