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Bayesian inference method for stochastic damage accumulation modeling

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  • Jiang, Xiaomo
  • Yuan, Yong
  • Liu, Xian

Abstract

Damage accumulation based reliability model plays an increasingly important role in successful realization of condition based maintenance for complicated engineering systems. This paper developed a Bayesian framework to establish stochastic damage accumulation model from historical inspection data, considering data uncertainty. Proportional hazards modeling technique is developed to model the nonlinear effect of multiple influencing factors on system reliability. Different from other hazard modeling techniques such as normal linear regression model, the approach does not require any distribution assumption for the hazard model, and can be applied for a wide variety of distribution models. A Bayesian network is created to represent the nonlinear proportional hazards models and to estimate model parameters by Bayesian inference with Markov Chain Monte Carlo simulation. Both qualitative and quantitative approaches are developed to assess the validity of the established damage accumulation model. Anderson–Darling goodness-of-fit test is employed to perform the normality test, and Box–Cox transformation approach is utilized to convert the non-normality data into normal distribution for hypothesis testing in quantitative model validation. The methodology is illustrated with the seepage data collected from real-world subway tunnels.

Suggested Citation

  • Jiang, Xiaomo & Yuan, Yong & Liu, Xian, 2013. "Bayesian inference method for stochastic damage accumulation modeling," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 126-138.
    • Handle: RePEc:eee:reensy:v:111:y:2013:i:c:p:126-138
    DOI: 10.1016/j.ress.2012.11.006
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    References listed on IDEAS

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    1. Jiang, Xiaomo & Mahadevan, Sankaran, 2009. "Bayesian structural equation modeling method for hierarchical model validation," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 796-809.
    2. Rebba, Ramesh & Mahadevan, Sankaran, 2006. "Validation of models with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 861-871.
    3. Xiaomo Jiang & Sankaran Mahadevan, 2009. "Bayesian inference method for model validation and confidence extrapolation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(6), pages 659-677.
    4. Tinga, Tiedo, 2010. "Application of physical failure models to enable usage and load based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(10), pages 1061-1075.
    5. Jiang, Xiaomo & Mahadevan, Sankaran, 2007. "Bayesian risk-based decision method for model validation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 707-718.
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    Cited by:

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    2. Coria, V.H. & Maximov, S. & Rivas-Dávalos, F. & Melchor, C.L. & Guardado, J.L., 2015. "Analytical method for optimization of maintenance policy based on available system failure data," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 55-63.
    3. Kondakci, Suleyman, 2015. "Analysis of information security reliability: A tutorial," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 275-299.
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    5. XiaoFei, Lu & Min, Liu, 2014. "Hazard rate function in dynamic environment," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 50-60.
    6. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.

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