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• W4308105092 abstract "Many important issues linking signature-based models and age-based maintenance have been exposed in the comprehensive review paper written by M. Asadi, M. Hashemi and N. Balakrishnan1 where 96 references on this topic have been included. I would like to congratulate the authors for their insightful article and for their own research on this field where they have made substantial contributions in the last years. In this discussion, I shall mention different points which I would like to raise in the context of the analysis of this paper and a few suggestions for future research in this field. Section 2 of the paper is devoted to give the reader different basic concepts in the maintenance field. Specifically, in section 2.3 of the paper, the authors describe a classical maintenance model: the age-based replacement model. Age based preventive models are the cornerstone of Reference 1. The age-based model is a maintenance policy that, in many cases, allows to represent the expected cost per unit time in a general form studied in Reference 2 (pp. 151, 152). From a mathematical point of view, under different assumptions, the age-based maintenance allows to obtain analytic results according to the existence of the optimal maintenance policy. From a practical point of view, the age-based maintenance is widely used in many companies since only the time that a system is in service has to be recorded. Hence it is easy to implement in practice. However, applying this maintenance policy, significant remaining useful time can be wasted if the system is still in a reasonable working condition when preventive maintenance is performed. On the other hand, an unexpected system breakdown might occur if the system fails before it is expected. Aiming to perform preventive maintenance (PM) just in time and since the technology cost is decreasing rapidly, condition-based maintenance (CBM) has gained much popularity in the past decades. The condition-based maintenance policies are based on a real-time assessment of the system components health in order to make maintenance decisions. Linking sections 2 and 3 of Reference 1, it would be important to establish how the based-signature approaches could be used to evaluate performance metrics of the system in order to impose a condition-based maintenance on the system. Some early attempts to evaluate performance metrics using the signature tools have been explored. For example, In Reference 3 under the umbrella of based-signature techniques, a predictive distribution for the residual life distribution was obtained. This residual life distribution is used to design a condition-based maintenance for the system. In Reference 4 using the signature tool, a reliability metric was formulated (known as state-dependent-mean-residual life) to design the condition-based policy. Works expanding References 3 and 4 are very challenging but promising in the maintenance field. The use of a condition-based maintenance, in many cases, is connected with an inspection policy on the system. In Reference 1, different works including inspections under the signature model are shown. In Reference 5, for instance, authors consider single and double inspections. Analogously, in Reference 6, a two-dimensional signature is used to evaluate the failed components in two inspections times. Works combining the use of survival signature along with sequential inspections (more than two) can be useful to assess the application of signatures theory in maintenance beyond the age-based maintenance scheme. Section 3 of the paper is devoted to give a review of the literature on preventive maintenance strategies whose cost objective function is developed mainly from an age-based scheme. This review section is helpful for the researchers in the maintenance field. I appreciate the effort performed by the authors to sum up these works since there is an extensive literature on this topic. For this reason, this section is very dense. I miss a summary table that helps the reader to know the different advances and developments of each paper since the famous paper of Barlow and Hunter.7 Most of the literature on signature-based models applied in preventive maintenance theory shown in Reference 1 is obtained by minimizing the asymptotic expected cost per unit time (see table 16 of Reference 1 as an example). One of the major concerns with the use of this objective cost function is that the assumption that the system is used over infinite time horizons has to be imposed. Although the time horizon of a system is usually large, it is necessary finite. In practice, companies only require a system for a finite life cycle (not necessarily predefined beforehand). The policies obtained using this asymptotic criterion are approximations to the reality (References 8 and 9). For finite time horizons, a more appropriate criterion is to use the expected cost rate up to this finite time horizon. These two approaches of the time (finite and infinite) are briefly mentioned in the paper (section 2). However, linking to section 4 of Reference 1, it is interesting to explore how signature-based techniques can apply in finite time horizon maintenance problems. Last but not least, computational issues in signature techniques are paramount. In the case of the search of the optimal maintenance policy, most of the literature in Reference 1 is developed under a renewal framework. However, in order to obtain the optimal maintenance policy for a multicomponent system, the renewal techniques have not to be the less-consuming-time techniques from a computational point of view.10 Using a signature approach, different optimality criterion should be compared in terms of computing time. I also miss in the paper the thoughts of the authors on different algorithms available and the computational time involved in the calculation of the signature vector. This research was supported by Ministerio de Ciencia e Innovación, Spain (Project PID2021-123737NB-100). I would like to thank the Editor-in-Chief of the journal, Fabrizio Ruggeri, for the opportunity to contribute to the discussion of the paper and for his patience and comprehension. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study." @default.
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• W4308105092 date "2022-11-03" @default.
• W4308105092 modified "2023-09-25" @default.
• W4308105092 title "Discussion of signature‐based models of preventive maintenance" @default.
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