Discussion of "An overview of some classical models and discussion of the signature-based models of preventive maintenance"

First of all, we want to congratulate Asadi, Hashemi and Balakrishnan for this very interesting discussion that combines the detailed survey of the basic preventive maintenance models with a special emphasis on signature-based models and presentation and analysis of some potential directions of research in this area. The paper has around 50 pages of a journal format length, but one cannot say that it is ‘too long’ as it is versatile, well written and considers many interesting topics. Therefore, we think that this paper is a useful tool on general methods employed in preventive maintenance and specifically in signature-based reasoning. The survey is mostly focused on age-based maintenance. In accordance with the definition and usefulness of signatures the described models are mostly applied to coherent systems of i.i.d. or exchangeable components. In what follows, we would like to outline the new approach to preventive maintenance that hopefully can be generalized/modified using tools described in this valuable paper. It is mostly related to the first part of the paper describing conventional age-based maintenance; however, modified signature-based methods can be also employed in the further research (e.g., for populations of items operating in a random environment modeled by a shock process).