Little's law forms a part of queuing theory and has deep implications for the 'Improve' aspect of DMAIC within Lean Six Sigma. It calculates the average wait for a customer or item within a transactionary process.

On our Green Belt Six Sigma Training, you'll learn all about Little's law within the wider context of DMAIC and we've discussed using Six Sigma to improve queuing times before.

So what exactly is Little's law, how does it impact upon Six Sigma and why is it so useful and important?

What is Little's Law in Six Sigma?

Little's Law says that, under steady state conditions, the average number of items in a queuing system equals the average rate at which items arrive multiplied by the average time that an item spends in the system. 

Written as a formula it is:

L= ? W 

When:

L =average number of items in the queuing system,
W = average waiting time in the system for an item, and
? =average number of items arriving per unit time.

As Little himself says:

"This relationship is remarkably simple and general. We require stationarity assumptions about the underlying stochastic processes, but it is quite surprising what we do not require. We have not mentioned how many servers there are, whether each server has its own queue or a single queue feeds all servers, what the service time distributions are, or what the distribution of inter-arrival times is, or what is the order of service of items, etc

In good part because of its simplicity and generality, the equation is extremely useful. It is especially handy for "back of the envelope" calculations. The reason is that two of the terms in may be easy to estimate and not the third. Then Little's Law quickly provides the missing value."

How Does Little's Law Affect Six Sigma?

Little’s Law provides an equation for relating Lead Time, Work-in-Process and Average Completion Rate for a process. 

This falls into the "Improve" part of DMAIC in the sense that by reducing work-in-process while maintaining the same average completion rate, lead time will reduce.

Similarly, by improving the process to increase average completion rate while maintaining the same work-in-process, lead time will again be reduced.

Why is Little's Law so Important to Six Sigma?

As such, Little's Law becomes a particularly useful tool for almost any kind of process improvement because at its core, it's working with a flow of 'things'.

Whether those 'things' are people entering a queue to buy stamps or they're components being installed into a phone, you can use Little's Law to find any one of the missing values outlined above. 

If you're still unsure about how Little's Law works within Six Sigma, the following two resources are worth checking out. Firstly a Slideshare that illustrates Six Sigma in action:

And secondly a really interesting video in which John Little himself explains his own law (apologies for the sound quality):

And so there you have it: Little's law as explained by the man himself. If you'd like to find out more about Little's law and other aspects of Six Sigma, take a look at our range of Six Sigma Courses.