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Science and Technology of Nuclear Installations
Volume 2014, Article ID 242408, 8 pages
Research Article

Simplification of State Transition Diagrams in Average Unavailability Analysis by Using Generalized Perturbation Theory

Graduate Program of Nuclear Engineering, Federal University of Rio de Janeiro, Avenida Horácio Macedo 2030, Bloco G, Sala 206, 21941-914 Rio de Janeiro, RJ, Brazil

Received 30 October 2013; Revised 21 February 2014; Accepted 21 February 2014; Published 17 April 2014

Academic Editor: Borut Mavko

Copyright © 2014 R. C. Vicente et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Safety analysis studies in nuclear engineering, more specifically system reliability, usually handle a great number of components, so that computational difficulties may arise. To face the problem of many component systems a method for simplifying the state transition diagram in Markovian reliability analyses has been proposed, using the edges which can be cut, since these latter have a smaller influence on system failure probability. In order to extend the application of GPT (Generalized Perturbation Theory), this work uses GPT formalism to reduce the number of states in a transition diagram, not considering the state probability as the integral quantity of interest, but the mean system unavailability instead. Therefore, after simplifying the original diagram, the mean unavailability for the new system was calculated and the results were very close to those of the original diagram integral quantity (giving a relative error of about 2%), showing that the proposed simplification is quite reasonable and simple to apply.