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

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.