Multicomponent Systems With Multiplicative Aging and Dependent Failures

Anastasiadis, Simon; Arnold, Richard; Chukova, Stefanka; Hayakawa, Yu

doi:10.1109/tr.2013.2241152

Cited by 11 publications

(9 citation statements)

References 29 publications

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“…However, since the external shocks are unobserved, these ageing shocks can mimic the continuous process satisfactorily, and this is of course the mechanism underlying the Marshall-Olkin shock model among others. 26,29 Associating the ageing shocks exclusively with the actual failures, as our simplest model proposes in the absence of ghost components, might appear to be too extreme a modelling restriction. However, we have found that even in large datasets the identifiability of submodels of different types (with or without ghost components and transient damage) is weak when only failure time data are available.…”

Section: Discussionmentioning

confidence: 97%

“…Including such a set of ghost components is straightforward for simulation: the failures of the ghost components are simulated just as those of ordinary components. With this construction the index sets A(t + a , t b jt) in the expressions for the conditional survival function (20) and the conditional hazard rate function (22) simply include any failures of components m + 1,.,m + g. Since each ghost component can affect a separate set of ordinary components with separate damage parameters f j' , c j' , this construction provides an additional mechanism by which dependence can be induced amongst subgroups of components, and is the same mechanism used by Anastasiadis et al 26 However since the failures of any ghost component are unobserved, this approach is complicated for inference. This is because for inference we need to integrate out the unobserved shock sequences from the likelihood (23), but the integral is not in general available in closed form.…”

Section: External Shocksmentioning

confidence: 99%

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Failure distributions in multicomponent systems with imperfect repairs

Arnold

Chukova

Hayakawa

2015

Proceedings of the Institution of Mechanical Engineers, Part O:

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We present a model for correlated failures in multicomponent systems where failed components are repaired. Due to these repairs multiple failures of each component are observable. Repair is instantaneous, but imperfect: in general the component is not returned to the good-as-new condition. Correlation amongst failures and the overall ageing of the system are modelled by treating each component failure as a shock which damages the other components in the system. We construct the likelihood for observations generated by such a system, and show how to simulate from this model. We demonstrate inference of the model parameters with simulated data and two real-world examples.

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Section: Discussionmentioning

confidence: 97%

Section: External Shocksmentioning

confidence: 99%

Failure distributions in multicomponent systems with imperfect repairs

Arnold

Chukova

Hayakawa

2015

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…In our two examples, we have shown how to fit commonly used parametric models to the underlying failure hazard rate

λ false(normalt false)

. More complex parametric formulations of

λ false(normalt false)

are of course possible, including ageing through shocks . Nonparametric estimation of

λ false(normalt false)

might be fruitful in situations where little is known about the true form of the hazard rate .…”

Section: Discussionmentioning

confidence: 99%

“…More complex parametric formulations of (t) are of course possible, including ageing through shocks. 13,14 Nonparametric estimation of (t) might be fruitful in situations where little is known about the true form of the hazard rate. 15 Likewise, there are many possible alternative specifications of the the failure and repair time distributions than the simple exponential we have presented here.…”

Section: Discussionmentioning

confidence: 99%

Nonzero repair times dependent on the failure hazard

Arnold

Chukova

Hayakawa

et al. 2019

Quality & Reliability Eng

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It is common in the literature on the reliability and maintenance of repairable systems to model the repair times as instantaneous. However, this is an unreasonable assumption for some complex systems, especially those requiring a high level of reliability, and such systems may spend a significant proportion of their lifetimes under maintenance and repair. We model the ageing of such a system with alternating stochastic processes. Operational times are generated at random and may have an increasing failure rate. Repair times are generated from a random process where the repair time is related to the hazard rate at failure. This yields lengthened repair times at late stages in a system subject to an increasing failure hazard rate but also accommodates long repair times at young ages in systems with a bathtub‐shaped hazard rate function. We derive analytic results for a set of special cases of the model, show how simulation and inference can be carried out, and apply our method to real data from a large car manufacturer.

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“…Anastasiadis et al [14] study a multi-component system where random shocks cause damage in several components, and model the statistical dependence among the components. In these studies that model the complex multi-component systems, analytical methods are derived for simplified models with several key assumptions, such as multiplicative aging structure and Poisson shock processes [14], whereas simulations have been often utilized for evaluating the reliability of a system with a high degree of complexity [15].…”

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confidence: 99%

Reliability Evaluation of Large-Scale Systems With Identical Units

Byon

2015

IEEE Trans. Rel.

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The reliability assessment of a large-scale system that considers its units' degradation is challenging due to the resulting dimensionality problem. We propose a new methodology that allows us to overcome difficulties in analyzing large-scale system dynamics, and devise analytical methods for finding the multivariate distribution of the dynamically changing system condition. When each unit's degradation condition can be classified into a finite number of states, and the transition distribution from one state to another is known, we obtain the asymptotic distribution of the number of units at each degradation state using fluid and diffusion limits. Specifically, we use a uniform acceleration technique, and obtain the time-varying mean vector and the covariance matrix of the number of units at multiple degradation states. When a state transition follows a non-Markovian deterioration process, we integrate phase-type distribution approximations with the fluid and diffusion limits. We show that, with any transition time distributions, the distribution of the number of units at multiple degradation conditions can be approximated by the multivariate Gaussian distribution as the total number of units gets large. The analytical results enable us to perform probabilistic assessment of the system condition during the system's service life. Our numerical studies suggest that the proposed methods can accurately characterize the stochastic evolution of the system condition over time.Index Terms-Degradation process, fluid and diffusion limits, Gaussian process, phase-type distribution, stochastic process. ACRONYMS AND ABBREVIATIONS RHSright-hand side ODE ordinary differential equation SDE stochastic differential equation EM Expectation-Maximization NOTATION total number of degradation states total number of units in the system, or system size Manuscript

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Multicomponent Systems With Multiplicative Aging and Dependent Failures

Cited by 11 publications

References 29 publications

Failure distributions in multicomponent systems with imperfect repairs

Failure distributions in multicomponent systems with imperfect repairs

Nonzero repair times dependent on the failure hazard

Reliability Evaluation of Large-Scale Systems With Identical Units

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