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An efficient method for the estimation of parameters of stochastic gamma process from noisy degradation measurements

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  • Dongliang Lu
  • Mahesh D Pandey
  • Wei-Chau Xie

Abstract

The stochastic gamma process model is widely used in modeling a variety of degradation phenomena in engineering structures and components. If degradation in a component population can be accurately measured over time, the statistical estimation of gamma process parameters is a relatively straight-forward task. However, in most practical situations, degradation data are collected through in-service and non-destructive inspection methods, which invariably contaminate the data by adding random noises (or sizing errors) to the data. Therefore, a proper estimation method is needed to filter out the effect of sizing errors from the measured degradation data. This article presents an efficient method for estimating the parameters of the gamma process model based on a novel use of the Genz transform and quasi-Monte Carlo method in the maximum likelihood estimation. Examples presented show that the proposed method is very efficient compared with the Monte Carlo method currently used for this purpose in the literature.

Suggested Citation

  • Dongliang Lu & Mahesh D Pandey & Wei-Chau Xie, 2013. "An efficient method for the estimation of parameters of stochastic gamma process from noisy degradation measurements," Journal of Risk and Reliability, , vol. 227(4), pages 425-433, August.
    • Handle: RePEc:sae:risrel:v:227:y:2013:i:4:p:425-433
    DOI: 10.1177/1748006X13477008
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    References listed on IDEAS

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    1. Kallen, M.J. & van Noortwijk, J.M., 2005. "Optimal maintenance decisions under imperfect inspection," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 177-185.
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    Cited by:

    1. Qin, H. & Zhou, W. & Zhang, S., 2015. "Bayesian inferences of generation and growth of corrosion defects on energy pipelines based on imperfect inspection data," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 334-342.
    2. Wu, Fan & Niknam, Seyed A. & Kobza, John E., 2015. "A cost effective degradation-based maintenance strategy under imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 234-243.
    3. 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.
    4. Pulcini, Gianpaolo, 2016. "A perturbed gamma process with statistically dependent measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 296-306.
    5. Le Son, Khanh & Fouladirad, Mitra & Barros, Anne, 2016. "Remaining useful lifetime estimation and noisy gamma deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 76-87.
    6. Hao, Songhua & Yang, Jun & Berenguer, Christophe, 2018. "Nonlinear step-stress accelerated degradation modelling considering three sources of variability," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 207-215.

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