Optimal allocation of redundancies is one of the most important ways of improving system reliability. Generally, in these redundancy allocation problems, it is assumed that failures of components are independent. However, under this assumption failure rates can be underestimated since failure interactions can significantly affect the performance of systems. In this paper, we first propose an analytical model to describe the failure rates with failure interactions, followed by a modified analytical hierarchy process (MAHP) which is proposed to solve redundancy allocation problems with failure interactions. MAHP decomposes the system into several blocks and deals with those downsized blocks before diving deep into the most appropriate component for redundancy allocation. Being simple and flexible, MAHP provides an intuitive way to design a complex system and the explicit function of the entire system reliability is not required in the proposed approach. More importantly, with the help of the proposed analytical failure interaction model, MAHP can capture the effect of failure interactions. Results from case studies clearly demonstrate the applicability of the analytical model for failure interactions and MAHP for reliability design.

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