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ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction

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  • Toledo, Maria Luíza Guerra de
  • Freitas, Marta A.
  • Colosimo, Enrico A.
  • Gilardoni, Gustavo L.

Abstract

An appropriate maintenance policy is essential to reduce expenses and risks related to equipment failures. A fundamental aspect to be considered when specifying such policies is to be able to predict the reliability of the systems under study, based on a well fitted model. In this paper, the classes of models Arithmetic Reduction of Age and Arithmetic Reduction of Intensity are explored. Likelihood functions for such models are derived, and a graphical method is proposed for model selection. A real data set involving failures in trucks used by a Brazilian mining is analyzed considering models with different memories. Parameters, namely, shape and scale for Power Law Process, and the efficiency of repair were estimated for the best fitted model. Estimation of model parameters allowed us to derive reliability estimators to predict the behavior of the failure process. These results are a valuable information for the mining company and can be used to support decision making regarding preventive maintenance policy.

Suggested Citation

  • Toledo, Maria Luíza Guerra de & Freitas, Marta A. & Colosimo, Enrico A. & Gilardoni, Gustavo L., 2015. "ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 107-115.
    • Handle: RePEc:eee:reensy:v:140:y:2015:i:c:p:107-115
    DOI: 10.1016/j.ress.2015.03.035
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    4. Brito, Éder S. & Tomazella, Vera L.D. & Ferreira, Paulo H., 2022. "Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    5. Shang, Lijun & Liu, Baoliang & Qiu, Qingan & Yang, Li & Du, Yongjun, 2023. "Designing warranty and maintenance policies for products subject to random working cycles," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
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    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. 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).
    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. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    11. Vanderschueren, Toon & Boute, Robert & Verdonck, Tim & Baesens, Bart & Verbeke, Wouter, 2023. "Optimizing the preventive maintenance frequency with causal machine learning," International Journal of Production Economics, Elsevier, vol. 258(C).
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