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

摘要

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.