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.

The digital twinning concept stands as a remarkable opportunity to integrate sophisticated mathematical models within the context of existing manufacturing systems. Such models may provide shipyard management with predictive analytics, improving the final results at the strategic, tactical, and operational levels. Therefore, the possibility of integrating the Markovian-framework-based finite-state method into the context of ship production is presented in this study, including its outline, digital thread, and factory-floor data reliance. First, the predictive analytics problem is addressed by the finite-state method in the case of the shipyard’s fabrication line, and the obtained results are validated afterward using a numerical model through discrete-event theory. The predictive analytics indicate an almost ideal balancing of the fabrication line, except for the buffers storing stiffeners before the coat-dying and marking operations. In addition, the improvability analysis of the shipyard’s fabrication lines extended the scope of the predictive analytics using bottleneck identification and affecting the key performance indicators through a digital thread, as well as by improved maintenance strategies.

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.

The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses and preventive maintenance. This is especially relevant if nonhomogenous aspects of production systems are taken into account. An analytical and approximative solution to the problem of the transient response of homogenous and nonhomogenous Bernoulli production systems is developed in this paper based on the eigendecomposition of transition matrices, the eigenvalue problem, and the finite-state method. In particular, sub-resonant and resonant nonhomogeneous production lines are introduced for the first time. Also, the most significant key performance indicators are developed as functions of the time elapsed from the first cycle. Finally, the relationship between the number of eigenvalues and the accuracy of the results is inspected by employing a sensitivity analysis. The presented theoretical framework was employed in the case of a wood processing facility to present the potential application of the theory in the case of long- and short-term management of production systems.

Production lines are the backbone of the manufacturing industry. To gain the best profit out of a line it is necessary to design each line using the production system engineering. Therefore, three approaches can be used, the numerical, the analytical, and the semi-analytical approach. The aggregation method, finite state method, and the numerical approach are statistically compared concerning the analytical approach using the STATISTICA software. We analyzed the interaction between the input data and the output data for the finite state method in an illustrative example, using a full factorial design and the Design Expert software.

Production lines can be designed by an analytical, semi-analytical, or numerical approach. This paper gives a brief introduction to the analytical approach of a single buffer line, the aggregation method, and the analytical approach of a multi-buffer line. An automotive paint shop production system will be used as a figurative example to compare the aggregation method and the recently developed analytical approach for a multi-buffer line. A discussion at the end will show the advantages and disadvantages of the analytical approach.