## Sunday, June 24, 2012

### Is it 6 Sigma (6σ) or 4.5 Sigma (4.5σ)?

Time and again, I have come across this question – does Six Sigma (6σ) really translate to 3.4 defects per million opportunities (DPMO)? Is there any shift which is not known to us and hence it is actually 4.5σ? We will check what it actually is and hence put it to rest.

Whether you are following DMAIC or DMADV methodologies of Six Sigma, you have to be familiar with the below terms and gather metrics such as DPMO to calculate the final process improvement. These are addressed as part of the Critical to Quality or CTQ. Below are certain terms to have a better understanding.

Certain Terms:
1. Defects: Anything that does not meet the customer requirement.

2. Units: Something which is measurable by the customer. It is measurable and observable.

3. Opportunities: Total chances of having a defect in an Unit. Like Unit, it is also measurable and observable.

4. Total Opportunities = Total Number of Units * Opportunities

5. Defects per Unit (DPU): Number of defect in 1 Unit

6. Defects per Opportunities (DPO): Number of defects in 1 Opportunity = Total number of Defects / Total Number of Opportunities

7. Defects per Million Opportunities (DPMO):
DPMO

= DPO * 1 million

= DPO * 1,000,000

We will take an example to understand it.

Example:
A quality professional for web development has been assigned the work of performance improvement for a website. His job is to improve the response time of the website. Below are the identifications done by the Quality Team as part of the CTQ.

Area of Work: Web Development
Customer Voice: "I am seeing a very slow performance in the page for more than 1 mil objects in the user interface and sometimes it takes over 5 minutes." It is also known as Voice of Customer. And it is much note for any project.

CTQ Name: Responsiveness of the web page

CTQ Measure: Time to load the page when it has 1 mil object (in seconds)

CTQ Specification: Less than 10 seconds

Defect: If the page takes more than 10 seconds to load

Unit: Every Page Hit

Opportunity: 1 per Hit. (As every page may or may not take below 10 seconds to load)

And the Quality Professional took samples for 1,000,000 = 1 million page hits. After applying the aforementioned terms of Six Sigma for DMAIC methodology, he found out that:

Defects = 3.4

Units = 1,000,000

Opportunities = 1

Total Opportunities = 1 * 1,000,000 = 1,000,000

Note: I have kept the sample as 1 million as it will enable a quick understanding. Also the defect is kept at 3.4 defects for a million opportunities (or DPMO) to validate the claim.

Now, we will find out the sigma value for this activity by using NORMSINV function. One can check the NORMSINV value via a scientific calculator or on a Microsoft Excel sheet.

Process Sigma

= NORMSINV (1 – (Total Defects/ Total Opportunities))

= NORMSINV (1 – 3.4/1,000,000)

= 4.50005

= 4.5 sigma or 4.5 σ!

Yes, it is 4.5 when you put the formula for 3.4 defects per million opportunities.
But then, the big question is - Why it is called Six Sigma (or 6 σ)?
Reason: A process in the longer run is not expected to perform at 4.5 sigma level. It means even though you make corrections, there are good chances that variations will be present in the process. Hence, seasoned professionals, while going by a methodology to implement Six Sigma (DMAIC or DMADV), generally mention that the goal is "to have long term sigma of 4.5". Now there is a gap of 1.5 and this is known as a shift, or more specifically Z-Shift.

As a matter of fact, when Six Sigma professional state that the process is following six sigma, it actually means:

Short team capability of the process is 4.5 σ and long term capability is 6 σ.