Markov Chain-Based Reliability Models; A Comparative Study of Their Performance and Applicability in Complex Systems

Abstract

Markov processes are frequently used to model repairable and reconfigurable systems, but other systems are complicate due of redundancy or large number of states. If all components are repairable and non-aging, the initial state is the only slow state and exponential approximations for the system reliability are both accurate and relatively easy to calculate. On the other hand, if some components are subject to ageing, the system can still be modelled with a Markov process using the phase method. But a lot of states are then introduced and the abovementioned methods are no longer usable. This paper introduces a more tractable version of the well-known method that we called “cutting method”. This method is also valid if some repairs are delayed when repairs are initiated on the occurrence of a second failure. We propose two approaches to describe the system configuration: An global architecture, called network approach using the form of the parallel- series (or series-parallel) structure and heuristic approach based on decomposition to describe and compute measures. This new and computationally efficient heuristic model is developed for computing reliability and availability of the osmosis dialysis systems, these parameters will lead to an improvement in patient outcomes and overall quality of care. A numerical example is presented, and an implementation is developed