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Bayesian inference of multi-stage reliability for degradation systems with calibrations

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  • Dejing Kong
  • Lirong Cui

Abstract

The importance of degradation analysis as a method of reliability assessment has been increasing because the products become more and more reliable. Bayesian updating is important in the dynamic analysis of few degradation data collected in multiple stages. A problem of assessing the reliability of a degradation system, wherein calibration of a development program is carried out, within a multi-stage, by Bayesian inference, is proposed in this article. Two types of posterior distribution are obtained in each testing stage under an assumption that degradation performance follows a normal distribution for two cases. Then, two Bayesian models are presented to evaluate the system reliability. A conclusion is also derived, that is, the variance of a key random variable decreases as the number of testing stage grows. Finally, a numerical example illustrates the model, process and the analysis results.

Suggested Citation

  • Dejing Kong & Lirong Cui, 2016. "Bayesian inference of multi-stage reliability for degradation systems with calibrations," Journal of Risk and Reliability, , vol. 230(1), pages 18-33, February.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:1:p:18-33
    DOI: 10.1177/1748006X15580752
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    References listed on IDEAS

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    1. Pan, Zhengqiang & Balakrishnan, Narayanaswamy, 2011. "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 949-957.
    2. Wang, Lizhi & Pan, Rong & Li, Xiaoyang & Jiang, Tongmin, 2013. "A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 38-47.
    3. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
    4. Zhou, Xiaojun & Xi, Lifeng & Lee, Jay, 2007. "Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 530-534.
    5. Bae, Suk Joo & Kuo, Way & Kvam, Paul H., 2007. "Degradation models and implied lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 601-608.
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    Cited by:

    1. Kong, Dejing & Qin, Chengwei & He, Yong & Cui, Lirong, 2017. "Sensor-based calibrations to improve reliability of systems subject to multiple dependent competing failure processes," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 101-113.
    2. 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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