Approximate Analysis of a Serial Manufacturing System with Inserting Process

A serial manufacturing system with approximate analysis implies that each machine in the production line may process the items from the outer of the production line. The system includes production blocking due to the presence of finite buffers between successive machines. Owing to the presence of the inserting process, the system can not keep the conservation of flux, so analyzing this system is difficult. A tandem queueing theory is used for analyzing the Markov process associated with a 2-stage system. An approximate method is proposed for analyzing systems with an arbitrary number of stages. The approximate method is that utilizing the starving and blocking probabilities of machines in the decomposed 2-stage systems modifies the processing and failure rate of machines. The approximate method avoids difficulties caused by the complexity in evaluating performance of the system. Numerical experiments show that the proposed approximation yields fairly accurate results.