Optimization of the device of stages through genetic algorithms for non-Markovian systems reliability evaluation: An application to nuclear safety systems

When a safety system is under aging effects, failures times follow non-exponential distributions, and the transition rates become time-dependent. The stochastic process employed in the modeling becomes Non-markovian. In this paper, this analysis is developed using an alternative method, the device of stages, which allows the transformation of Non-markovian models into equivalent Markovian ones. The transformation consists in reshaping the initial state transition diagram into a new one where fictitious states (stages) are added and whose transition rate are constant. The number of added stages and their connections are identification parameters of the stage configuration used for the equivalentMarkovian model and depend on the initial transitions rate. Overcoming the aforementioned difficulties is a complex optimization problem. In order to perform a global search in such a topologically complex space, a genetic algorithm has been developed to automatically determine the combination of stages and the set of parameters which better represent the analyzed distribution. The developed genetic algorithm has demonstrated a good ability for optimizing the method of stages. Results concerning initial applications to nuclear safety system pumps are shown and discussed, for which Weibull and log-normal distributions are employed for modeling the failure times.