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

Vlad Stefan Barbu () and Nicolas Vergne ()
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Vlad Stefan Barbu: Université de Rouen
Nicolas Vergne: Université de Rouen

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1407-1429

Abstract: 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.

Keywords: Drifting Markov chains; Multi-state systems; Reliability theory; Survival analysis; Estimation; Asymptotic properties; 60J10; 60K15; 90B25; 62N02; 62F12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-018-9682-8

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