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Failure Time of Non Homogeneous Gamma Process

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  • Christian Paroissin
  • Ali Salami

Abstract

We consider the non homogeneous gamma process as a degradation model. The hitting time of a deterministic or random level is studied here. We provide its distribution (both cdf and pdf) explicitly in the first case and in the second case when the threshold is exponentially or gamma distributed. The general case for a random threshold can be approximated by considering mixtures of Erlang distributions. Aging properties are also discussed in this article.

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  • Christian Paroissin & Ali Salami, 2014. "Failure Time of Non Homogeneous Gamma Process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(15), pages 3148-3161, August.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:15:p:3148-3161
    DOI: 10.1080/03610926.2012.694546
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    Cited by:

    1. Song, Kai & Cui, Lirong, 2022. "A common random effect induced bivariate gamma degradation process with application to remaining useful life prediction," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    2. Nguyen, Khanh T.P. & Fouladirad, Mitra & Grall, Antoine, 2018. "Model selection for degradation modeling and prognosis with health monitoring data," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 105-116.
    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. Chatenet, Q. & Remy, E. & Gagnon, M. & Fouladirad, M. & Tahan, A.S., 2021. "Modeling cavitation erosion using non-homogeneous gamma process," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    5. Liu, Bin & Zhao, Xiujie & Liu, Guoquan & Liu, Yiqi, 2020. "Life cycle cost analysis considering multiple dependent degradation processes and environmental influence," Reliability Engineering and System Safety, Elsevier, vol. 197(C).

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