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Lesson 11 out of 21: Calculating the Sigma Level - Toolset

Overview

When calculating the Sigma performance level for a product or process, the metric Defects Per Million

Opportunities (DPMO) is generally used. Because complex products like automobiles, aircraft, or

computers have many more opportunities for defects than simple products like pencils and paperclips,

DPMO was created to level the playing field and provide a fair comparison - often a problem within

companies that provide a wide range of products and services (see the Slide Show on DPMO). Theanimation below shows the relationship between Sigma Level, DPMO, and Yield.

To see how the Sigma Level, DPMO, and Yield are related, click on the hand and drag the distribution.

Example

Example 1

For perspective on Six Sigma, and what it really means, consider the average human life for a moment. If 

the average lifespan is 75 years, then there are 657,000 hours. At three defects per million, a Six Sigma

life would never have a bad day - only about two bad hours! If those two bad hours were the hour of 

birth and the hour of death, then everything in between would be perfect!

 

Defect Definition: A defect is defined as any failure of a product or process to meet customer requirements.

Customer requirements may or may not be expressed

accurately as internal specifications, so a product or

process might meet specifications but still be defective

in the customer's mind.

Calculating the Sigma Level

Deeper Dive:

DPMO

Discussion

The Sigma Level - Example

Deeper Dive:

Other

Quality

Metrics

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The chart below shows the relationship between Sigma Level, DPMO, and Yield at several different Sigma

Levels:

* Yield calculation assumes only one possible defect per unit, which is not usually the case.

Example 2

A mortgage company is embarking on a project to improve the performance of its underwriting and loan

closing process. The company wants to establish a Sigma Level baseline in order to gage its improvement

efforts. The company has identified four general steps in the process. Each of the process steps is shown

below, along with the potential number of defects for each step (this is a simplified example):

According to this information, there are a total of 35 possible defects that could occur during each loan

approval and documentation process. Company records indicate that 2,500 loans were processed during

the last year, and out of those 2,500 loans, 3,500 defects were identified.

So what is the Sigma Level ?

Each of the 2,500 loan applications represented 35 defect opportunities, for a total of 87,500

opportunities. Actual experience was 3,500 defects.

Defects per million opportunities is therefore: (3,500/87,500) x 1,000,000 = 40,000

At a level of 40,000 Defects Per Million Opportunities, the company is operating at a Sigma Level between

3.0 and 3.5.

In the "How" section of this lesson, we will review the Sigma Level calculation in greater detail.

How

Yield *

Defects Per

Million Opportunities Sigma Level

  69.15% 308,500 2.0

  84.13% 158,700 2.5

  93.32% 66,800 3.0

  97.73% 22,700 3.5

  99.38% 6,200 4.0

  99.87% 1,300 4.5

  99.977% 230 5.0

  99.997% 30 5.5

  99.9997% 3.4 6.0

Process StepPotential Defects Per

Application

Collect information fromapplicant

15

Verify applicant information 5

Evaluate credit quality 5

Prepare loan paperwork 10