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A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process

Author

Listed:
  • Hyunju Lee

    (Department of Statistics, Hankuk University of Foreign Studies, Yongin 17035, Korea)

  • Ji Hwan Cha

    (Department of Statistics, Ewha Womans University, Seoul 03760, Korea)

  • Maxim Finkelstein

    (Department of Mathematical Statistics, University of the Free State, Bloemfontein 9300, South Africa
    Department of Management Science, University of Strathclyde, Glasgow G1 1XQ, UK)

Abstract

Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover this important in-practice setting. Therefore, our paper is the first to deal with these issues by modeling dependence in the bivariate set up when a system consists of two dependent parts. We employ the bivariate generalized Polya process to model the corresponding failure and repair process. Relevant stochastic properties of this process have been obtained in order to propose and further discuss the new optimal bivariate preventive maintenance policy with two decision parameters: age and operational history. Moreover, introducing these two parameters in the considered context is also a new feature of the study. Under the proposed policy, the long-run average cost rate is derived and the optimal replacement policies are investigated. Detailed numerical examples illustrate our findings and show the potential efficiency of the obtained results in practice.

Suggested Citation

  • Hyunju Lee & Ji Hwan Cha & Maxim Finkelstein, 2022. "A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1833-:d:824913
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    References listed on IDEAS

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    1. Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
    2. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    3. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    4. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, June.
    5. Shey-Huei Sheu & Griffith, William S. & Toshio Nakagawa, 1995. "Extended optimal replacement model with random minimal repair costs," European Journal of Operational Research, Elsevier, vol. 85(3), pages 636-649, September.
    6. Hyunju Lee & Ji Hwan Cha, 2019. "A bivariate optimal replacement policy for a system subject to a generalized failure and repair process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 637-650, May.
    7. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, June.
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    Cited by:

    1. Francisco Germán Badía & María D. Berrade, 2023. "Special Issue “Probability Theory and Stochastic Modeling with Applications”," Mathematics, MDPI, vol. 11(14), pages 1-3, July.

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