Cycle time and WIP calculator (Little's law)
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KEY POINTS
In a steady-state fab, cycle time = WIP ÷ throughput (Little's law). Front-end wafers spend more time waiting than being processed, and leading-edge logic runs at an X-factor of about 3 to 4. Queue time at a tool grows as u/(1−u) with utilization u, so it rises steeply above 90%.
Whole fab: Little's law
Little's law holds when WIP and throughput are stable over the long term (steady state). It will not match actual cycle time in a fab that is ramping up or adjusting output.
Single tool: utilization and queue time (Kingman's formula)
Utilization and cycle time (operating curve)
Cycle time by utilization
| Utilization | Cycle time | X-factor |
|---|---|---|
| 70% | 2.74 h | 2.74 |
| 80% | 3.98 h | 3.98 |
| 85% | 5.22 h | 5.22 |
| 90% | 7.71 h | 7.71 |
| 95% | 15.15 h | 15.15 |
Queue time explodes as utilization rises
Front-end semiconductor manufacturing is a re-entrant flow that passes through the same tool groups dozens of times, and a wafer takes two to three months to complete. Most of that time is spent waiting in front of tools rather than being processed; in leading-edge logic the X-factor is around 3 to 4. By Little's law, the only way to shorten cycle time without changing throughput is to reduce WIP.
Queue time grows as u/(1−u) with utilization u, so it climbs steeply above 90%. The more expensive the tool, the more tempting high utilization becomes, but it is a trade-off against cycle time. Reducing variability in arrivals and processing (batched lot releases, setup changes, failures) shortens queue time substantially at the same utilization.
FAQ
What is the X-factor?
Cycle time divided by raw process time, the time a wafer would take with no waiting. An X-factor of 3 means two-thirds of the time is spent in queues.
What is days per mask layer (DPML)?
Cycle time in days divided by the number of mask layers. It lets fabs running processes of different complexity compare their speed.
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Last updated: October 23, 2026