A general model for reliability maximization problem under given redundancy

We present an abstract model, the domain-partition model, of fault-tolerant systems (FTSs) in order to solve the reliability maximization problem under given redundancy. The domain-partition model is an abstraction of a reconfigurable device with several versions of circuit configuration. Unlike existing models that deal with specific FTSs, our model is ´general´ so that many types of FTSs are formulated into this model. Therefore, with our domain-partition model, we can easily compare different types of FTSs. In addition. The model enables us to determine the FTS structure that provides maximum reliability under given redundancy. In this paper: we formulate the problem of finding the most reliable FTS under given redundancy as the reliability maximization problem of the circuit configurations for a reconfigurable device. Then, we derive theoretically the most reliable configurations and the most reliable structure for FTSs in terms of the Karush-Kuhn-Tucker (KKT) condition.