Photo by Chuck Coker
Photo by Chuck Coker

How do you calculate 6 Sigma, 5 Sigma, etc? Start here with your baseline sigma calculation.

This is part of the Data collection plan.

Determining Baseline Sigma

  1. Figure out the variables. (try to put these in terms of the output of the process)
    • Unit – the item produced or processed or created.
    • Defect – anything that causes a failure (i.e. misses the customer’s requirements.)
    • Opportunity – the number of critical to quality measures we are counting on each opportunity in defects. If there are 4 types of defects, this value is 4.
  2. Determine if Zero defects are needed or if there is partial credit.
    • If the process is only considered correct if there are no defects at all (100% correct): use the DPMU calculation (defects per million units)  DPMU = (Defects / Units) * 1,000,000
    • If partial credit is received for meeting some of the requirements: use the DPMO calculation (defects per million opportunities)  DPMO = (Defects / Units * Opportunities) * Total 1,000,000
      • Ex. Commercial Flight:
        • Unit is the # flights. (Say there are 10,000 flights a day for this example)
        • Defects types could be late arrival, lost luggage, poor in-flight experience. (Say 3 types of defects in this example.)
        • Opportunities would be 10,000 flights * 3 kinds of defect opportunities = 30,000
        • Defects: For this example, let’s say there are 10,000 defects (remember, a total of 30,000 defects are possible)
        • DPMO = (Defects / Units * Opportunities) * 1,000,000 = (10000 /10000*3) * 1,000,000 = (1/3) * 1M. = 333,333 defects per Million opportunities.
  3. Check the chart (and determine if you want to use the 1.5 sigma shift or not)
    • In our example, 333,333 DPMO translates to a sigma between 1.9 and 2.


Six Sigma DPMO to Sigma to Cpk Chart
Six Sigma DPMO to Sigma to Cpk Chart by

Why would you want your baseline sigma to be 1, 2, or 3?

You would want your baseline sigma to be 1, 2, or 3 because those are indicative of bad processes and you would like your team to be able to see an improvement in the process at the end of the project.

What is the reason behind calculating the sigma value?

The value in making a sigma calculation is that it abstracts your level of quality enough so that you can compare levels of quality across different fields (and different distributions.) In other words, the sigma value (or even DPMO) is a universal metric, that can help yourself with the industry benchmark / competitors.

Where was Sigma First Used?

Motorola engineers came up with the idea for sigma levels in the 1960s.

Does the data type (Discrete/Continuous data) have any effect on calculating the sigma value?

Data type does NOT have an effect on the sigma value so long as we are counting the total number of opportunities and defects properly.

Examples of Baseline Sigma

Question: A company is currently operating at a 2 sigma level of quality. What will be the number of defects expected if they are able to improve to a 3 sigma level of quality? A 4? A 5?

Answer: A sigma of 2 equates to 308,770 defects per million opportunities or 69.2% yield. A Sigma of 3 = 66,811. A Sigma of 4 = 6,210. A Sigma of 5 = 232.67. (See baseline Sigma)

Why Use Sigma Instead of Percent?

The other day I was asked why can’t we just use the percentage reduction in the defects as a means to assess the process rather than using the sigma value?

The answer is that of course you can. Many people do. My advice is to do what makes sense for your business.

However, measuring change in terms of sigma allows you to judge improvements and opportunities in a more consistent manner.

Comments (5)


Formulas are wrong! Should be as below:

 DPMO (Determine if Zero defects are needed)
 If 100% correct: use the DPMU calculation (defects per million units)
DPMU = (Defects / Units) * 1,000,000
 If partial credit: use the DPMO calculation (defects per million opportunities)
DPMO = DPO*1,000,000 = (Total Defects /Total Opportunities)* 1,000,000
=(Total Defects / (Opportunities per unit * Total Units)) * 1,000,000

Estimating long-term sigma from short-term observations is not achieved by adding an arbitrary shift of 1.5. The short-term measurements are your best long-term bet. A process can shift by much more than 1.5. It can also shift by much less.

As the argument is summarized here sigma shift doesn’t make much sense, especially outside Motorola’s then manufacturing process where it might have had an empirical basis. Reporting a 6 sigma process as 4.5 sigma makes just about as much sense as reporting a 4.5 sigma process as 6 sigma.

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