## How to Calculate Your DMAIC Process Sigma

written by: Heidi Wiesenfelder โข edited by: Jean Scheid โข updated: 7/6/2011

Six Sigma focuses on reducing defects and improving efficiency. Process sigma measures how a process performs relative to customer requirements. Earlier in this series we discussed how defects are defined and what process sigma tells us. Now we cover calculating sigma for your process.

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The DMAIC process follows a systematic methodology to clarify process performance and make improvements. By the Measure phase of the project, the team should be ready to calculate process sigma to assess process performance relative to the customer specifications established in the Define phase.

Since process sigma is just a measure of alignment with customer specs, the basic calculation steps are simple. First you will determine the percentage of output meeting customer specifications, and then you will convert that percentage to sigma using a conversion table.

Technically, calculating process sigma requires calculating the percentage of defect opportunities that do not result in a defect. So you would determine the number of defects and the number of defect opportunities, and subtract the defect percentage from 100% to get the Success Rate. But in most cases there is only one defect opportunity for each unit going through the process, so the number of opportunities is the same as the number of units. For instance a support call either results in problem resolution or does not, and a software CD is either defective or functional. So the percentage yield is the same as the percentage of process output that is defect-free, and we will treat them as the same for our purposes.

To calculate process sigma, simply follow these steps:

1. For a specific time period that is representative of your typical process performance, determine the number of units that went through the process. For example, you may have 23,138 support calls for the month of May, or 23,138 software CDs manufactured in the month of May.

2. For that same time period, determine how many of those units were not defective. Remember that the definition of a defect comes from the Voice Of the Customer, whether the customer for your process is internal or external. Let's say that you have 22,046 support calls that were resolved on the first contact, or 22,046 CDs that were fully functional.

3. Divide the second number by the first number to get a percentage. In our example, 22,046/23,138 gives us 0.9528 or 95.28%. This is our percentage yield or success rate.

4. Look up the sigma value that corresponds to your percentage. Just by eyeballing it we can determine that our sigma is somewhere between 3.0 and 3.5, which correspond to 93% and 98% success rates respectively. Using the sigma table located here we see that our process sigma is about 3.2.

There are a few issues you should be aware of in calculating process sigma for your DMAIC project or business process management system:

• To use this method you must have at least five defects and at least five non-defects in your data set. If you do not, try expanding your data set to include a larger sample, perhaps by increasing the time period.
• Your process sigma calculation is only as valid as your work in clarifying customer Critical To Quality metrics (CTQs) and specifications. Be sure you understand how to measure a defect before calculating sigma for your process.
• This type of calculation works best for simple processes. If you have a complex process with multiple steps, there is a more involved technique for calculating sigma for each step individually and then combining them to establish the overall process sigma.
• In Six Sigma we actually calculate what is known as short-term sigma. The originators of the methodology decided to build in the ability for a process to shift by 1.5 sigma over the long term and still provide the required quality.

#### Defects and Process Sigma in Six Sigma

Six Sigma improvements focus on reducing defects. Learn how defects are measured and how process sigma is used to measure process performance and compare processes.