Mathematical Problems in Engineering
Volume 2005 (2005), Issue 3, Pages 293-308

An analytical formula for throughput of a production line with identical stations and random failures

Dennis E. Blumenfeld and Jingshan Li

Manufacturing Systems Research Lab, R&D Center, General Motors, Mail Code 480-106-359, 30500 Mound Road, Warren 48090-9055, MI, USA

Received 22 November 2004

Copyright © 2005 Dennis E. Blumenfeld and Jingshan Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We derive a simple formula for the throughput (jobs produced per unit time) of a serial production line with workstations that are subject to random failures. The derivation is based on equations developed for a line flow model that takes into account the impact of finite buffers between workstations. The formula applies in the special case of a line with identical workstations and buffers of equal size. It is a closed-form expression that shows the mathematical relationships between the system parameters, and that can be used to gain basic insight into system behavior at the initial design stage.