A model for optimal design of multi-state parallel-series systems

In this paper, we consider the problem of optimal design of the multi-state parallel-series system. The system has n subsystems connected in series and each subsystem has a number of components connected in parallel. The system and each component may be in states 0, 1, ..., M. The state of a subsystem is equal to the state of the best component in the subsystem. The state of the system is equal to the state of the worst subsystem. The state distribution of each component is known, that is, the probability for the component to be in each possible state is given. The state distribution of the system is a function of the state distributions of the components. Our objective is to find the number of components that each subsystem should have in order to maximize the expectation of the system utility. The optimization model for the system design is developed in this paper. A heuristic method is used to find the approximate optimal solution to the problem. The proposed multi-state system design model may be extended to handle more complicated system design problems. Additional research topics are also discussed in this paper.