A Generic Framework for Generalized Virtual Age Models

Discussion of “Virtual age, is it real?”

“…Therefore, the age correspondence model seems to be closer to an Accelerated failure Time model (AFT) than to a virtual age model. Note that Peña et al 16 and Doyen et al 6 have proposed similar virtual age models in a recurrent events setting. The advantage of these models is that they can take into account diverse kinds of repair effect.…”

“…We agree with the authors that one drawback of the basic Kijima/ARA virtual age model is that the failure intensity after repair has the same shape as before. As explained in Reference 6, other models that can be considered as virtual age models, such as the Geometric Process 7 or Quasi‐Renewal model, 8 overcome this difficulty. It is also the case of some imperfect repair models which are not virtual age models: the Arithmetic Reduction of Intensity model 2 and Geometric Failure Rate Reduction model 9 .…”

“…Li and Hanson 12 have considered that covariates can have an effect on maintenance efficiency through age reduction. Doyen et al 6 have studied the introduction of constant covariates in the initial intensity. Brenière et al 13 have generalized this approach to dynamic covariates.…”

Discussion of “Virtual age: Is it real?”

“…Other related works include Dijoux and Ide (2013) 8 who considered virtual age models for systems going through a burn‐in period and Doyen et al (2020) 9 who presented a general framework for virtual age models where covariate effects can be considered. However, their development was limited to time invariant covariates.…”

Discussion of “Virtual age, is it real?”

“…On the one hand, the virtual age is a kind of time‐transformation that has shown to be useful in reliability analysis. Doyen et al 1 provided a general discussion/overview of virtual age models. A few recent works, Nafisah et al 2 and Kahle, 3 also discussed this modeling approach.…”