Little’s Law
Plus process cycle efficiency and how much of the lead time is queue.
Ref: Little 1961 · Hopp & Spearman, Factory Physics · Rother & Shook
IFlow — fill in any two
IIOptional — value-added time
IIIFlow
| Quantity | Value | Unit |
|---|
IVLead time against WIP
VConditions at analysis
VIWhat the law says
Little’s Law is the one piece of arithmetic that holds for any stable process, regardless of how the work arrives, how variable the steps are, or what order things are done in. It needs no distribution and no simulation.
Rearranged, it is the most useful sentence in lean: lead time = WIP ÷ throughput. Throughput is set by your bottleneck, so if you are not adding capacity, the only lever left on lead time is WIP. A queue of 1,800 units in front of a line that finishes 900 a day is two days of lead time no matter how fast any individual step runs — and cutting the queue in half halves the lead time without touching a single machine.
Process cycle efficiency is value-added time divided by lead time. On most first-time value stream maps it lands between 0.1% and 5%, which is not a sign of a badly run plant — it is what queueing looks like when you finally measure it. The number is useful because it puts a ceiling on what faster equipment can buy you: if 99% of the lead time is queue, doubling machine speed changes the total by half a percent.
The law assumes a stable process over the window you measure — average WIP, average throughput and average lead time, with no systematic build-up or drain of inventory. Measured across a period when the queue is growing, it will quietly understate lead time.
This is one of the bench instruments, standing alone
The calculator above takes numbers you type, one set at a time. On the bench, the same solver runs against a dataset you keep — versioned, with the conditions held beside the result, so the number can still be explained to someone who asks six months from now.