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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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    References listed on IDEAS

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    1. Zhi-Ming Wang & Xia Yu, 2013. "Log-linear process modeling for repairable systems with time trends and its applications in reliability assessment of numerically controlled machine tools," Journal of Risk and Reliability, , vol. 227(1), pages 55-65, February.
    2. García-Escudero, Luis A. & Fernández, Miguel A. & Duque, Oscar & Zorita, Angel, 2005. "Assessing trends in Duane plots using robust fits," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 106-113.
    3. Yadav, Om Prakash & Singh, Nanua & Goel, Parveen S., 2006. "Reliability demonstration test planning: A three dimensional consideration," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 882-893.
    4. Majeske, Karl D., 2007. "A non-homogeneous Poisson process predictive model for automobile warranty claims," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 243-251.
    5. Chattopadhyay, Gopinath & Rahman, Anisur, 2008. "Development of lifetime warranty policies and models for estimating costs," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 522-529.
    6. Ye, Zhi-Sheng & Xie, Min & Tang, Loon-Ching, 2013. "Reliability evaluation of hard disk drive failures based on counting processes," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 110-118.
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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. Talha Ahmed & Yasir Mahmood & Nita Yodo & Ying Huang, 2024. "Weather-Related Combined Effect on Failure Propagation and Maintenance Procedures towards Sustainable Gas Pipeline Infrastructure," Sustainability, MDPI, vol. 16(13), pages 1-31, July.
    8. 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).
    9. Slimacek, Vaclav & Lindqvist, Bo Henry, 2016. "Nonhomogeneous Poisson process with nonparametric frailty," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 14-23.
    10. 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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