How to determine baseline project sigma is one of the key aspects of the Measure phase. Baseline sigma calculation is part of the Data collection plan.

Sigma denoted by symbol σ (a Greek alphabet) represents standard deviation of a population. Primarily it characterizes the dispersion of a set of data values with respect to mean. It refers to the mathematical concept of standard deviation.

Six Sigma derives from the normal or bell curve in statistics, where each interval indicates one sigma or one standard deviation. Moreover, Sigma is a statistical term that refers to the standard deviation of a process about its mean. In a normally distributed process, 99.73% of measurement will fall within ±3σ and 99.99932% will fall within ±4.5σ.

The 68-95-99.7 rule also known as an empirical rule used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of one, two, and three standard deviations respectively.

## 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.

## 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.

## How to determine baseline project sigma for discrete data

Calculate the process capability is through the number of defects per opportunity. The acceptable number to achieve six sigma is 3.4 Defects Per Million Opportunities (DPMO).

• 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.
• DPO = Defects/(Units * Opportunity)
• DPMO =(Defects / Units * Opportunities) * Total 1,000,000
• Yield = 1-DPO (It is the ability of the process to produce defect free units).

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), then  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

## Examples of Baseline Sigma for Discrete Data

Example: XYZ is a commercial flight carrier operating 10,000 flights a day. There are three defect opportunities like late arrival, lost luggage and poor in-flight experience. Let’s assume 10,000 defects identified. Calculate process sigma level.

• Unit or sample size = 10,000 flights a day
• Defects types = 3 (could be late arrival, lost luggage, poor in-flight experience).
• Opportunities = 10,000 flights * 3 kinds of defect opportunities = 30,000
• Defects: 10,000 defects
• DPMO = (Defects / Units * Opportunities) * 1,000,000
• DPMO= (10000 /10000*3) * 1,000,000 = (1/3) * 1M. = 333,333 defects per Million opportunities.
• From the below chart, 333,333 DPMO translates to a sigma between 1.95 and 1.9.
• Or in excel use the formula = NORMSINV (1- (defects/ sample size * Number of defect opportunities per unit in the sample))+1.5

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, 4 sigma and 5 sigma level of quality?

Answer: A sigma of 2 equates to 308,538 defects per million opportunities or 69.2% yield. Further, A Sigma of 3 = 66,807, sigma of 4 = 6,210 and sigma of 5 = 233. (refer above table).

## How to Determine Baseline Project Sigma for continuous data

Process Capability is the determination of the adequacy of the process with respect to the customer needs. Process capability compares the output of an in-control process to the specification limits. We can say the process is capable when almost all the measurements fall within the specification limits. Cp and Cpk are considered short-term potential capability measures for a process.

In Six Sigma we want to describe processes quality in terms of sigma because this gives us an easy way to talk about how capable different processes are using a common mathematical framework.

Cpk is a measure to show how many standard deviations the specification limits are from the center of the process.

• Cplower = (Process Mean – LSL)/(3*Standard Deviation)
• Cpupper = (USL – Process Mean)/(3*Standard Deviation)
• Cpk is smallest value of the Cpl or Cpu:  Cpk= Min (CplCpu)

The main purpose of Cpk is to determine how close a process is performing when compared to its specification limits and considering the natural variability of the process. Always larger Cpk is better, it indicates the less probability of any item will be outside the specification limits.

Process sigma = 3* Cpk. Hence We generally want a  Cpk of at least 1.33 [4 sigma] or higher to satisfy most customers.

## Examples of Baseline Sigma for Continuous Data

Example: The specification limits of rubber sheet is 5±1cm. Operator randomly recorded 4 subgroups of values every half an hour in three shifts. While the average mean is 4.7 and short term pooled standard deviation is 0.2 cm. Calculate the process sigma level.

• USL=6cm
• LSL = 4cm
• Standard deviation σR= 0.2 cm
• Process mean=4.7cm
• Cplower = (Process Mean – LSL)/(3*Standard Deviation) = 1.16
Cpupper = (USL – Process Mean)/(3*Standard Deviation) = 2.16
• Cpk = min (Cpu, Cpl) = 1.16
• Sigma =3*1.16= 3.5

## Why Use Sigma Instead of Percent?

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. but it would makes sense for your business.

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

## Authors

• I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams. Overtime I've grown the site to help tens of thousands of Six Sigma belt candidates prepare for their Green Belt & Black Belt exams. Go here to learn how to pass your Six Sigma exam the 1st time through!

•  victor says:

Hello

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 Six Sigma Study Guide says:

Thanks, Victor. You were right. I updated the post and added an example. Thanks! Moreno Castro says:

How can I calculate baseline sigma when the DPMO is already given? Six Sigma Study Guide says:

Hi Moreno,

Just look at the chart above and find the corresponding Sigma level that equates to your DPMO.

Thanks, Ted. George says:

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 https://www.gigacalculator.com/articles/what-is-six-sigma-process-control-and-why-most-get-it-wrong-1-5-sigma-shift/ 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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