The Digital Twinning of Manufacturing Systems is continuously gaining in importance concerning the optimization of production processes and requirements for production efficiency improvements. Therefore, the finite state method will be presented in this work as a semi-analytical approach of the Production System Engineering based on Markov Chains. The presented method can efficiently calculate the probability distributions associated with each possible system state defined according to the number of buffers and their capacities. In this study, the finite state method is employed to describe the ship steel hull process as a platform for the implementation of digital twinning technology. The method is employed to rebuild a model of a real ship production process using a combination of serial and splitting lines. The key performance indicators such as the production rate, the work in process, and probabilities of starvation and blockade are calculated and compared to the corresponding results obtained through a simulation approach using the software tool Enterprise Dynamics. The conclusion highlights the advantages and disadvantages of methods employed in the context of Digital Twin Technology.