###### Abstract
Therefore, assembly systems often became considered as a company's growth indicator, standing alongside serial production lines as the workhorse of the industry [4,6]. However, rather expensive production assets came to be associated with the introduction of new assembly systems including demanding management and production organizations, considerable warm-up stages, and additional investments through dedicated education, labor, or factory space [7]. Hence, a rational approach to the problem of assembly system evaluation including the communication between work-stations, material flow plans, and work schedules is a necessary prerequisite, underpinning the companies' strategic decisions and opening new perspectives of business development. Otherwise, an eventual failure in the system could seriously affect the production process through slowdowns and ineffectiveness, manifested as starvations, blockages, and finally, decreased production rates [8]. Usually, the effectiveness of a particular production system is expressed in terms of the key performance indicator (KPI) for each element of the production system, while the more general concept of overall equipment effectiveness (OEE) is taken into account when considering losses at a systemic level. Both KPI and OEE are of great significance when implementing the lean philosophy principle, particularly in the context of value stream mapping [9]. From a general perspective, KPIs can be classified as quantitative or qualitative values, reflecting objective and measurable facts as well as personal opinions or interpretations. Quantitative KPIs are of particular importance in the context of production system engineering, and these can be categorized into four groups related to revenue, production cost, process improvements, and customer satisfaction. A list of relevant KPIs and their further classification is presented in detail by [10]. Aside from KPIs, the OEE plays a significant role in modern production system management, as a framework providing classification, measurement, and the minimization of production losses and, thus, an increase in effectiveness [11]. The OEE is a measure of the production system's efficiency, based on a ratio of \(T_{I}/T_{R}\), where \(T_{I}\) is the time required for the manufacture of high quality products in ideal conditions, and \(T_{R}\) is the time required for their manufacture in realistic conditions, taking into account the production system availability, breakdowns, scheduled maintenance, defective parts, rework requirements, material supply uncertainties, financial capability, and others [10]. These may be considered as deterministic or stochastic variables and thus will have an impact on the reliability of OEE estimates. The evaluation of KPIs and OEE requires the application of suitable mathematical models, particularly when variables of a stochastic nature are considered. Some examples include queuing networks, process algebra, Petri nets, or stochastic automata. However, the Markov chain theory is employed as a reliable approach in most cases, yielding joint probability distributions, reflecting the likelihoods of systems in certain states [4]. This approach has therefore been the main focus of the majority of research publications and papers, especially those primarily addressing issues related to serial production lines including different machine reliability definitions. Other line arrangements such as ones including material flow splitting, assembly systems, or lines with reworking stations and quality control have been considered to a significantly smaller extent. This is particularly valid in the case of assembly production lines that are dominantly evaluated through a reduction in the Markovian framework, due to the so-called \"dimensionality curse\", to semi-analytical methods such as the aggregation procedure [12] and the decomposition method [13].