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Gamma processes and peaks-over-threshold distributions for time-dependent reliability

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  • van Noortwijk, J.M.
  • van der Weide, J.A.M.
  • Kallen, M.J.
  • Pandey, M.D.

Abstract

In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural component. The deterioration process is modelled as a gamma process, which is a stochastic process with independent non-negative increments having a gamma distribution with identical scale parameter. The stochastic process of loads is generated by a Poisson process. The variability of the random loads is modelled by a peaks-over-threshold distribution (such as the generalised Pareto distribution). These stochastic processes of deterioration and load are combined to evaluate the time-dependent reliability.

Suggested Citation

  • van Noortwijk, J.M. & van der Weide, J.A.M. & Kallen, M.J. & Pandey, M.D., 2007. "Gamma processes and peaks-over-threshold distributions for time-dependent reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1651-1658.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:12:p:1651-1658
    DOI: 10.1016/j.ress.2006.11.003
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    Cited by:

    1. Huynh, K.T. & Barros, A. & Bérenguer, C. & Castro, I.T., 2011. "A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 497-508.
    2. Huynh, K.T. & Castro, I.T. & Barros, A. & Bérenguer, C., 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," European Journal of Operational Research, Elsevier, vol. 218(1), pages 140-151.
    3. Pan, Zhengqiang & Balakrishnan, Narayanaswamy, 2011. "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 949-957.
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    7. Chang, Miaoxin & Huang, Xianzhen & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2021. "Reliability analysis for systems based on degradation rates and hard failure thresholds changing with degradation levels," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Jiang, Chen & Yan, Yifang & Wang, Dapeng & Qiu, Haobo & Gao, Liang, 2021. "Global and local Kriging limit state approximation for time-dependent reliability-based design optimization through wrong-classification probability," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    9. Houda Ghamlouch & Mitra Fouladirad & Antoine Grall, 2019. "The use of real option in condition-based maintenance scheduling for wind turbines with production and deterioration uncertainties," Post-Print hal-02365402, HAL.
    10. Finkelstein, Maxim & Ludick, Zani, 2014. "On some steady-state characteristics of systems with gradual repair," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 17-23.
    11. Guida, M. & Postiglione, F. & Pulcini, G., 2012. "A time-discrete extended gamma process for time-dependent degradation phenomena," Reliability Engineering and System Safety, Elsevier, vol. 105(C), pages 73-79.
    12. Junxiang Li & Jianqiao Chen & Zhiqiang Chen, 2020. "A new cumulative damage model for time-dependent reliability analysis of deteriorating structures," Journal of Risk and Reliability, , vol. 234(2), pages 290-302, April.
    13. Wang, Zhonglai & Liu, Jing & Yu, Shui, 2020. "Time-variant reliability prediction for dynamic systems using partial information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    14. Cheng, Tianjin & Pandey, Mahesh D. & van der Weide, J.A.M., 2012. "The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 65-76.
    15. Song, Sanling & Coit, David W. & Feng, Qianmei, 2014. "Reliability for systems of degrading components with distinct component shock sets," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 115-124.
    16. George-Williams, H. & Wade, N. & Carpenter, R.N., 2022. "A probabilistic framework for the techno-economic assessment of smart energy hubs for electric vehicle charging," Renewable and Sustainable Energy Reviews, Elsevier, vol. 162(C).
    17. Junyu Guo & Hong-Zhong Huang & Weiwen Peng & Jie Zhou, 2019. "Bayesian information fusion for degradation analysis of deteriorating products with individual heterogeneity," Journal of Risk and Reliability, , vol. 233(4), pages 615-622, August.
    18. 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.
    19. Petchrompo, Sanyapong & Li, Hao & Erguido, Asier & Riches, Chris & Parlikad, Ajith Kumar, 2020. "A value-based approach to optimizing long-term maintenance plans for a multi-asset k-out-of-N system," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    20. Aryai, Vahid & Baji, Hassan & Mahmoodian, Mojtaba & Li, Chun-Qing, 2020. "Time-dependent finite element reliability assessment of cast-iron water pipes subjected to spatio-temporal correlated corrosion process," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    21. Ghamlouch, Houda & Fouladirad, Mitra & Grall, Antoine, 2019. "The use of real option in condition-based maintenance scheduling for wind turbines with production and deterioration uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 614-623.
    22. Xiaojia Wang & Ting Huang & Keyu Zhu & Xibin Zhao, 2022. "LSTM-Based Broad Learning System for Remaining Useful Life Prediction," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    23. 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.
    24. Wang, Zequn & Wang, Pingfeng, 2013. "A new approach for reliability analysis with time-variant performance characteristics," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 70-81.
    25. 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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