Statistical Six Sigma Definition

What does it mean to be “Six Sigma”? Six Sigma at many organizations simply means a measure of quality that strives for near perfection. But the statistical implications of a Six Sigma program go well beyond the qualitative eradication of customer-perceptible defects. It’s a methodology that is well rooted in mathematics and statistics.

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The objective of Six Sigma quality is to reduce process output variation so that on a long term basis, which is the customer’s aggregate experience with our process over time, this will result in no more than 3.4 defect parts per million (PPM) opportunities (or 3.4 defects per million opportunities – DPMO).

For a process with only one specification limit (upper or lower), this results in six process standard deviations between the mean of the process and the customer’s specification limit (hence, Six Sigma).

For a process with two specification limits (upper and lower), this translates to slightly more than six process standard deviations between the mean and each specification limit such that the total defect rate corresponds to equivalent of six process standard deviations.

statistical six sigma

Many processes are prone to being influenced by special and/or assignable causes that impact the overall performance of the process relative to the customer’s specification. That is, the overall performance of our process as the customer views it might be 3.4 DPMO (corresponding to long term performance of 4.5 sigma). However, our process could indeed be capable of producing a near perfect output (Short Term capability – also known as process entitlement – of Six Sigma).

The difference between the “best” a process can be, measured by short term process capability, and the customer’s aggregate experience (long term capability) is known as Shift depicted as Zshift or sshift. For a “typical” process, the value of shift is 1.5; therefore, when one hears about Six Sigma, inherent in that statement is that the short term capability of the process is 6, the long term capability is 4.5 (3.4 DPMO – what the customer sees) with an assumed shift of 1.5.

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Typically, when reference is given using DPMO, it denotes the long term capability of the process, which is the customer’s experience. The role of the Six Sigma professional is to quantify the process performance (short term and long term capability) and based on the true process entitlement and process shift, establish the right strategy to reach the established performance objective

As the process sigma value increases from zero to six, the variation of the process around the mean value decreases. With a high enough value of process sigma, the process approaches zero variation and is known as ‘zero defects.’

Statistical Take Away

Decrease your process variation (remember variance is the square of your process standard deviation) in order to increase your process sigma. The end result is greater customer satisfaction and lower costs.

Comments 27

  1. Benito Arbo

    its very important to learn this six sigma, pls enumerate each

  2. james.buie

    I know that I this methology is out dated and yet is a proven means for understanding many more important stictical factoring agents. the Need for a clear understanding is fundamental to understanding more high level concepts.

  3. deepak paudyal

    nice article to get introduced to six sigma

  4. devenpatel

    Good article! Captures the essence of the concept in few words.

  5. kanchan

    I think this methodology has been ancient yet still has caught fascination of the whole world.

  6. doraisrinivasan

    This is very usefull in industries. good article

  7. Karnak

    All of the tools used in QC/QA and 6 sigma are outdated, so to speak. Tagushi methods were used in agricultural experiments in the mid 1800’s, hence the ‘row’ and ‘treatment’ labels. However, the rules of mathematical inferrence never change, so the methods are never outdated, they are timeless. I will say that doing it by hand or sliderule is severely outdated. Thanks God we have computers!

    John Price, PE

  8. Camilo Reyes

    I think these metodology is very succesful when the companies want to becoming multinational companies.

  9. Essam

    its very good and interesting subject , but anybody have an idea on how it can be implemented in the Public Sector or the government

  10. OverFlow

    I think this is applicable for government also. For example we want to eliminate corrupt officials in the public offices. We just need to set a Lean Sigma for the malpractices based on audit standards that these particular officials have missed to improve. Very simple, right? :) Just kidding…

  11. LSSArmy

    This is my opinion for those that wonder if LSS can be applicable to your job. Yes it can however, you need to learn the fundementals of inferential statistics and how this and all the tools of LSS are used as a whole so you can understand how to pick and choose what to use. Experience helps also but learning the fundementals without the use of software is essential. I have noticed that many, many green belts and black belts don’t even know how to read data, charts, or graphs because they never took inferential statistics and never worked in developing their calculations long-hand, instead, they let a computer do the work for them. This is a major hindrance and you’re not a true LSS change agent unless you know the fundementals.

    As for John Price’s comment, with all due respect, you’re incorrect about QC/QA and LSS being outdated. How? Your statement is contradictory. QC/QA entails LSS. As for computers? They only supply the answer but few people understand how to actually read the data because of a lack of stat’s skills. Unless you understand the fundementals of stat’s and can calculate them by long-hand, you are severely challenged and undereducated to be an effective LSS agent.

    Anyone that thinks that LSS is outdated doesn’t understand.

  12. Nandam.Hemalatha

    I am in the field of pcb designing. How will six sigma help me?

  13. kumar

    I want to know more information about it.

  14. David Billa

    Let me know some more details about this one?


    if i am in the field of mechanical engineering how will six sigma help me ????

  16. venkat

    i did green belt project in six sigma. i would like to do research in six sigma. anyone can u help to do?

  17. hanif

    Is six sigma can be used in warehouse and logistics?

  18. Marcus Watt

    Hello to all!! Just from my research and reading of six sigma, in a nut shell it’s giving your customer a great product with less. In the concert light manufacturing industry its the “lean process” meaning you only take to the line what going to build for that day, and have a back up plan if you have some faulty product and/or if you have one of your top performers not show up for work that day. Covering your bases to ensure you meet your deadlines for customer product support. Putting your employees with strengths in the right spot to accomplish your mission, and your weak employees in training so you don’t come up short on “PROVIDING YOUR CUSTOMER THERE PRODUCT” ERROR FREE AND ON TIME.

  19. Derrick Truett

    Six Sigma when deployed is bottom up and top down throughout the entire business. Often it can also be required of suppliers and vendors etc.. IT from my knowledge however typically focuses more on ITIL. I believe the two have many commonalities as well. Though not exact.. Check out articles comparing the two to learn more. I believe Six Sigma is more in-depth than ITIL as well. An easy place to deploy six sigma in IT for example would be a help desk. How many successful tickets closed per million without recurrence. Then between site help desk you can compare which are performing best and benchmark between them. IT and Business sometime have a barrier regarding these concepts simply because Six Sigma is a all in one (That IT typically do not understand) for the business while ITIL is (The opposite) for IT that the business does not understand. Thus a communication and understanding difference there. Not sure if this is what you were looking for but thought I’d respond..

  20. jamshaid hasan

    good article, it really informative & i learned more about six sigma

  21. Billy

    this is not an “out dated” methodology. its not a “here it is program” you down load and can never change or update it.

    the “people” Side of it is meant to be i constant state of improvements. never get ” comfortable” or “relax” because somethings is working. always think. what works today my not work tomorrow so always be ready to change or adapt to new circumstances or a change in the business.

  22. Rosauro Feliciano

    I am interested to know more about this sigma, which I prefer to call it as Process Analysis because it is all about processes. My question is how and why we arrive to this figure 3.4 mathematically?

  23. Rosauro Feliciano

    As for me this Sigma is an invention of people to want to make more money because there is nothing new here as it is a combination of mathematics and statistical control and it is all about processes where we transformed our desires (inputs) into realities (outputs); everything we do or every project we are into involves process. My question is why and how the 3.4 has been pop up? Please show mathematically why we centered to 3.4 as defects per million opportunities?

  24. Roger Shurter

    This analytical process does not apply to human (animal) life/linear experiences.


    Suppose, I got 5 defectives out of 100 units means 5% rejection OR defectives. There are 30 type of defects is potential for the unit defect opportunities are
    100 X 30 = 3000 opportunities.
    In 5 defectives, I found 50 defects.
    So I got 50 defects per 3000 opportunities, Right ???
    Finally, it is 16,667 defects per million opportunities & sigma level is 3.63.
    I request to all to correct me if I am wrong, also suggest further.

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