Stemming from a consulting project about a gas distribution network, a new, Bayesian model is proposed to describe failures in a complex, expanding over time, repairable system, which is split into components installed over different years. Both exchangeable and independent Poisson processes, homogeneous in space but not in time, are used to model the components. The model takes also into account missing data, due either to unrecorded early failures or unknown installation dates of failed parts. Actual escape data from a gas distribution network illustrate the implementation of the model, which relies on the use of Markov chain Monte Carlo methods.
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Pievatolo et al. (2004) studied this question.
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