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Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case

Author

Listed:
  • Vlad Stefan Barbu

    (Laboratoire de Mathématiques Raphaël Salem, Université de Rouen-Normandie, UMR 6085, Avenue de l’Université, BP.12, F76801 Saint-Étienne-du-Rouvray, France)

  • Alex Karagrigoriou

    (Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Samos, Greece)

  • Andreas Makrides

    (Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Samos, Greece)

Abstract

Semi-Markov processes are typical tools for modeling multi state systems by allowing several distributions for sojourn times. In this work, we focus on a general class of distributions based on an arbitrary parent continuous distribution function G with Kumaraswamy as the baseline distribution and discuss some of its properties, including the advantageous property of being closed under minima. In addition, an estimate is provided for the so-called stress–strength reliability parameter, which measures the performance of a system in mechanical engineering. In this work, the sojourn times of the multi-state system are considered to follow a distribution with two shape parameters, which belongs to the proposed general class of distributions. Furthermore and for a multi-state system, we provide parameter estimates for the above general class, which are assumed to vary over the states of the system. The theoretical part of the work also includes the asymptotic theory for the proposed estimators with and without censoring as well as expressions for classical reliability characteristics. The performance and effectiveness of the proposed methodology is investigated via simulations, which show remarkable results with the help of statistical (for the parameter estimates) and graphical tools (for the reliability parameter estimate).

Suggested Citation

  • Vlad Stefan Barbu & Alex Karagrigoriou & Andreas Makrides, 2021. "Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1834-:d:607946
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    References listed on IDEAS

    as
    1. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
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    4. Mustafa Nadar & Alexander Papadopoulos & Fatih Kızılaslan, 2013. "Statistical analysis for Kumaraswamy’s distribution based on record data," Statistical Papers, Springer, vol. 54(2), pages 355-369, May.
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