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Doubly geometric processes and applications

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  • Shaomin Wu

Abstract

The geometric process has attracted extensive research attention from authors in reliability mathematics since its introduction. However, it possesses some limitations, which include that: (1) it can merely model stochastically increasing or decreasing inter-arrival times of recurrent event processes and (2) it cannot model recurrent event processes where the inter-arrival time distributions have varying shape parameters. Those limitations may prevent it from a wider application in the real world. In this paper, we extend the geometric process to a new process, the doubly geometric process, which overcomes the above two limitations. Probability properties are derived, and two methods of parameter estimation are given. Application of the proposed model is presented: one is on fitting warranty claim data, and the other is to compare the performance of the doubly geometric process with the performance of other widely used models in fitting real-world datasets, based on the corrected Akaike information criterion.

Suggested Citation

  • Shaomin Wu, 2018. "Doubly geometric processes and applications," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(1), pages 66-77, January.
    • Handle: RePEc:taf:tjorxx:v:69:y:2018:i:1:p:66-77
    DOI: 10.1057/s41274-017-0217-4
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    Citations

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    Cited by:

    1. Yevkin, Alexander & Krivtsov, Vasiliy, 2020. "A generalized model for recurrent failures prediction," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Beutner, Eric, 2023. "A review of effective age models and associated non- and semiparametric methods," Econometrics and Statistics, Elsevier, vol. 28(C), pages 105-119.
    3. Luo, Ming & Wu, Shaomin, 2019. "A comprehensive analysis of warranty claims and optimal policies," European Journal of Operational Research, Elsevier, vol. 276(1), pages 144-159.
    4. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    5. Mingjuan Sun & Qinglai Dong & Zihan Gao, 2022. "An Imperfect Repair Model with Delayed Repair under Replacement and Repair Thresholds," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    6. Richard Arnold & Stefanka Chukova & Yu Hayakawa & Sarah Marshall, 2019. "Warranty cost analysis with an alternating geometric process," Journal of Risk and Reliability, , vol. 233(4), pages 698-715, August.
    7. Syamsundar, A. & Naikan, V.N.A. & Wu, Shaomin, 2021. "Extended Arithmetic Reduction of Age Models for the Failure Process of a Repairable System," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    8. Miaomiao Yu & Yinghui Tang, 2024. "Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method," Journal of Risk and Reliability, , vol. 238(2), pages 233-246, April.
    9. 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.
    10. Junyuan Wang & Jimin Ye, 2022. "A new repair model and its optimization for cold standby system," Operational Research, Springer, vol. 22(1), pages 105-122, March.
    11. 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.

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