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A non-parametric monotone maximum likelihood estimator of time trend for repairable system data

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  • Heggland, Knut
  • Lindqvist, Bo H.

Abstract

The trend-renewal process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a non-homogeneous Poisson process (NHPP). A non-parametric maximum likelihood estimator of the trend function of a TRP is obtained under the often natural condition that λ(·) is monotone. An algorithm for computing the estimate is suggested and examined in detail in the case where the renewal distribution of the TRP is a Weibull distribution. The case where one has data from several systems is also briefly studied.

Suggested Citation

  • Heggland, Knut & Lindqvist, Bo H., 2007. "A non-parametric monotone maximum likelihood estimator of time trend for repairable system data," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 575-584.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:5:p:575-584
    DOI: 10.1016/j.ress.2006.05.007
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    References listed on IDEAS

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    1. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
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    Cited by:

    1. Amer Ibrahim Al-Omari & Amjad D. Al-Nasser & Enrico Ciavolino, 2019. "A size-biased Ishita distribution and application to real data," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(1), pages 493-512, January.
    2. Badía, Francisco German & Sangüesa, Carmen & Cha, Ji Hwan, 2018. "Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 174-184.
    3. Gámiz, Maria Luz & Lindqvist, Bo Henry, 2016. "Nonparametric estimation in trend-renewal processes," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 38-46.
    4. Chien-Lin Su & Russell J. Steele & Ian Shrier, 2021. "The semiparametric accelerated trend-renewal process for recurrent event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 357-387, July.

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