RELIABILITY IMPORTANCE MEASURES IN MARKOV CHAINS

Reliability importance measures are significant and effective tools for analyzing systems reliability, risk and safety. These measures are traditionally defined in fault tree context, and are widely used in eminent methods such as probabilistic safety and risk assessment. Although fault tree is a well-known and powerful tool in systems risk analysis, but it has remarkable weaknesses. The most important weakness of fault tree is its inability in considering dynamic dependencies between system components that is caused by its restriction in considering the effect of time of failure of the system components. Another significant weakness is that fault tree considers system components to be unrepairable, while most of the real world systems are repairable and have repairable components and parts. The other weakness is rare-event approximation that has remarkable effect on the results obtained from fault tree. On the other hand, Markov chain is influential tool for systems risk analysis that can overcome the mentioned weaknesses. Markov models are outstanding tools for dynamic analysis of the systems operations. In fact, the effect of failure times of the system components on the whole system functioning and failure can be easily captured by using Markov models. Furthermore, failure and repair rates of the system components can both be considered in Markov models when modeling the system operation. Markov models are efficient tools for considering repairable components and has straightforward scheme for simultaneous consideration of failure and repair rates. So, extending the definitions of the importance measures in Markov chain is an important issue which is addressed in this paper. Extending a new modeling basis, i.e. Markov models, for the importance measures equips them with Markov models capabilities in resolving the mentioned weaknesses. The obtained results of implementation of the extended Importance measures in Markov chain on a real world case study taken from literature, illustrates their effectiveness.