## 1 Introduction
[13] presents a framework for modeling the reliability of mechatronic systems throughout their life cycle. Based on the data records, and both functional and dysfunctional analysis of the system, it estimates the predictive reliability using deterministic stochastic Petri nets. Then, based on data from reliability tests with the precedent predictive reliability, the experimental reliability is estimated using the Bayesian restoration maximization method. Operational reliability is also obtained with the BRM method, using previously defined experimental reliability and data extracted from experience feedback. Ref. [14] develops a methodology for modeling the dependability of two-feedwater nuclear turbo-pumps using hierarchical, timed, colored Petri nets and probabilistic distributions. A physical model, a logic model, and a top model were constructed, and Monte Carlo simulations were performed to evaluate different dependability mean times. Ref. [15] gives an insight into probabilistic models for assessing the dependability of industrial systems. They first introduce several static Boolean approaches, such as fault tree analysis, reliability block diagram, and event trees, then emphasize dynamic models featuring examples of Markovian approaches such as Markov graphs as well as behavioral approaches using stochastic Petri nets and Monte Carlo simulations. The above-mentioned works are founded on the use of Petri nets in the context of assessing the dependability of industrial systems. The authors suggest different methods for assessing dependability, although, in most of the cited cases, they focus on specific dependability attributes while neglecting others. For instance, Petri net models are developed by [4] to evaluate losses incurred by extreme events, mitigation processes, the health status of the systems involved, and recovery and maintenance processes. However, other dependability attributes, such as reliability and availability, have not been assessed. From the same perspective, ref. [5] presents a methodology for assessing the reliability of a photovoltaic module that is subjected to a stochastic condition using Petri nets. Yet, the author has not addressed other dependability attributes such as availability and maintainability. Ref. [7] provides a reliability and availability calculation model during the maintenance of a reactor protection system. Nevertheless, he did not consider the maintainability attribute. Similarly, ref. [8] suggests a reliability and availability estimation based on DFMCA and stochastic Petri nets, and the author did not evaluate maintainability and other attributes. Ref. [9] proposes a methodology to assess reliability, availability, and global production time using stochastic and deterministic Petri nets without considering other dependability attributes, like maintainability. Ref. [10] suggests a model allowing for the assessment of reliability and dynamic safety for a system without taking into consideration availability and maintainability. Based on fault Petri nets and Markov chains, ref. [11] provides a generalization of the ordinary fault tree to assess reliability including dependencies between the basic events, variable failure, and repair rates, but maintainability and availability have not been addressed. The reliability assessment of mechatronic systems, while considering their multi-technological characteristics, has been addressed in the works of [12; 13]. In fact, ref. [12] proposes a global methodology to assess the predictive reliability of mechatronic systems considering their dynamic aspect in the design stage, while [13] proposes an overall methodology to assess the reliability of mechatronic systems throughout their life cycle. Both suggested methodologies focused on reliability attributes only. Refs. [6; 14] estimate the dependability attributes: reliability, availability, and maintainability. Ref. [6] evaluates reliability availability and maintainability including spares management of system of systems using stochastic Petri nets and Monte Carlos simulations. Ref.