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A Mixed Kijima Model Using the Weibull-Based Generalized Renewal Processes

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  • Ricardo José Ferreira
  • Paulo Renato Alves Firmino
  • Cláudio Tadeu Cristino

Abstract

Generalized Renewal Processes are useful for approaching the rejuvenation of dynamical systems resulting from planned or unplanned interventions. We present new perspectives for the Generalized Renewal Processes in general and for the Weibull-based Generalized Renewal Processes in particular. Disregarding from literature, we present a mixed Generalized Renewal Processes approach involving Kijima Type I and II models, allowing one to infer the impact of distinct interventions on the performance of the system under study. The first and second theoretical moments of this model are introduced as well as its maximum likelihood estimation and random sampling approaches. In order to illustrate the usefulness of the proposed Weibull-based Generalized Renewal Processes model, some real data sets involving improving, stable, and deteriorating systems are used.

Suggested Citation

  • Ricardo José Ferreira & Paulo Renato Alves Firmino & Cláudio Tadeu Cristino, 2015. "A Mixed Kijima Model Using the Weibull-Based Generalized Renewal Processes," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-17, July.
    • Handle: RePEc:plo:pone00:0133772
    DOI: 10.1371/journal.pone.0133772
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    References listed on IDEAS

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    1. Madhu Jain & Sandhya Maheshwari, 2006. "Generalized Renewal Process (Grp) For The Analysis Of Software Reliability Growth Model," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 215-227.
    2. Love, C. E. & Zhang, Z. G. & Zitron, M. A. & Guo, R., 2000. "A discrete semi-Markov decision model to determine the optimal repair/replacement policy under general repairs," European Journal of Operational Research, Elsevier, vol. 125(2), pages 398-409, September.
    3. Scarsini, Marco & Shaked, Moshe, 2000. "On the value of an item subject to general repair or maintenance," European Journal of Operational Research, Elsevier, vol. 122(3), pages 625-637, May.
    4. Makis, Viliam & Jardine, Andrew K. S., 1993. "A note on optimal replacement policy under general repair," European Journal of Operational Research, Elsevier, vol. 69(1), pages 75-82, August.
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    Cited by:

    1. Cláudio Tadeu Cristino & Piotr Żebrowski & Matthias Wildemeersch, 2020. "Assessing the time intervals between economic recessions," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-20, May.
    2. Hu, Wei & Yang, Zhaojun & Chen, Chuanhai & Wu, Yue & Xie, Qunya, 2021. "A Weibull-based recurrent regression model for repairable systems considering double effects of operation and maintenance: A case study of machine tools," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

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