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Superposed Poisson process models with a modified bathtub intensity function for repairable systems

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  • Tao Yuan
  • Tianqiang Yan
  • Suk Joo Bae

Abstract

Bathtub-shaped failure intensity is typical for large-scaled repairable systems with a number of different failure modes. Sometimes, repairable systems may exhibit a failure pattern different from the traditional bathtub shape, due to the existence of multiple failure modes. This study proposes two superposed Poisson process models with modified bathtub intensity functions to capture this kind of failure pattern. The new models are constructed by the superposition of the generalized Goel–Okumoto process and power law process (or log-linear process). The proposed models can be applied to masked failure-time data from repairable systems where the modes of collected failure-times are unobserved or unavailable. Bayesian posterior computation algorithms based on the data augmentation method are developed for the inference on the parameters or their functions of the superposed Poisson process models. This study also examines the best model selection among the candidate models in the Bayesian framework and modeling check using the residuals. A practical case study with a data set of unscheduled maintenance events for complex artillery systems illustrates potential applications of the proposed models for the purpose of reliability prediction for the repairable systems.

Suggested Citation

  • Tao Yuan & Tianqiang Yan & Suk Joo Bae, 2021. "Superposed Poisson process models with a modified bathtub intensity function for repairable systems," IISE Transactions, Taylor & Francis Journals, vol. 53(9), pages 1037-1051, June.
  • Handle: RePEc:taf:uiiexx:v:53:y:2021:i:9:p:1037-1051
    DOI: 10.1080/24725854.2020.1820630
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    Cited by:

    1. Patawa, Rohit & Pundir, Pramendra Singh, 2023. "Inferential study of single unit repairable system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 503-516.
    2. Chen, Yuan & Qiu, Qingan & Zhao, Xian, 2022. "Condition-based opportunistic maintenance policies with two-phase inspections for continuous-state systems," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    3. Zhao, Xian & Guo, Bin & Chen, Yuan, 2024. "A condition-based inspection-maintenance policy for critical systems with an unreliable monitor system," Reliability Engineering and System Safety, Elsevier, vol. 242(C).

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