Analysis of joint multiple failure mode and linear degradation data with renewals

Bagdonavičius, Vilijandas; Bikelis, A.; Kazakevičius, Vytautas; Nikulin, Mikhaïl

doi:10.1016/j.jspi.2006.07.002

Cited by 24 publications

(9 citation statements)

References 13 publications

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“…Here, we discuss the estimation of parameters required to implement the reliability function in (20). The unknown parameters are…”

Section: Statistical Inferential Methods For Unknown Parametersmentioning

confidence: 99%

“…From (17), (18), and (20), we know that the model not only has nine parameters but also is very complicated from Mathematical Problems in Engineering 5 a computational viewpoint. For this reason, the MCMC with the Gibbs sampling techniques is employed in this study to estimate model parameters.…”

Section: Statistical Inferential Methods For Unknown Parametersmentioning

confidence: 99%

“…There is little literature to consider multivariate PCs. Related work can be found in [17][18][19][20]. However, these works use either independence assumption of the multiple PCs or multivariate normal distribution.…”

Section: Introductionmentioning

confidence: 99%

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Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

Hao

2014

Mathematical Problems in Engineering

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A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

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“…Here, we discuss the estimation of parameters required to implement the reliability function in (20). The unknown parameters are…”

Section: Statistical Inferential Methods For Unknown Parametersmentioning

confidence: 99%

Section: Statistical Inferential Methods For Unknown Parametersmentioning

confidence: 99%

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Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

Hao

2014

Mathematical Problems in Engineering

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“…Lehmann surveyed some approaches to model the relationship between failure time data and covariate data like internal degradation and external environment models [13]. Bagdonavičius et al made use of the half updating process of the linear degradation model to study the non-parameter estimation method of competing failure model, and to simplify the calculation, the model used decomposition method [1]. Pareek et al studied the problem of censored data processing for competing failures [16].…”

Section: Introductionmentioning

confidence: 99%

Operation reliability analysis based on fuzzy support vector machine for aircraft engines

Gao

Wang

2015

Eksploatacja i Niezawodnosc - Maintenance and Reliability

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“…There are some works on the estimation of product reliability of bivariate or multivariate degradation data; see Huang and Askin (2003), Bagdonavicius et al (2004Bagdonavicius et al ( , 2007. But they only considered independence assumption or multivariate normal distribution of the multiple PCs.…”

Section: Introductionmentioning

confidence: 99%

Reliability Modeling and Inference with Multiple Performance Characteristics

Hao¹,

Su²

2014

Computers and Advanced Technology in Education / 820: Modelling, Simulation and Identification / 821: Environmental Management

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Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e. illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that a product has two performance characteristics, and each performance characteristic is governed by a random effected Wiener process where random effects capture the unit to unit differences. The random effected model is fitted to the actual data and corresponding goodness of fit tests are carried out. The dependency of performance characteristics is described by a Frank copula function. The inference for margins method and Markov chain Monte Carlo method are used to obtain the estimators of the corresponding model unknown parameters. A numerical example about an actual LED lamps experiment data is given to demonstrate the usefulness and validity of the proposed model and method.

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Analysis of joint multiple failure mode and linear degradation data with renewals

Cited by 24 publications

References 13 publications

Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

Operation reliability analysis based on fuzzy support vector machine for aircraft engines

Reliability Modeling and Inference with Multiple Performance Characteristics

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