# Process Lead Time and Little’s Law

Perhaps you’ve heard of process lead time, a common metric in manufacturing that gives you an idea of how long you’ll have to wait on a widget if you start working on it right now. But you might not know that it’s closely related to a queue theory concept called Little’s Law.

These are fundamental concepts that have paved the way for waves of improvement in many fields.

At Veryable, we champion the importance of operational improvements, no matter where you are in your journey. We help businesses every day to reach new levels of efficiency through the application of on-demand labor in their operations. We won’t talk about that solution here, because we’re going to focus on explaining the fundamental concept of process lead time.

In this article, you’ll learn about Little’s Law, how it can help you calculate process lead times quickly, and how you can use that information to make operational improvements.

## What is Little’s Law?

Little’s Law was theorized by John Little, a professor at MIT and an awarded operations researcher, to determine how many people are in a given system (e.g. traffic light) at any time.

###### The equation is as follows:

###### L=ƛW

In this equation, L is the average number of people in line, ƛ is the average exit rate, and W is the average time spent in the queue.

### Little’s Law example situation

A practical example of Little’s Law in action would be a checkout line. Imagine that a store owner only has one checkout line, and it’s creating a backup in the store because the line is getting too long. So he grabs a notepad, watches his checkout line in action, and does some quick math to figure out what’s causing the problem.

He notices that 16 people enter the store and check out every hour, and they spend an average of 15 minutes (0.25 hours) in line. Using Little’s Law, he calculates that this results in four people in line at any given time.

The store owner might seek to influence the length of the queue by speeding up checkouts from its current rate of four minutes per customer. Or, he might open more lines to serve more customers at once.

That leads us to the practical applications of little’s law as it relates to lead times and inventory.

## Process lead time calculation using Little’s Law

The process lead time equation is analogous to Little’s Law, but uses manufacturing terminology. With a little algebra, you end up with the following equation:

###### PLT = WIP / ER

###### Process lead time (PLT) is equivalent to the work in process (WIP) divided by the exit rate (ER).

For example, if you have 20 widgets in process and they exit the line at 2 every minute, then you have a process lead time of 10 minutes.

### What is process lead time used for?

The process lead time calculation using Little’s Law gives you a quick, back of the napkin way to see where you stand. When you know your process lead time, you have a baseline for making operational improvements.

Using this information, you can decide whether you need to speed up your process or run more lines in parallel to improve output. In other words, you could seek to speed up the exit rate for each line or reduce the work in process per line.

### How to improve process lead time

Based on the equation above derived from Little’s Law, you can improve process lead time by reducing the work in process or by making process improvements to speed up the exit rate. That would mean either adding more lines running in parallel or reducing the time each worker spends on their step in the process.

There are other ways outside of this simplification to achieve process lead time improvements. Learn more ways to improve lead time in our blog about using on-demand labor to improve lead time.

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