Little’s Law: A Simple Rule for Work, Output and Time That’s Easy to Misuse
On average, the amount of unfinished work equals the output rate times the time each item spends inside. It’s a handy check, but only if all three are measured the same way.
The rule
A clinic sees 4 patients an hour, and each patient spends half an hour from check-in to checkout. So on average, 2 patients are inside at any moment. That’s Little’s Law. Here’s the general version. Take a stable system, where work isn’t piling up more and more over time, and watch it long enough. Then the average work in progress (WIP) equals the average throughput times the average flow time. In symbols, that’s L = λW. L is the average amount of work inside. λ (the Greek letter lambda) is the average throughput, meaning how fast work finishes. W is the average flow time, meaning how long each item spends inside. The rule is short enough to memorize. It’s also strong enough to catch stories about a process that don’t add up.
Say a factory reports three things. Throughput is the same, WIP has doubled, and cycle time (the time each job spends inside) hasn’t changed. Those numbers don’t fit together. Maybe something is measured from a different start or finish point. Maybe an assumption is off. Either way, it’s worth a closer look.
Use the same start and finish line
All three numbers have to use the same boundary: the same start line and finish line. Say you count WIP from the moment a job is sent out to the factory floor. But you only start the clock on cycle time after the job reaches some later step. Now you’re mixing two different definitions. Other things can throw off a quick reading too. Think of parts that have to be redone, parts that get scrapped, or a changing mix of products.
Little’s Law doesn’t tell you what caused what. It only links long-run averages. To learn why things are the way they are, you need more. Pair it with knowledge of the process, queueing theory (the math of waiting lines) and a look at how much things vary.
A good habit
Before you reach for fancy models, use the equation as a quick bookkeeping check. Work that comes in has to either go out or still be inside. Good industrial engineering often starts by making the basic flow numbers agree with each other.