IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i8p1183-1189.html
   My bibliography  Save this article

Mean first passage times of two-dimensional processes with jumps

Author

Listed:
  • Bo, Lijun
  • Lefebvre, Mario

Abstract

In this paper, we incorporate a jump component into the model based on a two-dimensional degenerate diffusion process for the remaining lifetime of machines in the recent paper [Lefebvre, M., 2010. Mean first-passage time to zero for wear processes. Stochastic Models 26, 46-53] by the second author. We calculate explicitly the expected value of first passage times associated to the two-dimensional process when the jump component is taken to be a compound Poisson process with exponential jumps and random proportion of jumps.

Suggested Citation

  • Bo, Lijun & Lefebvre, Mario, 2011. "Mean first passage times of two-dimensional processes with jumps," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1183-1189, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1183-1189
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521100099X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Mimi & Gaudoin, Olivier & Xie, Min, 2015. "Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 245(2), pages 531-541.
    2. Song, Kai & Shi, Jian & Yi, Xiaojian, 2020. "A time-discrete and zero-adjusted gamma process model with application to degradation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    3. 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.
    4. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    5. Tianyu Liu & Zhengqiang Pan & Quan Sun & Jing Feng & Yanzhen Tang, 2017. "Residual useful life estimation for products with two performance characteristics based on a bivariate Wiener process," Journal of Risk and Reliability, , vol. 231(1), pages 69-80, February.
    6. Pang, Zhenan & Li, Tianmei & Pei, Hong & Si, Xiaosheng, 2023. "A condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    7. Xudan Chen & Guoxun Ji & Xinli Sun & Zhen Li, 2019. "Inverse Gaussian–based model with measurement errors for degradation analysis," Journal of Risk and Reliability, , vol. 233(6), pages 1086-1098, December.
    8. Zhai, Qingqing & Chen, Piao & Hong, Lanqing & Shen, Lijuan, 2018. "A random-effects Wiener degradation model based on accelerated failure time," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 94-103.
    9. Jin, Guang & Matthews, David E. & Zhou, Zhongbao, 2013. "A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 7-20.
    10. David T. Abdul‐Malak & Jeffrey P. Kharoufeh & Lisa M. Maillart, 2019. "Maintaining systems with heterogeneous spare parts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 485-501, September.
    11. 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.
    12. Huang, Zhelin & Xu, Fan & Yang, Fangfang, 2023. "State of health prediction of lithium-ion batteries based on autoregression with exogenous variables model," Energy, Elsevier, vol. 262(PB).
    13. Liu, Di & Wang, Shaoping & Cui, Xiaoyu, 2022. "An artificial neural network supported Wiener process based reliability estimation method considering individual difference and measurement error," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    14. Shengjin Tang & Chuanqiang Yu & Xue Wang & Xiaosong Guo & Xiaosheng Si, 2014. "Remaining Useful Life Prediction of Lithium-Ion Batteries Based on the Wiener Process with Measurement Error," Energies, MDPI, vol. 7(2), pages 1-28, January.
    15. Zhou, Shirong & Tang, Yincai & Xu, Ancha, 2021. "A generalized Wiener process with dependent degradation rate and volatility and time-varying mean-to-variance ratio," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    16. Wang, Changxi & Elsayed, Elsayed A., 2020. "Stochastic modeling of corrosion growth," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    17. Yi Xiong & W. John Braun & X. Joan Hu, 2021. "Estimating duration distribution aided by auxiliary longitudinal measures in presence of missing time origin," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 388-412, July.
    18. Wang, Huan & Wang, Guan-jun & Duan, Feng-jun, 2016. "Planning of step-stress accelerated degradation test based on the inverse Gaussian process," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 97-105.
    19. Wang, Zhijie & Zhai, Qingqing & Chen, Piao, 2021. "Degradation modeling considering unit-to-unit heterogeneity-A general model and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    20. Hao, Songhua & Yang, Jun & Berenguer, Christophe, 2019. "Degradation analysis based on an extended inverse Gaussian process model with skew-normal random effects and measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 261-270.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1183-1189. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.