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A perturbed gamma process with statistically dependent measurement errors

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  • Pulcini, Gianpaolo

Abstract

This paper proposes a new perturbed gamma process, where the distribution of the measurement errors is assumed to be statistically dependent on the level (or state) of the hidden process. The main distributional characteristics of the proposed model, such as the marginal and conditional probability distributions of the level of the hidden process, of the measured level, and of the measurement errors, are then provided. Other quantities of large interest, such as the “failed†and “false†alarm probabilities and the reliability functions, are also provided. The maximum likelihood estimate of the model parameters is discussed, both when the inspections are not destructive and when they are invasive or destructive. In case the inspections are destructive and the standard deviation of the measurement error depends linearly on the actual process level, some distributional approximations are also suggested in order to facilitate the parameters estimation. Finally, two numerical applications are used to illustrate the feasibility of the proposed perturbed model in an applicative framework.

Suggested Citation

  • Pulcini, Gianpaolo, 2016. "A perturbed gamma process with statistically dependent measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 296-306.
    • Handle: RePEc:eee:reensy:v:152:y:2016:i:c:p:296-306
    DOI: 10.1016/j.ress.2016.03.024
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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.
    2. Rensheng Zhou & Nagi Gebraeel & Nicoleta Serban, 2012. "Degradation modeling and monitoring of truncated degradation signals," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 793-803.
    3. 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.
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    Cited by:

    1. Xudan Chen & Guoxun Ji & Xinli Sun & Zhen Li, 2019. "Inverse Gaussian–based model with measurement errors for degradation analysis," Journal of Risk and Reliability, , vol. 233(6), pages 1086-1098, December.
    2. Liu, Xingheng & Matias, José & Jäschke, Johannes & Vatn, Jørn, 2022. "Gibbs sampler for noisy Transformed Gamma process: Inference and remaining useful life estimation," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    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. Duan, Fengjun & Wang, Guanjun, 2022. "Bayesian analysis for the transformed exponential dispersion process with random effects," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    5. 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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