Methodology and Computing in Applied Probability

, Volume 12, Issue 3, pp 431–449 | Cite as

Numerical Approach for Assessing System Dynamic Availability Via Continuous Time Homogeneous Semi-Markov Processes

  • Márcio das Chagas MouraEmail author
  • Enrique López Droguett


Continuous-time homogeneous semi-Markov processes (CTHSMP) are important stochastic tools to model reliability measures for systems whose future behavior is dependent on the current and next states occupied by the process as well as on sojourn times in these states. A method to solve the interval transition probabilities of CTHSMP consists of directly applying any general quadrature method to the N 2 coupled integral equations which describe the future behavior of a CTHSMP, where N is the number of states. However, the major drawback of this approach is its considerable computational effort. In this work, it is proposed a new more efficient numerical approach for CTHSMPs described through either transition probabilities or transition rates. Rather than N 2 coupled integral equations, the approach consists of solving only N coupled integral equations and N straightforward integrations. Two examples in the context of availability assessment are presented in order to validate the effectiveness of this method against the comparison with the results provided by the classical and Monte Carlo approaches. From these examples, it is shown that the proposed approach is significantly less time-consuming and has accuracy comparable to the method of N 2 computational effort.


Homogeneous semi-markov processes Integral equations Quadrature methods Availability assessment Reliability 

AMS 2000 Subject Classification

60K10 60K15 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Márcio das Chagas Moura
    • 1
    Email author
  • Enrique López Droguett
    • 1
  1. 1.Department of Production EngineeringFederal University of PernambucoRecifeBrazil

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