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

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.