A Finite State Method in the Performance Evaluation of the Bernoulli Serial Production Lines

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.