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Reliability and survival analysis for drifting Markov models: modeling and estimation

Abstract : In this work we focus on multi-state systems modeled by means of a particular class of non-homogeneous Markov processes introduced in [37], 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.
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Submitted on : Tuesday, October 29, 2019 - 12:52:33 PM
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Vlad Stefan Barbu, Nicolas Vergne. Reliability and survival analysis for drifting Markov models: modeling and estimation. Methodology and Computing in Applied Probability, Springer Verlag, 2018, ⟨10.1007/s11009-018-9682-8⟩. ⟨hal-02337216⟩

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