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Little’s law calculator for manufacturing lead time

Enter work in process (WIP) and the line’s throughput to get the manufacturing lead time. Or solve for WIP, or throughput, from the other two. Add the value-added time to see process cycle efficiency.

Process data

units
Units between order release and finished goods: on machines, in queues and in internal supermarkets.
units
Good units leaving the process, on average.

Working calendar

h
days
The time the unit is actually being transformed. For process cycle efficiency.

Result

3days of manufacturing lead time

L = λ × W: 1,200 units = 400 units/day × 3 days.

Lead time
48 h
3 days
0.6 weeks
Throughput
25 units/h
400 units/day
2,000 units/week
WIP
1,200 units
Process cycle efficiency
0.42%

Only 0.42% of the lead time adds value. The rest is the unit waiting in a queue.

With half the WIP (600 units) and the same throughput, lead time drops to 1.5 days.

The formula

WIP = throughput × lead time, or lead time = WIP ÷ throughput

Term What it is
WIP (work in process) units released to production and not yet finished: on machines, in queues and in internal supermarkets
Throughput good units leaving the process per unit of time, on average
Manufacturing lead time average time a unit takes from release to finished goods (Factory Physics calls it cycle time)

John Little proved the relation in 1961 for queues in general. Hopp and Spearman, in Factory Physics, put it at the heart of how plants behave: at the same throughput, more WIP means more lead time and not a single extra unit sold.

The calculator converts hours, days and weeks through your working calendar (hours per day, days per week), because the line only moves parts during the hours it works.

Worked example

The calculator starts with 1,200 units in process, a throughput of 400 units a day, and 16 hour working days.

  1. Lead time = 1,200 ÷ 400 = 3 working days
  2. In hours: 3 × 16 = 48 h. Throughput per hour: 400 ÷ 16 = 25 units/h
  3. Each unit gets 12 minutes of value-added work. Process cycle efficiency = 0.2 h ÷ 48 h = 0.42%

In plain words: the part spends 3 days in the plant and only 12 minutes being worked on. The rest of the time it waits.

Why cutting WIP cuts lead time

Think of a checkout line. If the cashier serves one person a minute and ten people are ahead of you, you wait ten minutes. The cashier is not slow, the line is long. A plant works the same way. If the line ships 400 units a day, with half the WIP (600 units) lead time drops to 1.5 days, at the same throughput with the same machines.

That is why kanban, smaller lots and WIP limits shorten lead time. Smaller lots depend on short changeovers: see what a setup reduction is worth with the SMED changeover calculator.

Common mistakes

  • Using the logistics lead time. This is time inside production, not from order to delivery.
  • Mixing calendar and working time. Throughput per 16 hour day and lead time in calendar days do not match. Pick one basis and keep it.
  • Applying it to a few days of data. The law holds for averages of a stable process. During a ramp up or a long stop the numbers will not add up.
  • Believing more WIP means more output. Beyond what keeps the bottleneck busy, extra WIP only adds lead time.

The pace demand asks for is your takt time, and what the line can deliver is its production capacity.

Frequently asked questions

What is Little’s law?

L = λ × W, proved by John Little in 1961: the average number of items in a system equals the arrival rate times the average time each item spends in it. On the shop floor: WIP = throughput × lead time. It holds for long-run averages of any stable process.

How do you calculate manufacturing lead time?

Lead time = WIP ÷ throughput. Count the units between order release and finished goods and divide by average daily output. With 1,200 units in process and 400 units a day, lead time is 3 days.

How do you calculate WIP?

Count it, or run Little’s law backwards: WIP = throughput × lead time. A line shipping 400 units a day where each unit takes 3 days from release to finish holds 1,200 units in process on average.

What is process cycle efficiency?

The share of lead time spent on value-added work: PCE = value-added time ÷ lead time. In traditional plants it is often under 10%, and frequently under 1%. The rest of the time the part sits in a queue.

Does adding WIP increase throughput?

Only up to the point where the bottleneck never starves. Past that, extra WIP adds lead time and nothing else. Factory Physics calls the WIP level where a line reaches full throughput with minimum lead time the critical WIP.

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