Little's Law
Solves Little’s Law for whichever of its three quantities you don’t know: the work in process, the throughput rate or the flow time. Production and industrial engineers use it to estimate lead time from a WIP count, to set WIP caps for a target lead time, and to check whether a line’s figures hang together [2].
Little’s Law
L = λ·W
L is the average number of units in the system (the work in process, WIP), λ the average throughput rate (units leaving, which over a long run equals units arriving) and W the average flow time, the time one unit spends in the system from entry to exit [1]. The page takes λ in units per hour and W in hours, and shows the flow time in minutes as well.
The law needs no assumption about arrival patterns, process times or the order in which units are served. It holds for any stable system observed over a long enough period, whether a machine, a line, a whole plant or a warehouse [1], [2]. That is why it is useful for a quick check, and also why it gives only averages: it says nothing about how much a single unit’s flow time varies.
Limits and common mistakes
- Draw the system boundary once and count everything inside it. WIP must include units waiting in queues and in transit, not only those on machines.
- Use the throughput the system actually achieves, not its capacity. A line rated at 30 parts an hour but shipping 24 has a throughput of 24.
- Keep the units consistent. If throughput is per shift, the flow time comes out in shifts, whatever the label says.
- The law holds for long-run averages of a stable system. During a ramp-up, a shutdown or a growing backlog, a single WIP count and that day’s output can mislead.
- Lead time falls only if WIP falls at the same throughput. Adding WIP to a busy line raises the flow time, not the output [2].
Worked example
A count on a machining line finds 340 parts between the saw and final inspection. The line ships an average of 24 parts an hour. How long does a part take to get through?
- Choose Solve For Flow time / cycle time (W).
- Enter WIP — units in system (L) 340 and Throughput rate (λ, units per hour) 24.
- Press Solve. The Solution shows:
Flow time W = L / λ: 14.1667 hr
Flow time W = L / λ: 850 min
Check: 340 / 24 = 14.17 hours, and × 60 = 850 minutes. If the parts’ total machining time is only about two hours, more than 85 % of the flow time is waiting, a sign that a WIP cap would shorten the lead time.