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Precision of power-law NHPP estimates for multiple systems with known failure rate scaling

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  • Van Dyck, Jozef
  • Verdonck, Tim

Abstract

The power-law non-homogeneous Poisson process, also called the Crow-AMSAA model, is often used to model the failure rate of repairable systems. In standard applications it is assumed that the recurrence rate is the same for all systems that are observed. The estimation of the model parameters on the basis of past failure data is typically performed using maximum likelihood. If the operational period over which failures are observed differs for each system, the Fisher information matrix is numerically inverted to quantify the precision of the parameter estimates.

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  • Van Dyck, Jozef & Verdonck, Tim, 2014. "Precision of power-law NHPP estimates for multiple systems with known failure rate scaling," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 143-152.
    • Handle: RePEc:eee:reensy:v:126:y:2014:i:c:p:143-152
    DOI: 10.1016/j.ress.2014.01.019
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    Cited by:

    1. Peng, Yizhen & Wang, Yu & Zi, YanYang & Tsui, Kwok-Leung & Zhang, Chuhua, 2017. "Dynamic reliability assessment and prediction for repairable systems with interval-censored data," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 301-309.
    2. Awad, Mahmoud, 2016. "Economic allocation of reliability growth testing using Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 273-280.
    3. Garmabaki, A.H.S. & Ahmadi, Alireza & Block, Jan & Pham, Hoang & Kumar, Uday, 2016. "A reliability decision framework for multiple repairable units," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 78-88.
    4. Xin-Yu Tian & Xincheng Shi & Cheng Peng & Xiao-Jian Yi, 2021. "A Reliability Growth Process Model with Time-Varying Covariates and Its Application," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
    5. Slimacek, Vaclav & Lindqvist, Bo Henry, 2017. "Nonhomogeneous Poisson process with nonparametric frailty and covariates," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 75-83.
    6. Zhou, Yu & Kou, Gang & Xiao, Hui & Peng, Yi & Alsaadi, Fawaz E., 2020. "Sequential imperfect preventive maintenance model with failure intensity reduction with an application to urban buses," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    7. Yizhen, Peng & Yu, Wang & Jingsong, Xie & Yanyang, Zi, 2020. "Adaptive stochastic-filter-based failure prediction model for complex repairable systems under uncertainty conditions," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Slimacek, Vaclav & Lindqvist, Bo Henry, 2016. "Nonhomogeneous Poisson process with nonparametric frailty," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 14-23.
    9. Wei Wang & Yaofeng Xu & Liguo Hou, 2019. "Optimal allocation of test times for reliability growth testing with interval-valued model parameters," Journal of Risk and Reliability, , vol. 233(5), pages 791-802, October.

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