Reliability of Some Ageing Nuclear Power Plant Systems: a Simple Stochastic Model

The random number of failure-related events in certain repairable ageing systems, like certain nuclear power plant components, during a given time interval, may be often modelled by a compound Poisson distribution. One of these is the Polya-Aeppli distribution. The derivation of a stationary Polya-Aeppli distribution as a limiting distribution of rare events for stationary Bernouilli trials with first order Markov dependence is considered. But if the parameters of the Polya-Aeppli distribution are suitable time functions, we could expect that the resulting distribution would allow us to take into account the distribution of failure-related events in an ageing system. Assuming that a critical number of damages produce an emergent failure, the abovementioned results can be applied in a reliability analysis. It is natural to ask under what conditions a Polya-Aeppli distribution could be a limiting distribution for non-homogeneous Bernouilli trials with first order Markov dependence. In this paper this problem is analyzed and possible applications of the obtained results to ageing or deteriorating nuclear power plant components are considered. The two traditional ways of modelling repairable systems in reliability theory: the “as bad as old” concept, that assumes that the replaced component is exactly under the same conditions as was the aged component before failure, and the “as good as new” concept, that assumes that the new component is under the same conditions of the replaced component when it was new, are briefly discussed in relation with the findings of the present work.