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Methodology and Computing in Applied Probability

, Volume 21, Issue 4, pp 1407–1429 | Cite as

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

  • Vlad Stefan BarbuEmail author
  • Nicolas Vergne
Article
  • 32 Downloads

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 

Mathematics Subject Classification (2010)

60J10 60K15 90B25 62N02 62F12 

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Notes

Acknowledgments

This research work was partially supported by the projects MMATFAS - Mathematical Methods for System Reliability and Survival Analysis (2014–2015) and MOUSTIC–Random Models and Statistical, Informatics and Combinatorics Tools (2016–2019), within the Large Scale Research Networks from the Region of Normandy, France.

The authors would like to thank their colleagues Dr. Anatoly Lisnianski and Dr. Gregory Levitin from the Israel Electric Corporation Ltd. for pointing out important aspects and references on multi-state systems and also to Prof. Ilia Frenkel and his colleagues from Sami Shamoon College of Engineering, Israel, for organizing the series of conferences International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management, to which, indirectly, the research developed in this article owes much.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Raphaël SalemUniversité de RouenSaint-Étienne-du-RouvrayFrance

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