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Two new stochastic models of the failure process of a series system

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  • Wu, Shaomin
  • Scarf, Philip

Abstract

Consider a series system consisting of sockets into each of which a component is inserted: if a component fails, it is replaced with a new identical one immediately and system operation resumes. An interesting question is: how to model the failure process of the system as a whole when the lifetime distribution of each component is unknown? This paper attempts to answer this question by developing two new models, for the cases of a specified and an unspecified number of sockets, respectively. It introduces the concept of a virtual component, which corresponds to the part of the system that is replaced upon system failure. It then discusses the probabilistic properties of the models and methods for parameter estimation. Based on six datasets of artificially generated system failures and a real-world dataset, the paper compares the performance of the proposed models with four other commonly used models: the renewal process, the geometric process, Kijima’s generalised renewal process, and the power law process. The results show that the proposed models outperform these comparators on the datasets, based on the Akaike information criterion.

Suggested Citation

  • Wu, Shaomin & Scarf, Philip, 2017. "Two new stochastic models of the failure process of a series system," European Journal of Operational Research, Elsevier, vol. 257(3), pages 763-772.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:3:p:763-772
    DOI: 10.1016/j.ejor.2016.07.052
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    References listed on IDEAS

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    1. Zhang, Mimi & Gaudoin, Olivier & Xie, Min, 2015. "Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 245(2), pages 531-541.
    2. Wu, Shaomin & Scarf, Philip, 2015. "Decline and repair, and covariate effects," European Journal of Operational Research, Elsevier, vol. 244(1), pages 219-226.
    3. Asfaw, Zeytu Gashaw & Lindqvist, Bo Henry, 2015. "Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 53-58.
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    Citations

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    Cited by:

    1. Zhang, Chao & Xu, Xin & Dui, Hongyan, 2020. "Analysis of network cascading failure based on the cluster aggregation in cyber-physical systems," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    2. Do, Phuc & Assaf, Roy & Scarf, Phil & Iung, Benoit, 2019. "Modelling and application of condition-based maintenance for a two-component system with stochastic and economic dependencies," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 86-97.
    3. Syamsundar, A. & Naikan, V.N.A. & Wu, Shaomin, 2020. "Alternative scales in reliability models for a repairable system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Junyuan Wang & Jimin Ye & Qianru Ma & Pengfei Xie, 2022. "An extended geometric process repairable model with its repairman having vacation," Annals of Operations Research, Springer, vol. 311(1), pages 401-415, April.
    5. Yang, Li & Ye, Zhi-sheng & Lee, Chi-Guhn & Yang, Su-fen & Peng, Rui, 2019. "A two-phase preventive maintenance policy considering imperfect repair and postponed replacement," European Journal of Operational Research, Elsevier, vol. 274(3), pages 966-977.
    6. Nafisah, Ibrahim & Shrahili, Mansour & Alotaibi, Naif & Scarf, Phil, 2019. "Virtual series-system models of imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 604-613.
    7. Shen, Jingyuan & Cui, Lirong & Ma, Yizhong, 2019. "Availability and optimal maintenance policy for systems degrading in dynamic environments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 133-143.
    8. Junyuan Wang & Jimin Ye & Liang Wang, 2022. "Extended age maintenance models and its optimization for series and parallel systems," Annals of Operations Research, Springer, vol. 312(1), pages 495-517, May.
    9. Wu, Shaomin, 2021. "Two methods to approximate the superposition of imperfect failure processes," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    10. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    11. Wenke Gao, 2020. "An extended geometric process and its application in replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 88-103, February.
    12. Wu, Shaomin, 2019. "A failure process model with the exponential smoothing of intensity functions," European Journal of Operational Research, Elsevier, vol. 275(2), pages 502-513.
    13. Renyan Jiang, 2022. "A novel parameter estimation method for the Weibull distribution on heavily censored data," Journal of Risk and Reliability, , vol. 236(2), pages 307-316, April.

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