Availability optimization of a redundant system through dependency modeling

This paper presents a constructive approach to optimize the availability of a system through modeling the dependency of the components. Our goal is to minimize the system cost under the constraint that system availability must not be less than a given level. In particular, the components are dependent of each other. A function noted as the dependence function is introduced to model the dependency. It is demonstrated that, for a general form of the system cost, the dependence function guarantees a finite set of feasible solutions. An approach is then developed with the help of the dependence function to obtain the optimal solution. The resolution is illustrated by an interesting example, in which the system cost depends on the strength of the dependency. Our study reveals that the dependency is an essential and effective option to improve system reliability. Moreover, the modeling of dependency, i.e. the introduction of the dependence function is valuable for resolving the optimization problem.