Parts spawn onto a moving conveyor and queue at a robotic station with a fixed processing (cycle) time. If parts arrive faster than the station can process them, a queue backs up — a classic bottleneck. Random defects are diverted off the line.
throughput ≤ min(spawn rate, 1/cycle time)
queue grows when spawn rate > 1/cycle time
utilization = busy time / total time
- Belt speed — how fast items travel along the conveyor between stations.
- Station cycle time — seconds the robot arm needs to process one part; the true throughput ceiling is 1/cycle time.
- Spawn rate — how often new parts enter the line; exceeding the station's rate builds a queue.
- Defect rate — fraction of parts diverted to the reject bin instead of continuing down the line.
Real use: Manufacturing engineers balance line takt time against station cycle times exactly like this to avoid bottlenecks and size buffers correctly.