Bayesian inference for the power law process

Bar‐Lev, Shaul K.; Lavi, Idit; Reiser, Benjamin

doi:10.1007/bf00053394

Cited by 52 publications

(18 citation statements)

References 13 publications

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“…A two-stage non-homogeneous Poisson process is considered and the approach that is employed was first described by Maul and Robinson (2006). There are similarities with problems that are considered in reliability modelling where a power law intensity function is considered (see, for example Guida et al (1989), Bar-Lev et al (1992), Kim et al (2005) and Yu et al (2007)). The key differences between the present problem and these studies are as follows.…”

Section: Fig 3 Stresses In a Graphite Brickmentioning

confidence: 95%

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Statistical Modelling of Graphite Brick Cracking in Advanced Gas-Cooled Reactors

Maul

Robinson

Northrop

2011

Journal of the Royal Statistical Society Series C: Applied Statistics

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Graphite cores in advanced gas-cooled nuclear reactors contain bricks which are subject to cracking and periodic inspections provide information on the state of a sample of the bricks. Statistical models are fitted to the historic data and used to predict the numbers of cracked bricks that are expected to be seen at reactor inspections. As more data have become available the complexity of the best performing models has increased. By repeatedly making blind predictions of core behaviour the predictive performance of the models can be quantified and they can then be used to forecast behaviour of the core over longer periods.

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Section: Fig 3 Stresses In a Graphite Brickmentioning

confidence: 95%

“…When K = 1 the hazard function follows the power law intensity function that was employed in the reliability modelling studies that were previously referred to (Guida et al, 1989;Bar-Lev et al, 1992;Kim et al, 2005;Yu et al, 2007).…”

Section: Statistical Modelsmentioning

confidence: 99%

Statistical Modelling of Graphite Brick Cracking in Advanced Gas-Cooled Reactors

Maul

Robinson

Northrop

2011

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…However, even if the mathematics is conceptually different, the posterior prediction on t n+m and that on M τ are still given by (15) and (19), respectively, with V = n i=1 t i and Z (β) = T β Whenever no overhaul is assumed to be performed at T, then the failure process evolves as a PLP also after T, and hence, the Bayes prediction procedures proposed for the PLP (see, for example, Calabria et al [9], Bar-Lev et al [10] and Beiser and Rigdon [11]) can be applied.…”

Section: Final Remarksmentioning

confidence: 99%

On the Prediction of Future Failures for a Repairable Equipment Subject to Overhauls

Pulcini

2001

Communications in Statistics - Theory and Methods

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This paper deals with the prediction, from a Bayes viewpoint, of future failures for a repairable equipment subjected both to minimal repairs and periodic overhauls. The effect of major overhauls on the reliability of the equipment is modeled by a proportional age reduction model, while the failure process between two successive overhaul epochs is modeled by the power law process. Prediction both of the future failure times and of the number of failures in a future time interval are provided on the basis of the observed data and of a number of suitable prior densities, which reflect different degrees of belief on the failure mechanism and overhaul effectiveness. Finally, a numerical application illustrates the proposed prediction procedures and their use in assessing the adequacy of the model to describe the observed data set.

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“…Failures of such repairable systems are often described by means of nonhomogeneous Poisson processes (NHPP), mainly the Power Law process (PLP); see, among others Ascher and Feingold (1984), Bain and Engelhardt (1991), Crow (1974), Crow (1982), Thompson (1988) and, for a review of Bayesian literature on PLP, Bar-Lev et al (1992). Other NHPPs have been considered in, e.g.…”

Section: Introductionmentioning

confidence: 99%