In reliability design, allocating redundancy through various optimization methods is one of the important ways to improve the 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. This paper first proposed an analytical model describing the failure rates with failure interactions. Then a Modified Analytic Hierarchy Process (MAHP) is proposed to solve the redundancy allocation problems for systems with failure interactions. This method decomposes the system into several blocks and deals with those down-sized 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 complex explicit objective functions for the entire system 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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