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Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection

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  • Kuniewski, Sebastian P.
  • van der Weide, Johannes A.M.
  • van Noortwijk, Jan M.

Abstract

The paper presents a sampling-inspection strategy for the evaluation of time-dependent reliability of deteriorating systems, where the deterioration is assumed to initiate at random times and at random locations. After initiation, defects are weakening the system's resistance. The system becomes unacceptable when at least one defect reaches a critical depth. The defects are assumed to initiate at random times modeled as event times of a non-homogeneous Poisson process (NHPP) and to develop according to a non-decreasing time-dependent gamma process. The intensity rate of the NHPP is assumed to be a combination of a known time-dependent shape function and an unknown proportionality constant. When sampling inspection (i.e. inspection of a selected subregion of the system) results in a number of defect initiations, Bayes’ theorem can be used to update prior beliefs about the proportionality constant of the NHPP intensity rate to the posterior distribution. On the basis of a time- and space-dependent Poisson process for the defect initiation, an adaptive Bayesian model for sampling inspection is developed to determine the predictive probability distribution of the time to failure. A potential application is, for instance, the inspection of a large vessel or pipeline suffering pitting/localized corrosion in the oil industry. The possibility of imperfect defect detection is also incorporated in the model.

Suggested Citation

  • Kuniewski, Sebastian P. & van der Weide, Johannes A.M. & van Noortwijk, Jan M., 2009. "Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection," Reliability Engineering and System Safety, Elsevier, vol. 94(9), pages 1480-1490.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:9:p:1480-1490
    DOI: 10.1016/j.ress.2008.11.013
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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. 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.
    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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    Citations

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    Cited by:

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    2. Caballé, N.C. & Castro, I.T. & Pérez, C.J. & Lanza-Gutiérrez, J.M., 2015. "A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 98-109.
    3. Bautista, Lucía & Castro, Inma T. & Landesa, Luis, 2022. "Condition-based maintenance for a system subject to multiple degradation processes with stochastic arrival intensity," European Journal of Operational Research, Elsevier, vol. 302(2), pages 560-574.
    4. David Randell & Michael Goldstein & Philip Jonathan, 2014. "Bayes linear variance structure learning for inspection of large scale physical systems," Journal of Risk and Reliability, , vol. 228(1), pages 3-18, February.
    5. 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.
    6. Cha, Ji Hwan & Finkelstein, Maxim, 2018. "On information-based residual lifetime in survival models with delayed failures," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 209-216.
    7. Cha, Ji Hwan & Finkelstein, Maxim, 2019. "Stochastic modeling for systems with delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 118-124.
    8. 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.
    9. 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.

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