Bayesian imperfect repair model

Lim, Jae‐Hak; Lu, Kun-Liang; Park, Dong Ho

doi:10.1080/03610929808832138

Cited by 31 publications

(14 citation statements)

References 7 publications

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“…This model was proposed by Brown and Proschan [30] and it is known as imperfect repair model. Following [31], we can generalize this model assuming that p i depends on some m-dimensional random environment , that is, given = θ, then p i = p i (θ). If we denote by Π(θ) the joint distribution function of , and S = (S 1 , .…”

Section: Respectivelymentioning

confidence: 99%

Stochastic comparisons of multivariate mixture models

Belzunce

Mercader

Ruiz

et al. 2009

Journal of Multivariate Analysis

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Likelihood ratio Hazard rate and mean residual life orders Multivariate mixture models a b s t r a c tIn this paper we consider sufficient conditions in order to stochastically compare random vectors of multivariate mixture models. In particular we consider stochastic and convex orders, the likelihood ratio order, and the hazard rate and mean residual life dynamic orders. Applications to proportional hazard models and mixture models in risk theory are also given.

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Section: Respectivelymentioning

confidence: 99%

Stochastic comparisons of multivariate mixture models

Belzunce

Mercader

Ruiz

et al. 2009

Journal of Multivariate Analysis

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“…Lim et al [8] proposed that the probability of perfect repair in Model 1.1 may not be predetermined in the most real situations. It is reasonable to view the probability of perfect repair as a variable and to consider its prior distribution, instead of fixing the probability in advance.…”

Section: Downloaded By [Chulalongkorn University] At 16:58 27 Decembementioning

confidence: 99%

Bayesian multivariate imperfect repair model

Sheu¹,

Chang²

2010

Journal of Statistics and Management Systems

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This paper generalizes a multivariate imperfect repair model by adapting a Bayesian approach. We concern with modeling a system whose components have specific multivariate distribution of dependent lifelengths. Upon failure, each components undergoes imperfect repair. Different sources of failure which affect the probabilities of perfect and minimal repair are distinguished. Each probability of perfect (minimal) repair is assumed unknown and assigned a prior distribution. Based on the proposed model, we derive the distribution of waiting time between two successive perfect repairs and its corresponding failure rates. We also study some preservation properties for certain nonparametric classes of life distributions and describe the singularity for the resulting distribution.

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“…According to Lim et al (1998) consider a lifetime unit with cdf G. Let P be a random probability (that is, P takes on values in [0, 1]), where the realized value of P is the probability of minimal repair of the unit. The waiting time X for the first perfect repair has the sfF(x) = E(Ḡ V (x)), in which V = 1 − P plays the role of a frailty variable here.…”

Section: Theorem 42 Let η(V) Be Star-shaped (Anti-star-shaped) Inmentioning

confidence: 99%