Lead time: Applying Little’s Law to track it


“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.” ~ John Little, 1961
The text above is from “A Proof for the Queuing Formula” by Little, J. D. C. (1961). It is knows as the Little’s law.
By solving this simple first equation you are able to find out the average time for work items in your system. My whiskey bar provides us a great stable system example to illustrate how you can apply Little’s law to track the average lead time.
My whiskey bar
my bar

My wife and I have a combination. The right side of the bar is mine, the left side is hers. I only drink whiskey. My side of the bar fits 12 bottles of whiskey. 

Whenever a bottle finishes, I remove it from the bar. Then I open a new one, and add it to the bar. My bar is a stable system: the rate at which whiskey bottles enter the bar is the rate at which they exit.
 

The number of whiskey bottles at my bar is constant: 12 bottles. Per year, I finish an average of 6 whiskey bottles.So, what is the average time for whiskey bottle in my bar?

 
Let’s apply Little’s law
Little’s law:“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.”
Or
The average number of work items in a stable system
=
average completion rate
X
average time in the system
Using  my bar terms:
12 bottles (number of whiskey bottles in my bar)
=
6 bottles / year (average completion rate)
X
average time in my bar
Therefore, the average time a whiskey bottle stays in my bar is 2 years.
Give it a try! Go ahead and apply the Little’s Law formula to your stable system. Similarly to  my bar example, given the average work items in the system (WIP) and the completion rate (throughput), you can derive the average time in the system (lead-time).