# Little’s Law

A theorem that describes how the long-term average number of items (L) in a stationary system (work in process or WIP) is equal to the long-term average arrival or exit rate or throughput (λ) multiplied by the average time (W) that an item spends (wait time) in the system. It is used to estimate the Lead Time, Work In Process (WIP) or Throughput Rate of a process.

The formula is shown as L = λ x W, or could be written as WIP = Exit Rate x Lead Time

It can also be written as W = L / λ, or Lead Time = WIP / Exit Rate

A simple explanation is that the more items in the queue, the longer it will take (lead time) for items to be completed if the throughput rate stays the same.

Example: If a drive-thru restaurant has 10 cars in line (WIP), and it takes 80 seconds on average to give out food at the window, then we can calculate the wait or lead time for the 11th car approaching the drive-thru line.

L = λ x W

WIP = Exit Rate x Lead Time

10 cars in line = cars leaving the drive-thru per minute (60 sec / 80 secs) x Lead Time

Lead Time = 10 / 0.75 = 13.33 minutes wait time. If you only have 15 minutes, that might be cutting it close. If you only have 10 minutes, you will likely be late to your next appointment and don’t have time to stop.

To reduce lead time, you can either:

- Increase the throughput (complete items faster)
- Reduce the number of items in queue (reduce or restrict work in process)

Reminder, you need to have a stable system without major changes, and these numbers are based on averages, and do not reflect the variation in the values. This means the model works well in the long term, but may vary greatly when viewing it in the short term.

Links

- Little’s Law – Wikipedia
- What is Little’s Law – B-2 Bomber Example
- Little’s Law – All About Lean
- Applying Little’s Law to Business – Shmula

### Additional Resources

- Calculating Overall Equipment Effectiveness (OEE)– creativesafetysupply.com
- Toyota Donates What Money Couldn’t Buy: Efficiency– kaizen-news.com
- Theory of Constraints: Part 3– lean-news.com
- Changeover – Creating Flow and Eliminating Waste– blog.5stoday.com
- Panda Express – The Relationship Between Speed and Quality In Business– blog.creativesafetysupply.com
- Back to Basics and a Little Humor– creativesafetypublishing.com
- Lean Management And The 5s Principles– 5snews.com
- Stationary Process Container Safety for Food Processing– safetyblognews.com
- Basic Overview of Kanban– iecieeechallenge.org