###### Abstract  
Assembly lines are one of the cornerstones of modern production systems, significantly affecting the global society, economy, and other ancillary sectors. This is why the evaluation of assembly lines is particularly significant. Hence, the research on modeling approaches is presented in this paper, yielding an efficient mathematical tool that enables the evaluation of the steady-state performance of assembly lines at low CPU cost. First, the analytical model and the transition matrix were developed for the general case, and second, dimensionality issues and demanding computational requirements were tackled by applying the finite state method. Both approaches were employed in different theoretical cases in order to validate the finite state method against the analytical solution. Additionally, the developed evaluation framework was applied in the case of a realistic assembly system, and the obtained results were successfully validated against the factory floor measurements. The comparison of the obtained results proves the finite state method as a reliable and CPU-efficient method, suitable for the evaluation of its key performance indicators as well as implementation within more sophisticated design procedures. This kind of predictive analytics is intended to support production management and enhance the reliability of long- and short-term decision-making in the context of the digital twinning of production systems. production system engineering; Bernoulli assembly line; analytical solution; finite state method; assembly systems; key performance indicators; digital twinning; factory floor measurements; transition-rich Markov process  
-network demands) factors of a predominantly stochastic nature [3]. Therefore, production systems may be considered as inherently stochastic, requiring a suitable mathematical approach that will enable their improvement, design, and management, while at a same time being governed by the principle of profit increase. Such mathematical models have been considered for many years by the production system engineering community [4]. Production systems include the different arrangements of machines, work stations, buffers, and transport devices. Some of the most representative ones are the serial production line, production lines with the splitting of material flow, lines with rework and quality control, lines with assembly operations, or any of their combinations. In such a context, the assembly system represents a production process in which different elements are sequentially added until an end product is created. Therefore, assembly systems involve at least two serial lines and one merging operation, yielding assembled parts delivered for further production activities or, conversely, end products [5]. Depending on the nature of the production process, the product either moves through the production system or is kept stationary in cases when it is of a large scale. In the former case, the machinery and working stations are strictly arranged and kept stationary, while in the latter, workers perform sequential assembly operations according to a predefined layout. Thus, assembly systems are sometimes characterized as concurrent processes (i.e., as multiple parallel production activities) that add value to parts and provide intermediate products to a following or final assembly stage. Starting with the Industrial Revolution, assembly systems were considered as one of the first mass-production enablers, simultaneously enhancing production efficiency and profit margins, while introducing product quality, reliability, and uniformity. This would consequently be reflected in the development of new management strategies. In addition, the specialization of various work-stations along the assembly line contributed to the standardization of working procedures, the employment of low-wage personnel, and the simpler replacement of departing employees.