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.