# Little Law, cycle time and throughput

In this blog entry I talk about whisky and Little Law. While sitting at my dining table I was thinking about a way to explain **Little Law**, **cycle time** and **throughput**. This idea came to mind once I did pour myself a glass of whisky. It was the last dose of a Macallan 12 bottle. I removed the empty bottle from the bar, and took a note to buy another one.

**Problem Statement A**: At home, I have 12 bottles of whisky at my bar. I consume and purchase an average of 6 whisky bottles per year. What is the average time each whisky bottle stays in my bar?

Or, stating the same problem in a different way:

**Problem Statement B**: At home, I have 12 bottles of whisky at my bar. In average, I finish (and purchase) one whisky bottle every two months. What is the average time each whisky bottle stays in my bar?

From the problem statements I can get the following parameters:

The inventory or **WIP** is 12 bottles. (Problem statement A and B)

**Throughput** is 6 bottles per 12 months (Problem statement A)

**Average Cycle tim**e is 2 months per bottle(Problem statement B)

And the question is the average lead time

I will solve the problem two ways:

**Solution 1:**

**WIP** = **Throughput** x **Average Lead Time**

12 bottles = 6 bottles /12 months x Average Lead Time,

Therefore, Average Lead Time = 24 months

**Solution 2:**

**Average Lead Time** = **WIP** x **Average Cycle Time**

Average Lead Time = 12 bottles x 2 months/bottle

Therefore, Average Lead Time = 24 months

The formulas used on both solutions are equivalent:

WIP = Throughtput x Lead time<=>

Lead Time = WIP x Cycle Time

Here are the definitions for these equations’ parameters:

**lead time**is the time between the initiation and delivery of a work item.**cycle time**is the time between two successive deliveries**throughpu**t is the rate at which items are passing through the system.**WIP**– Work in progress; the number of work items in the system. Work that has been started, but not yet completed

Although these formulas are intuitively reasonable, it’s quite a remarkable result. And this is the main theorem in the **Queuing Theory**, which is also known as **Little’s Law** (It was described by John Little in 1961):

The average number of work items in a stable system is equal to their average completion rate, multiplied by their average time in the system.

The average completion rate can be represented by either **throughput**, or its inverse, **average cycle time**. This duality is shown at problem statements A and B. These equivalent statements are made in terms of, respectively, throughput and average cycle time.

I don’t know about you, but before digging into Lean, I was a little confused by Throughput and cycle time (and I did not measure it). I hope this blog post you a simple way to understand and explain it. I also hope more people start measuring such important parameters (I can’t believe I did not use these before going Lean!).

### This content is from my FREE e-book: Cumulative Flow Diagram. Download it here.

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