An adaptive approach for determining batch sizes using the hidden Markov model

Determining an optimal batch size is one of the most classic problems in manufacturing systems and operations research. A typical approach is to construct and solve mathematical models of a batch size under several assumptions and constraints in terms of time, cost, or quality. In spite of the partly success in somewhat static processes, wherein the system variability does not change as the process runs, recent proliferation of data-driven process analysis techniques offers a new way of determining batch sizes. Taking into account for dynamic changes in variability in the middle of the process, we suggest a model to determine batch size which can adapt to changes in the process variability using the hidden Markov model which exploits sequence of product quality data obtained points of recalibration dynamically by continuously predicting the level of process variability which is inherent in a system but is unknown explicitly. The proposed model enables to determine points of recalibration dynamically by continuously predicting the level of process variability which is inherent in a system but is unknown explicitly. For the illustrative purpose, a system which consists of a material handler and a machining processor is considered and numerical experiments are conducted. It is shown that the proposed model can be useful in determining batch sizes while assuring desired product quality level as well.