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Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation

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  • Vlad Stefan Barbu

    (Université de Rouen)

  • Nicolas Vergne

    (Université de Rouen)

Abstract

In this work we focus on multi-state systems modeled by means of a particular class of non-homogeneous Markov processes introduced in Vergne (Stat Appl Genet Mol Biol 7(1):1–45, 2008), called drifting Markov processes. The main idea behind this type of processes is to consider a non-homogeneity that is “smooth”, of a known shape. More precisely, the Markov transition matrix is assumed to be a linear (polynomial) function of two (several) Markov transition matrices. For this class of systems, we first obtain explicit expressions for reliability/survival indicators of drifting Markov models, like reliability, availability, maintainability and failure rates. Then, under different statistical settings, we estimate the parameters of the model, obtain plug-in estimators of the associated reliability/survival indicators and investigate the consistency of the estimators. The quality of the proposed estimators and the model validation is illustrated through numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9682-8
    DOI: 10.1007/s11009-018-9682-8
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    Cited by:

    1. He Yi & Lirong Cui & Narayanaswamy Balakrishnan, 2022. "On the Derivative Counting Processes of First- and Second-order Aggregated Semi-Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1849-1875, September.
    2. Yousif Alyousifi & Kamarulzaman Ibrahim & Mahmod Othamn & Wan Zawiah Wan Zin & Nicolas Vergne & Abdullah Al-Yaari, 2022. "Bayesian Information Criterion for Fitting the Optimum Order of Markov Chain Models: Methodology and Application to Air Pollution Data," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    3. 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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