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Lifetime prognostics for deteriorating systems with time-varying random jumps

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  • Zhang, Jian-Xun
  • Hu, Chang-Hua
  • He, Xiao
  • Si, Xiao-Sheng
  • Liu, Yang
  • Zhou, Dong-Hua

Abstract

In this paper, we propose a jump diffusion process with non-homogeneous compound Poisson process to model the degradation process with randomly occurring jumps, which combines two stochastic processes, i.e., traditional diffusion process to describe the continuous degradation and non-homogeneous compound Poisson process to depict random jumps with a time-varying intensity. The approximated analytical lifetime under the concept of the first passage time (FPT) is obtained by a time–space transformation technique. To identify the model parameters, we first present a general method based on Maximum Likelihood Estimation (MLE) for the proposed model, and then specifically provide a two-step approach for linear jump diffusion process via combining MLE and Expectation Conditional Maximization (ECM) algorithm. Finally, a numerical example and a study on the furnace wall are provided to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Zhang, Jian-Xun & Hu, Chang-Hua & He, Xiao & Si, Xiao-Sheng & Liu, Yang & Zhou, Dong-Hua, 2017. "Lifetime prognostics for deteriorating systems with time-varying random jumps," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 338-350.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:338-350
    DOI: 10.1016/j.ress.2017.05.047
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    References listed on IDEAS

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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
    3. Michael E. Cholette & Dragan Djurdjanovic, 2014. "Degradation modeling and monitoring of machines using operation-specific hidden Markov models," IISE Transactions, Taylor & Francis Journals, vol. 46(10), pages 1107-1123, October.
    4. Le Son, Khanh & Fouladirad, Mitra & Barros, Anne & Levrat, Eric & Iung, Benoît, 2013. "Remaining useful life estimation based on stochastic deterioration models: A comparative study," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 165-175.
    5. Chen, Nan & Ye, Zhi-Sheng & Xiang, Yisha & Zhang, Linmiao, 2015. "Condition-based maintenance using the inverse Gaussian degradation model," European Journal of Operational Research, Elsevier, vol. 243(1), pages 190-199.
    6. Li, Mingyang & Liu, Jian, 2016. "Bayesian hazard modeling based on lifetime data with latent heterogeneity," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 183-189.
    7. Mario Abundo, 2010. "On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 473-490, September.
    8. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    9. Altun, Mustafa & Comert, Salih Vehbi, 2016. "A change-point based reliability prediction model using field return data," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 175-184.
    10. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    11. Sheng-Tsaing Tseng & Nan-Jung Hsu & Yi-Chiao Lin, 2016. "Joint modeling of laboratory and field data with application to warranty prediction for highly reliable products," IISE Transactions, Taylor & Francis Journals, vol. 48(8), pages 710-719, August.
    12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    13. Hao Peng & Qianmei Feng & David Coit, 2010. "Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes," IISE Transactions, Taylor & Francis Journals, vol. 43(1), pages 12-22.
    14. Ye, Zhi-Sheng & Chen, Nan & Shen, Yan, 2015. "A new class of Wiener process models for degradation analysis," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 58-67.
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    Cited by:

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    2. Jingyuan Shen & Alaa Elwany & Lirong Cui, 2018. "Reliability modeling for systems degrading in K cyclical regimes based on gamma processes," Journal of Risk and Reliability, , vol. 232(6), pages 754-765, December.
    3. Yan, Tao & Lei, Yaguo & Li, Naipeng & Wang, Biao & Wang, Wenting, 2021. "Degradation modeling and remaining useful life prediction for dependent competing failure processes," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    4. Jianxun Zhang & Xiao He & Xiaosheng Si & Changhua Hu & Donghua Zhou, 2017. "A Novel Multi-Phase Stochastic Model for Lithium-Ion Batteries’ Degradation with Regeneration Phenomena," Energies, MDPI, vol. 10(11), pages 1-24, October.

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