Reliability-redundancy allocation for multi-state series-parallel systems

Current studies of the optimal design of multi-state series-parallel systems often focus on the problem of determining the optimal redundancy for each stage. However, this is only a partial optimization. There are two options to improve the system utility of a multi-state series-parallel system: 1) to provide redundancy at each stage, and 2) to improve the component state distribution, that is, make a component in states with respect to higher utilities with higher probabilities. This paper presents an optimization model for a multi-state series-parallel system to jointly determine the optimal component state distribution, and optimal redundancy for each stage. The relationship between component state distribution, and component cost is discussed based on an assumption on the treatment on the components. An example is used to illustrate the optimization model with its solution approach, and that the proposed reliability-redundancy allocation model is superior to the current redundancy allocation models.