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Reliability Measures of Semi-Markov Systems with General State Space

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  • Nikolaos Limnios

    (University of Technology of Compiègne)

Abstract

The aim of this paper is to present a systematic modeling of reliability and related measures: availability, maintainability, failure rate, rate of occurrence of failures, mean times, etc., known in the literature under the term dependability. This model includes the continuous and discrete time semi-Markov processes with general state space. This is one of the most general models in reliability theory since it includes as particular cases the Markov and renewal processes.

Suggested Citation

  • Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:4:d:10.1007_s11009-011-9211-5
    DOI: 10.1007/s11009-011-9211-5
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    References listed on IDEAS

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    1. Ouhbi, Brahim & Limnios, Nikolaos, 2002. "The rate of occurrence of failures for semi-Markov processes and estimation," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 245-255, October.
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    Cited by:

    1. Wu, Xiaoyue & Hillston, Jane, 2015. "Mission reliability of semi-Markov systems under generalized operational time requirements," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 122-129.
    2. Brenda Garcia-Maya & Nikolaos Limnios & Bo Henry Lindqvist, 2022. "Competing Risks Modeling by Extended Phase-Type Semi-Markov Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 309-319, March.
    3. María Luz Gámiz & Nikolaos Limnios & Mari Carmen Segovia-García, 2023. "The continuous-time hidden Markov model based on discretization. Properties of estimators and applications," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 525-550, October.
    4. Lijun Shang & Baoliang Liu & Kaiye Gao & Li Yang, 2023. "Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity," Mathematics, MDPI, vol. 11(15), pages 1-22, July.
    5. Inma T Castro & Sophie Mercier, 2016. "Performance measures for a deteriorating system subject to imperfect maintenance and delayed repairs," Journal of Risk and Reliability, , vol. 230(4), pages 364-377, August.
    6. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.
    7. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    8. Delia Montoro-Cazorla & Rafael Pérez-Ocón & Alicia Pereira das Neves-Yedig, 2021. "A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    9. Guglielmo D'Amico, 2016. "Generalized semi-Markovian dividend discount model: risk and return," Papers 1605.02472, arXiv.org.
    10. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.
    11. N. C. Caballé & I. T. Castro, 2019. "Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 255-290, March.
    12. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    13. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.

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