Research on the performance measure evaluation of Bernoulli serial production lines is presented in this paper. Important aspects of the modeling and analysis using transition systems within the Markovian framework are addressed, including analytical and approximation methods. The “dimensionality curse” problems of the large scale and dense transition systems in the production system engineering field are pointed out as one of the main research and development obstacles. In that respect, a new analytically-based finite state method is presented based on the proportionality property of the stationary probability distribution across the systems’ state space. Simple and differentiable expressions for the performance measures including the production rate, the work-in-process, and the probabilities of machine blockage and starvation are formulated. A finite state method’s accuracy and applicability are successfully validated by comparing the obtained results against the rigorous analytical solution.

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The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the modeling of steady-state behavior of serial Bernoulli production lines were considered in this study, namely, the analytical approach, the finite state method, the aggregation procedure, and numerical modeling. The accuracy of the performance measures determined using the semi-analytical methods and the numerical approach was validated using numerous theoretical examples and the results obtained using the analytical model. All of the considered methods demonstrated relevant reliability, regardless of the different theoretical backgrounds.

The ship production process is a complex manufacturing system involving numerous working stations mutually interconnected by transport devices and buffers. Such a production system can be efficiently modeled using the stochastic system approach and Markov chains. Once formulated, the mathematical model enables analysis of the governing production system properties like the production rate, work-in-process, and probabilities of machine blockage and starvation that govern the production system bottleneck identification and its continuous improvement. Although the continuous improvement of the production system is a well-known issue, it is usually based on managerial intuition or more complex discrete event simulation yielding sub-optimal results. Therefore, a semi-analytical procedure for the improvability analysis using the Markov chain framework is presented in this paper in the case of the shipyard’s fabrication lines. Potential benefits for the shipyards are pointed out as the main gain of the improvability analysis.