Discussion of "Virtual age, is it real?"

Abstract

I congratulate the authors on this very interesting article discussing various aspects of the virtual age concept, which has been in active use in reliability and lifetime analyses for at least three decades. At the same time, the authors should be acknowledged for their own long time research on the subject, some of which is reviewed in their present article. The authors have chosen a title of the article that at once settles the question to be discussed. Their main idea at the outset is that real maintenance actions do not usually conform with a pure age reduction. It might not be difficult to agree in such a view, but still virtual age models have proven useful in modeling and understanding of many complicated maintenance processes.

My focus in the present discussion article will mainly be on topics from my own research. This typically applies to the study of repairable systems, where recurrent events is a keyword. The seminal articles on virtual ages of Kijima1 and Doyen and Gaudoin2 indeed consider repairable and maintainable systems where event processes are behind the models. The authors of the article under discussion have, on the other hand, been able to concentrate on the imperfect repair part of the issue, which essentially plays the key role in their presentation.

In order not to confuse equation numbers from the article with equation numbers from the present discussion contribution, I let the former be marked as (FC1) and so on.