How is Little's Law Used in Lean Six Sigma?

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Understanding Little’s Law

This law is termed Little’s Law because it was postulated by a former professor from the Massachusetts Institutes of Techology named John D. C. Little.

In its original form, the law can be explained using queuing theory as follows,

L = λ W

• ‘L’ denotes the long-term number of customers in the system.
• ‘λ’ denotes the long-term average arrival rate.
• ‘W’ denotes the long-term average time a customer spends in the system.

A more generalized version of Little’s Law is shown below:

No. of Units in the Process = Completion Time per Unit X Time in the System

Applications of Little’s Law

Little’s Law has a variety of applications and can be used in the following areas.

• Queuing
• Project Management
• Transactional Processes
• Lean Six Sigma
• Manufacturing Processes

A Simple Example

The applications of Little’s Law in Lean Six Sigma are illustrated below with a simple example.

A Lean journey usually attempts to reduce or eliminate waste in the system and improve speed, efficiency and overall effectiveness of the system. Minimizing waste includes an analysis of inventory on-hand and taking appropriate steps in order to reduce that inventory.

This can be done using the Little’s Law equation which addresses the relationship between Work In Progress (WIP) inventory, the Lead Time and the Average Completion Rate (ACR).

WIP = Lead Time X ACR

Little’s Law is also known as the Law of Velocity and is one of the Five Laws of Lean Six Sigma.

Assume that there is a small company, and from the historical data it is seen that the company’s average project completion rate is 5 projects every month, and each project takes an average of 8 months to complete.

Then the Little’s Law equation is given by:

40 Projects = 5 Projects Per Month X 8 Months Per Project

Now, if the company has used process improvement via Lean Six Sigma techniques in order to improve the completion rate, and the average completion rate increases to 6 projects per month, then the improvement in the lead time of completion can be visualized as follows.

• New Lead Time = (40 Projects / 6 Projects Per Month) = 6.67 Months

• Improvement in Lead Time of Completion = ((8-6.67)/8) *100 = 16.67% Improvement

Thus Little’s Law can be utilized to judge the impact of Lean Six Sigma.