The manufacturing industry is part of the global economy, and its development is closely related to modern civilization's historical progress based on science and technology. The introduction part of chapter one is highlighting these achievements and shows the relationship between the manufacturing industry and the economic growth of a country. The first subheading of chapter one shortly describes the historical tradition of the global shipbuilding industry and shows which countries are the major players. The next subheading gives a short review of the Croatian shipbuilding industry followed by a summary on design and analysis of production systems. The main goal of this doctoral thesis as well as the hypothesis are outlined after the literature review. The main goal is the development of a new simulation model which will enable the evaluation of key performance indicators of serial Bernoulli lines. The hypotheses address the possibility that a new model for serial and splitting production lines can be established using a new method named the finite state method employed to calculate the key performance indicators. As compared to conventional methods, such a new approach will result in better design solutions of manufacturing systems, especially of the ship prefabrication and fabrication lines. The second chapter contains an overview the theory of sets and stochastic processes, namely the Markovian chains. Therefore, the basic terms on Ven diagrams, set operators, set algebra, probability theory and stochastic processes are outlined. The discrete time Markovian chains are elaborated and explained more deeply, the Chapman-Kolmogorov equation is shown and the eigenvalue problem is briefly presented. Chapter three deals with the definition of serials lines and the necessary assumptions needed to describe a Bernoulli distribution. In the first subheading the system state space is presented and explained. The next subheading briefly presents the recently developed general analytical solution to formulate the transition matrix. However, this approach is quite challenging and time consuming due to the exceptional complexity of the system state space. Therefore, the finite state method was developed based on the proportionality of the system state space to reduce the evaluation time for lager system states. The aggregation method and a simulation approach are briefly presented for the purpose of comparison with the finite state method and the analytical approach. Such a comparison was done for the first time. The results are highlighted in a short discussion with the conclusion that the new finite state method is worth to be further developed for the case of splitting lines. The chapter four presents the definition of splitting lines and defines the analytical approach. The finite state method for splitting lines was elaborated in the next subheading. The finite state method for splitting lines was validated against the analytical approach and via application case using various expressions for the key performance indicators. At the end, the results prove that the finite state method is capable to model a splitting line and to calculate the required key performance indicators. The finite state method is employed to calculate the eigenvector for the entire system state. This feature enables evaluation of bottlenecks for all key performance indicators. The expressions for such operations are listen in the chapter five. At the end of this chapter the differential evolution theory, is combined with the finite state method and a new design methodology is presented. The chapter six contains the scheme of the new simulation tool ShipProLab developed in FORTRAN using the analytical approach and the finite state method. In chapter seven an illustrative example of a prefabrication and fabrication production line is presented. In this example, the developed theory is employed to determine the key performance indicators and to calculate the time required to compete production of two typical ship sections. Therefore, a brief description of the facility is given including the substitute models. A new facility is designed using the differential evolution theory. The last chapter summarizes the main conclusions of the research. The newly developed finite state method is highlighted as a powerful tool to calculate the key performance indicators for serial and splitting lines that, in combination with the differential evolution theory, enables a sophisticated approach to design issues related to production system engineering.