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Use este identificador para citar ou linkar para este item: https://repositorio.ufba.br/handle/ri/15571
Tipo: Artigo de Periódico
Título: Bayesian inference for power law processes with applications in repairable systems
Título(s) alternativo(s): Journal of Statistical Planning and Inference
Autor(es): Oliveira, Maristela Dias de
Colosimo, Enrico A.
Gilardoni, Gustavo L.
Autor(es): Oliveira, Maristela Dias de
Colosimo, Enrico A.
Gilardoni, Gustavo L.
Abstract: Statistical models for recurrent events are of great interest in repairable systems reliability and maintenance. The adopted model under minimal repair maintenance is frequently a nonhomogeneous Poisson process with the power law process (PLP) intensity function. Although inference for the PLP is generally based on maximum likelihood theory, some advantages of the Bayesian approach have been reported in the literature. In this paper it is proposed that the PLP intensity be reparametrized in terms of (β,η)(β,η), where ββ is the elasticity of the mean number of events with respect to time and ηη is the mean number of events for the period in which the system was actually observed. It is shown that ββ and ηη are orthogonal and that the likelihood becomes proportional to a product of gamma densities. Therefore, the family of natural conjugate priors is also a product of gammas. The idea is extended to the case that several realizations of the same PLP are observed along overlapping periods of time. Some Monte Carlo simulations are provided to study the frequentist behavior of the Bayesian estimates and to compare them with the maximum likelihood estimates. The results are applied to a real problem concerning the determination of the optimal periodicity of preventive maintenance for a set of power transformers. Prior distributions are elicited for ββ and ηη based on their operational interpretation and engineering expertise.
Palavras-chave: Conjugate prior
Optimal maintenance
Poisson Process
Posterior distribution
Reference priors
Tipo de Acesso: Acesso Aberto
URI: http://repositorio.ufba.br/ri/handle/ri/15571
Data do documento: 2012
Aparece nas coleções:Artigo Publicado em Periódico (IME)

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