Numerical solution of reliability models described by stochastic automata networks

•Steady–state solution of Markov chain reliability models is considered.•Block Gauss–Seidel method can be efficiently implemented for steady–state solution.•Reliability model with ∼2 millions of states can be solved in just a few seconds. This paper presents the solution of Markov chain reliability...

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Bibliographic Details
Published in:Reliability engineering & system safety 2018-01, Vol.169, p.570-578
Main Authors: Šnipas, Mindaugas, Radziukynas, Virginijus, Valakevičius, Eimutis
Format: Article
Language:English
Subjects:
Electrical transmission
Gauss-Seidel method
Markov analysis
Markov chains
Network reliability
Numerical methods
Probability
Reliability analysis
Reliability engineering
Reliability modelling
Steady-state probabilities
Stochastic automata networks
Stochastic models
Studies
System reliability
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Summary:•Steady–state solution of Markov chain reliability models is considered.•Block Gauss–Seidel method can be efficiently implemented for steady–state solution.•Reliability model with ∼2 millions of states can be solved in just a few seconds. This paper presents the solution of Markov chain reliability models with a large state-space. To specify a system reliability model, we use our previously proposed methodology, which is based on the Stochastic Automata Networks formalism. We model parts of the system by arrowhead matrices with functional transition rates. As a result, the infinitesimal generator matrix of the reliability model has a distinctive structure. In this paper, we demonstrate that a block Gauss–Seidel method can be applied very efficiently to such a structure. The application of the proposed methodology is illustrated by an example of a standard 3/2 substation configuration. Even though its Markov chain reliability model has almost two million states, its steady-state probabilities can be estimated in just a few seconds of CPU time.
ISSN:0951-8320
1879-0836
DOI:10.1016/j.ress.2017.09.024