The Bernoulli Assembly Line: The Analytical and Semi-Analytical Evaluation of Steady-State Performance

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.