  Competing risks models for a repairable system subject to several failure
modes are discussed. Under minimal repair, it is assumed that each failure mode
has a power law intensity. An orthogonal reparametrization is used to obtain an
objective Bayesian prior which is invariant under relabelling of the failure
modes. The resulting posterior is a product of gamma distributions and has
appealing properties: one-to-one invariance, consistent marginalization and
consistent sampling properties. Moreover, the resulting Bayes estimators have
closed-form expressions and are naturally unbiased for all the parameters of
the model. The methodology is applied in the analysis of (i) a previously
unpublished dataset about recurrent failure history of a sugarcane harvester
and (ii) records of automotive warranty claims introduced in [1]. A simulation
study was carried out to study the efficiency of the methods proposed.
