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Life distribution analysis based on Lévy subordinators for degradation with random jumps

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  • Yin Shu
  • Qianmei Feng
  • David W. Coit

Abstract

For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumps using a single stochastic process based on the characteristics of Lévy subordinators, the class of nondecreasing Lévy processes. Based on the inverse Fourier transform, we derive a new closed‐form reliability function and probability density function for lifetime, represented by Lévy measures. The reliability function derived using the traditional convolution approach for common stochastic models such as gamma degradation process with random jumps, is revealed to be a special case of our general model. Numerical experiments are used to demonstrate that our model performs well for different applications, when compared with the traditional convolution method. More importantly, it is a general and useful tool for life distribution analysis of stochastic degradation with random jumps in multidimensional cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 483–492, 2015

Suggested Citation

  • Yin Shu & Qianmei Feng & David W. Coit, 2015. "Life distribution analysis based on Lévy subordinators for degradation with random jumps," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 483-492, September.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:6:p:483-492
    DOI: 10.1002/nav.21642
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    References listed on IDEAS

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    Cited by:

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    2. Narayanaswamy Balakrishnan & Chengwei Qin, 2019. "First Passage Time of a Lévy Degradation Model with Random Effects," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 315-329, March.
    3. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    4. Chengyu Zhou & Xiaolei Fang, 2024. "A Supervised Tensor Dimension Reduction-Based Prognostic Model for Applications with Incomplete Imaging Data," INFORMS Joural on Data Science, INFORMS, vol. 3(1), pages 84-104, April.
    5. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    6. Dong, Qinglai & Cui, Lirong, 2019. "A study on stochastic degradation process models under different types of failure Thresholds," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 202-212.

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