Efficient Approximate Reliability Evaluation Using the Markovian Minimal Cut Approach

Hans-Dieter Kochs (Gerhard Mercator University Duisburg, Germany)

Holger Hilmer (Gerhard Mercator University Duisburg, Germany)

Thomas Nisbach (Gerhard Mercator University Duisburg, Germany)

Abstract: The Reliability analysis of information and automation systems has to cope with complex system structures and a large number of different components. Adapted to these requirements, the Markovian minimal cut approach has been developed. The Markovian minimal cut approach combines the advantages of two well-known approaches, the minimal cut and the Markovian path approach. The minimal cut approach allows the efficient evaluation of large scale systems. The Markovian path approach is able to model and evaluate real operation and outage behavior under realistic conditions. It includes outage and disconnection partitions, maintenance strategies (inspection, maintenance, repair), and operation and control strategies, which may lead to complicated stochastic dependencies. The Markovian minimal cut approach reduces the modelling and evaluation effort of real systems significantly because only a small number of Markovian states have to be modelled. In some applications the use of this approach first makes it possible to model and calculate the reliability of the system. The error of the approximations, induced by the Markovian path models have been proven to be less than 0.1% in practical systems. The approximations give the advantage of a result in an analytical context vs. pure computer-based numerical- or simulation-methods.

Keywords: Markovian minimal cuts, Markovian processes, minimal cuts, reliability of information and automation systems, system reliability