A virtual age model based on a bathtub shaped initial intensity

Dijoux, Yann

doi:10.1016/j.ress.2008.11.004

Cited by 33 publications

(32 citation statements)

References 12 publications

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“…Also, in this paper, a unique value was assumed for the parameter r and it may not be the same for all periods of system's lifecycle when it is related to non-monotone failure intensities. Dijoux [41] addressed this problem with the Weibull-GRP making assumptions of repairs and using different virtual ages to each phase of the bathtub curve resulting in a complex system with an elevated number of parameters to be estimated, which is rather not viable in practice. These issues are topics of ongoing research, along with the investigation of other q-distributions to be coupled with GRP.…”

Section: Discussionmentioning

confidence: 99%

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Lins

Moura

Droguett

et al. 2018

Entropy

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Abstract:The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis' non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters' estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.

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Section: Discussionmentioning

confidence: 99%

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Lins

Moura

Droguett

et al. 2018

Entropy

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“…The majority of the approaches of the maintenance are based on reliability such as Peña and al., 2007, Y. Dijoux (2009), L. Doyen (2012). However, the reliability of the industrial systems depend closely on the efficiency of these maintenance actions and the effective management of the maintenance policy wich requires a realistic modeling of their effects.…”

Section: Introductionmentioning

confidence: 99%

Expectation-Maximization Algorithms for Obtaining Estimations of Generalized Failure Intensity Parameters

Krit¹,

Mili²

2016

ijacsa

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Abstract-This paper presents several iterative methods based on Stochastic Expectation-Maximization (EM) methodology in order to estimate parametric reliability models for randomly lifetime data. The methodology is related to Maximum Likelihood Estimates (MLE) in the case of missing data. A bathtub form of failure intensity formulation of a repairable system reliability is presented where the estimation of its parameters is considered through EM algorithm . Field of failures data from industrial site are used to fit the model. Finally, the interval estimation basing on large-sample in literature is discussed and the examination of the actual coverage probabilities of these confidence intervals is presented using Monte Carlo simulation method.

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“…Relevant literature presents mathematical models that assist the process of reaction to object failure e.g. [2,3,10,12], procedures that describe and compare classes of forecast models (e.g. [4,17]) or assist in the forecasting of failures of nonrenewable technical objects in the wear-out period (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In [2] a method is proposed of detecting the onset of the object wear-out period and determining the maintenance efficiency based on, as the authors of [2] would call it, a step model of aging and the Bayes techniques. In [3] a new reliability model is presented of complex repaired technical objects/systems based on the bathtub curve.…”

Section: Introductionmentioning

confidence: 99%

The determination procedure of the onset of the object wear-out period based on monitoring of the empirical failure intensity function

Gill

Kadziński

2015

Eksploatacja i Niezawodnosc - Maintenance and Reliability

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A virtual age model based on a bathtub shaped initial intensity

Cited by 33 publications

References 12 publications

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Expectation-Maximization Algorithms for Obtaining Estimations of Generalized Failure Intensity Parameters

The determination procedure of the onset of the object wear-out period based on monitoring of the empirical failure intensity function

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