Approximate analysis of re-entrant lines with Bernoulli reliability models

Re-entrant lines are widely used in many manufacturing systems, such as semiconductor, electronics, etc. However, the performance analysis of re-entrant lines is largely unexplored due to its complexity. In this paper, we present iterative procedures to approximate the production rate of re-entrant lines with Bernoulli reliability of machines. The convergence of the algorithms, uniqueness of the solution, and monotonic properties, have been proved analytically. The accuracy of the procedures is investigated numerically. Finally, a case study of automotive ignition component line with re-entrant washing operations is introduced to illustrate the applicability of the method. The results of this study suggest a possible route for modeling and analysis of re-entrant systems.