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BAYESIAN INFERENCE FOR REPAIR MODEL SUBJECT TO MULTITYPE RECURRENT EVENTS
Multitype events (or competing risks) models for a repairable system subject to multiple failure types are discussed. Under minimal repair, it is assumed that each failure type 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 The methodology is applied in the analysis of (i) a previously unpublished dataset about recurrent failure history of a sugarcane harvester and (ii) records of automotive warranty claims. A simulation study was carried out to study the efficiency of the methods proposed.
Bayesian analysis, competing risks, power law process, reference prior, Jeffreys prior, repair
Marco Pollo Almeida, Vera L D Tomazella, Gustavo L Gilardoni Avalle , Pedro L Ramos, Francisco Louzada Neto