Modeling of a two-machine line with assignable cause quality failures

Quantity modeling has long been studied separately from quality modeling of production lines. The quantitative and qualitative objectives are highly coupled, and hence it is desirable to formulate a model to achieve these objectives simultaneously. We therefore propose a two-machine line model known as the machine-buffer-inspection model, that will be used as the building block for the eventual integration of quality and quantity modeling of production lines with assignable cause quality failures. A Markov model with additional quality states is presented for the machine-buffer-inspection system. Unlike traditional models, this machine-buffer-inspection model enables inspection for quality failures, and is capable of approximating both quality and quantity performance measures. Numerical experiments demonstrate that the model provides good accuracy.