An efficient decomposition technique for Markov-chain analysis

A current trend in system design is to emphasize integration of various functionalities. This results in a complex environment to be handled by a fault tolerant system. The fault tolerance in the system is achieved by means of redundancy in the components, built in fault diagnosis, and sophisticated recovery/reconfiguration techniques. Reliability analysis of such systems is usually done using a Markov representation of the system. However, Markov chains tend to grow exponentially with the number of components, and beyond a certain size they become intractable. We propose techniques to manage the modeling of a class of systems by means of decomposing the system Markov chain into smaller Markov chains of manageable size. Our decomposition techniques facilitate modeling both repairable and nonrepairable systems with reduced complexity. These decomposition techniques are proved to be accurate analytically. The applicability of these schemes is shown through an example.