Availability Analysis and Design Optimization for a Repairable Series-parallel System with Failure Dependencies

In this paper, the design of a repairable series-parallel system with failure dependencies is studied. The key point is that failure dependency and limited repair teams can affect the state transition rates of each subsystem, and thus affect the state distribution of the subsystem and the availability of the system. Taking this into consideration, we present a dependence function to determine the failure rate of components in each subsystem and a Markov model to determine state distribution of the subsystem. An optimal allocation problem is proposed and is aimed at minimizing the system cost consisting of costs associated with components and costs associated with repair teams subject to the system availability constraint. To solve the optimization problem, the dependence function is specified and genetic algorithm is used to determine the optimal allocation solutions due to its flexibility in representing discrete design variables and its robust search capability. A numerical example is presented to illustrate that different dependencies make the allocation strategies different.