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Repairable systems are subject to different repair protocols upon each failure of the system. These include minimal, imperfect andperfect repairs. In this study, we are proposing a unifying virtual age model, which combines all three repair types and introduce generalizations of the repair models existing in the literature. Virtual age concept differentiates between the operational age and the current condition of the repairable system. Operational age is described in terms of the total time elapsed since the system was first put to work, whereas the virtual age represents the condition of the system subjected to repairs. At each repair, the virtual age is reevaluated based on the type of repair applied to the system and keeps increasing at the same pace as the operation time between the failures. The introduced models under the unifying model structure are extended further based on the dependencestructure between the latent variables. Another generalization of the unifying model is considered by incorporatinga random environment which modulates the failure behavior of the system. The random environment which captures theexternal effects on the operational environment is latent and assumed to be following a Markovian evolution. Another extension proposed in this study is age-dependent virtual age models. Different than the models introduced so far, the age-dependent model considers the repair type probabilities varying according to the virtual age of the system. Finally, for developing statistical inference for these models, a Bayesian framework is considered and the posterior and posterior predictive analyses are developed. In doing so, Markov Chain Monte Carlo methods are used both for inference and to check the accuracy and validity of these models.

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