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A time-discrete extended gamma process for time-dependent degradation phenomena

Author

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  • Guida, M.
  • Postiglione, F.
  • Pulcini, G.

Abstract

The non-stationary Gamma process is a widely used mathematical model to describe degradation phenomena whose growth rate at time t depends only on the current age of the item and not on the accumulated damage up to t. Nevertheless, the Gamma process is not a proper choice when there is empirical evidence that the variance-to-mean ratio of the process varies with time, because the Gamma process implies a constant variance-to-mean ratio. This paper proposes a generalization of the non-stationary Gamma process, which can be viewed as a time discretization of the extended Gamma process and allows one to describe time-dependent degradation phenomena whose variance varies with time t, not necessarily in proportion to the mean. A way to approximate the exact distribution of the degradation growth over a given time interval is given and a test for assessing whether the assumption of the Gamma process can be rejected or not is discussed. Finally, the proposed model is applied to a real dataset consisting of the sliding wear data of four metal alloy specimens.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:105:y:2012:i:c:p:73-79
    DOI: 10.1016/j.ress.2011.12.016
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    References listed on IDEAS

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    1. Nicolai, Robin P. & Dekker, Rommert & van Noortwijk, Jan M., 2007. "A comparison of models for measurable deterioration: An application to coatings on steel structures," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1635-1650.
    2. 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.
    3. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
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    Cited by:

    1. Yang, Yiming & Peng, Jianxin & Cai, C.S. & Zhou, Yadong & Wang, Lei & Zhang, Jianren, 2022. "Time-dependent reliability assessment of aging structures considering stochastic resistance degradation process," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    2. Wang, Xiaofei & Wang, Bing Xing & Hong, Yili & Jiang, Pei Hua, 2021. "Degradation data analysis based on gamma process with random effects," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1200-1208.
    3. 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).
    4. Guida, Maurizio & Postiglione, Fabio & Pulcini, Gianpaolo, 2015. "A random-effects model for long-term degradation analysis of solid oxide fuel cells," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 88-98.
    5. Geng, Yixuan & Wang, Shaoping & Shi, Jian & Zhang, Yuwei & Wang, Weijie, 2023. "Reliability modeling of phased degradation under external shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    6. Sophie Mercier & Carmen Sangüesa, 2023. "A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 91-129, January.
    7. Pedersen, Tom Ivar & Liu, Xingheng & Vatn, Jørn, 2023. "Maintenance optimization of a system subject to two-stage degradation, hard failure, and imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    8. Wang, Lizhi & Pan, Rong & Li, Xiaoyang & Jiang, Tongmin, 2013. "A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 38-47.
    9. Guida, M. & Pulcini, G., 2013. "The inverse Gamma process: A family of continuous stochastic models for describing state-dependent deterioration phenomena," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 72-79.
    10. Zeina Al Masry & Sophie Mercier & Ghislain Verdier, 2017. "Approximate Simulation Techniques and Distribution of an Extended Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 213-235, March.
    11. Peng, Weiwen & Li, Yan-Feng & Mi, Jinhua & Yu, Le & Huang, Hong-Zhong, 2016. "Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 75-87.
    12. Ayman Hijazy & András Zempléni, 2021. "Gamma Process-Based Models for Disease Progression," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 241-255, March.

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