###### Abstract  
Due to the augmented complexity of the factory on the one hand and the increased availability of information on the other hand, nowadays it is possible to design models of production lines able to consider the state of the health of the production system. Such models must combine both the deterministic and the stochastic behaviours of a system, with the former accounting for the mechanics and physics of the industrial process and the latter for randomness, including reliability of the production systems and the unpredictability of the maintenance and of the manufacturing lines. This study proposes the application of a Hybrid Dependability Modelling based on Monte Carlo simulation to estimate the performances of a repairable production line modelled with a queueing G/G/1 system. The model proposed is characterized by random interarrival and service times and by the wearing and dynamic aging phenomena of the machine tools that depend on the working and operating conditions. Keywords:industry 4.0; hybrid dependability modelling; production scheduling; dynamic failure rate; discrete event simulation; time-driven simulation +
Footnote †: journal:  
_Applied_  
_Acticle_  
Performance Analysis of a Repairable Production Line Using a Hybrid Dependability Queueing Model Based on Monte Carlo Simulation. via IoT (the Internet of Things) and Internet and improve the overall management and scheduling of industrial processes, from the production to the maintenance. From the field-level of a production department, it is now possible to capture many important signals that can be collected and used to evaluate the status of the system. Moreover, the diffusion of data analytics tools is helping the organizations in the understanding of meaningful information from the produced data. Nowadays, it looks possible to code models able to capture information data of operational behaviours that link environmental conditions, workloads and cumulative aging of materials which were not available before. As highlighted by [7], systems are generally working under time-varying operating conditions that can influence the failure time of systems. In the modelling of a queueing system [8], the trivial hypothesis of a dyadic state (working, failed) is not realistic because industrial and electromechanical equipment are deteriorating from wearing and ageing effects. As discussed in [9], one of the main challenges is the unpredictability of the manufacturing lines that can be tackled with novel tools, including digital twin and simulation, of the Industry 4.0 generation. In this context, in order to better assess the main performance and dependability attributes of the system, including reliability, availability and maintainability [10], the development looks promising in the investigation of a methodology that can combine a realistic model of a production line with up-to-date and more detailed information data of the equipment. A general dependability framework has been proposed in [11], and in this research paper, it has been modified in order to integrate it into a dynamic reliability problem [12]: a non-exponential queueing system subjected to non-exponential failure and repair and characterized by dynamic working conditions (process scheduling and workloads). Due to the numerous physical and stochastic interdependencies typical of a multi-state system, the choice for the use of the simulation paradigm over any other mathematical formalism appears the most suitable. The simulation model is fed by the mechanical differential equations of the machine tool wearing which are integrated numerically. Moreover, the proposed simulation environment, coded within the electronic spreadsheet, can be easily interconnected (using many plugins, such as OPC-DA, Modbus, ODBC, etc.) to a production line to get real-time data from the field level (operational variables), communicate the diagnosis of its status (evaluation of aging) and control the operations (assessing its remaining useful life) as a cyber physical system.