What’s So Special about 3-Sigma?

So what’s the big deal about 3-sigma? Is it just 6-Sigma for under-achievers? Is it only for statistical geeks? Why should anyone give a hoot?

As with all powerful ideas, 3-sigma is simple, yet difficult to get your head around. Although there is no short explanation, here’s the shortest answer I can provide.  It goes like this…

First of all,  3-sigma isn’t the stuff of slogans and marketing literature. There are no black-belts in 3-Sigma and it is not a magic pill for certain riches or true love. At its core, 3-sigma refers to a theory of knowledge that gives rise to a methodology for prediction. Once you get it, for whatever purposes, your ability to understand the present and foresee the future, can be dramatically improved.

Three sigma, or three “Standard Deviations”, is a statistical value that can be written using the greek letter “sigma”. It looks like this:

3sig

A Standard Deviation is a measuring stick used to describe how data are dispersed around their average.

400px-standard_deviation_diagram

For what is called a normal distribution, which takes the shape of a nice “bell curve, one Standard Deviation encompasses about 68% of all observation data. Two Standard Deviations includes about 95% of all observations. And three Standard Deviations encompasses a bit more than 99% of all observations. It actually doesn’t matter if the shape of a distribution is pretty, like the “bell curve” shown above. All that matters is that all measurements you make as an observer of the world, will vary, and understanding why measurements always vary and what that variation means, is the key to understanding how we know the world and how we make predictions about the future.

Three sigma stands out from 1, 2, 4, 5, 6 . . . sigma because it alone, represents the boundary point that Walter Shewhart determined can be used to signal the difference between events that are ordinary and predictable and those that are unusual and unpredictable.

At first blush, this idea of a statistical boundary between the ordinary and the extraordinary might seem rather silly and arbitrary. Our common sense tells us that we can easily discriminate between what is special and what is common in our daily experience without resorting to statistical reasoning. Why is this not the case?

Behind the concept of 3-sigma lies a theory of how we know the world. This theory asserts that we are genetically and culturally programmed to see assignable causes for every effect of interest to us. This way of knowing permits us to act upon the world. For every observation of interest, we seek out some button to push or some lever to actuate that will bend the world to our purposes. These buttons and levers are the theories we construct about how the world works.

Our minds tell us that for every problem we experience and every challenge we face, there is always a cause that can be acted upon. The Sun’s light and gravitation are causes. My neighbor’s barking dog is a cause. Temperature is a cause. The “economy” is a cause. God is a cause. Whistling in the wind is a cause. Things we observe and things we imagine can be designated as causes. We seek and see causes in all things that interest us. This is how we make predictions about  the world and how we guide our actions in the world. We are prediction machines and button-pushers, par excellence.

But do our intuitions about assignable causes serve us well or do they misguide us in our predictions about the future?

In his book, “Statistical Method from the Viewpoint of Quality Control“, Shewhart shows us that most of what a system (or process) does is a product of interactions that cannot be reduced to one or more assignable causes. Shewhart’s un-assignable cause is also called, “common cause“. In a sense, he is telling us that we cannot identify a cause that is in the system because everything  in the system is a cause. A system, he says, is irreducible.  This means that we when we start pushing buttons and pulling levers for observations that are not clearly produced by assignable causes, we only make a system increasingly unpredictable . If we fail to understand the nature of variation we will more likely than not, make a royal mess of things.

Based on a theory of knowledge, Shewhart created a statistical tool called a “control chart“, for monitoring what a system or process is doing as a whole, over time, and will likely continue doing into the future, barring the introduction of some assignable cause (sometimes called “special cause”). Some people like to say that Shewhart’s control charts are a way to listen to the “voice of the process”. It is a variation detector that tells us what variation is in the nature of the system we are observing and what variation is “special”. When assignable causes do start influencing the system, it will leave it’s state of control and become unpredictable. He assigns 3-sigma as the signaling point for differentiating cause that can and cannot be assigned.

chart-1

chart-2

When an assignable cause is signaled, Shewhart tells us that we can search for that cause in order to remove it and restore the system to its former state of predictability, which is a very good thing, OR we can act to change the system as a whole in ways that make it even more predictable and more suited to our purposes, which is sometimes, an even better thing.

So where did Shewhart get the 3-sigma limit from? He got it from lots and lots of empirical observation. He says it has no “truth” to it. It is just a value that works to minimize the consequences of the mistakes our minds trick us into making. 3-sigma is a tipping point that minimizes the two mistakes we can make—confusing common cause with assignable cause OR confusing assignable cause with common cause. In his own words,

“…knowledge…is a method of approximating a practical ideal of a minimum number of false predictions.”

You can learn a lot more about theory and techniques for using control charts by visiting Don Wheeler’s SPC Press Website and reading his books, but you still have to ask yourself….

Why would Shewhart’s ideas have importance in our daily lives?

Well, the variation that is everywhere in our experience of the world is invisible to us because most of our behavior in day-to-day life is habitual and common-sensical. Most of us simply take for granted all of the predictions we make when we get out of bed, get dressed, and drive to work. To our way of knowing, most of the world is in a steady and predictable state. It is only when we are first learning our every-day behaviors that we are forced to consider everyday causes and effects. Do you remember when the simple act of tying your shoes required a theory and a flow chart?

Our intentional behavior on the other hand, is geared toward solving problems and attaining goals and in these activities we put a great deal of effort toward identifying causes. The way we see it, if we can just push the right buttons and pull the right levers, we can make the things we want to happen, happen. But, like tying our shoes, our analyses remain rooted in our common-sense beliefs about cause and this habitual way of thinking makes us assign causes that cannot be deduced from the system. In other words, there is no “right” button to push. When we make the mistake of assigning causes that are actually common, we do more than just make incorrect predictions and push the wrong buttons, we actually make the system itself, increasingly unpredictable.

So what can we learn from Walter?

Before you start pushing buttons and pulling levers, listen to the “voice of the process” to see what it is actually doing! If the variation it produces does not show control—is not predictable, you have a theory that is not very useful and you need to rethink that theory. If on the other hand, the voice tells you that the process is predictable within some limits, you can work on the process to increase its predictability AND you can hear assignable causes that threaten to upset your apple cart in order to get things back on track. This new approach to knowing can do more than make better widgets. It can help prevent events like global warming, save marriages, fix cars, cross oceans, and help us do better in every enterprise we chose to undertake.

 

 

casue-warning-system3

Greatest opportunities for gain? It's the system, stupid!

 

Note: There are also ways to detect assignable cause signals (non-random events) within 3-sigma limits, but the principle of differentiating between assignable and common cause, remains the aim of this predictive methodology.)

Shewhart produced his control charts as a means for improving the manufacture of product, but in doing so he reached deep into a theory of knowledge. The implications of his discovery pertain to all human enterprise. Dr. W. Edwards Deming did much to draw out these implications for business enterprises, but even his profoundly important work did not fully explore just how important Shewhart’s ideas were to the success of the human enterprise as a whole.

Once you begin to understand the theory of knowledge that underlies Shewhart’s control charts, you begin to see how what you can know about the world is actually shaped by your aims and intentions, the observations you chose to make, and the measurement methods you have at your disposal. Benefiting from such an understanding does not require control charts or complicated statistical calculations. It is a way of seeing that fundamentally changes how you experience the world.

Walter Shewhart captured the essence of this transformation by quoting C. I. Lewis:

“…knowing begins and ends in experience, but it does not end in the experience in which it begins.”

Still confused? In various ways, all of the entries in this blog reflect my continuing efforts at understanding and exploring the implications of 3-sigma as theory and method. In future entries I will discuss in more specific terms how a theory of knowledge and methods based in that theory, can help us to do better in all of our enterprises. I hope you will drop in from time to time to see how I am doing.

Also see: Where Systems Come From

About marc

Instructional Design Consultant
This entry was posted in Great Thinkers, Methods, Quality, Science of Consciousness, statistical thinking, Theory of Knowledge. Bookmark the permalink.

24 Responses to What’s So Special about 3-Sigma?

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  5. John Dowd says:

    Nice post on a difficult subject. It’s interesting that 3 sigma as a choice point was picked rather arbitarily at first by Shewhart based on his understanding of the Normal model. It was first used by him around 1925 and no one has shown either experientially or mathematically that there is a better way to balance the frequency of committing the two erros (over-reacting and under-reacting).

  6. Calvin.K says:

    Both the three sigma and six sigma is in same concept. The only different is the process sigma or ppm. Three sigma being used previously but three sigma seem not satisfied by the big company now, they are looking for better ppm. Further might go to 12 sigma…..

  7. marc says:

    Calvin,

    Actually three sigma and sigma are very different concepts.

    Six sigma is a desired specification or tolerance for variation in some process outcome (product or service).

    Three sigma represents a theoretical boundary condition that an observer can use to differentiate between systemic and non-system causes that are influencing a process that produces outcomes (product or service).

    Six sigma is a wish. There sigma predicts.

    If you want to understand this, read Walter Shewhart.

  8. Calvin.K says:

    Hi Mac,

    Three sigma and six sigma have the same concept, six sigma just as a upgrade version of three sigma, some of the methodology are added. This happen on everyway just like ISO9000 and ISO9001, they are different requirement but the basic are same.

    Many people think in opposite way that need to achieve 3.4ppm to become six sigma, that’s not true. The actual is to use six sigma methodology to achieve the target six sigma which is 3.4ppm. Once achieve the target, the process is providing 3.4ppm defect.

    Also, as you mentioned that three sigma can use to differentiate between systemic and non-system causes but dont you know six sigma can do the same?

  9. marc says:

    Calvin,

    Welcome back. You correctly characterize six sigma as a target, but 3-sigma is NOT a target value. Rather, when plotted over time for some set of measures related to a process, it can be used as an indicator of the state of that process. Walter Shewhart asserted that 3-sigma constituted a boundary condition at which we can determine, with reasonable and economically sound belief, wheter a process is inherently predictable (stable) or inherently unpredictable (out of control). In other words, 6-sigma is about desired outcomes and 3-sigma is about what can and cannot be predicted.

    In this blog, my interest is how Shewhart understood the nature of prediction and knowing and the implications of his view. W. E. Deming built his philosophy of management on this foundation. Since my particular interest does not include the intricacies of statistical computation (nor do I have great expertise), I would like to refer you and other readers to an excellent paper by Donald Wheeler, the highly regarded SPC author and guru. In it, he provides a detailed explanation of why 6-sigma may be a useful target, but does not constitute a theory of process behavior.

    You can read the paper at: http://www.spcpress.com/pdf/The_Final_6_Sigma_Zone.pdf.

    Marc

  10. Mark says:

    At a recent local ASQ meeting I listened to a lecturer describe very succintly that 3-sigma is Hope and 6-sigma is Certainty.

  11. marc says:

    Mark,

    I have not heard that idea put forth before and without some context, I can’t say just what the speaker meant.

    3-sigma might be described as conditional, evidence-based, belief in some specified future outcomes.

    Since 3-sigma is conceived as means of addressing the uncertainty that is characteristic of all systems and processes (variation), the idea of 6-sigma is certainty is problematic. Maybe the speaker is suggesting that 6-sigma is the illusion of certainty that characterizes unconditional belief. This is for example, is a characteristic of religious faith.

    I never thought about 6-sigma that way, but the idea might have some merit.

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  14. Owen Abrey says:

    Thank you for this discussion. I am a profoundly ignorant man. However, I am curious from time to time. In this case, there is a rumor that there is a 3 sigma event in the Large Hadron Collider that *may* indicate a light higgs. The discussion here has been helpful for me to “sketch out” the implications of that statement.

  15. Vijaya says:

    Hi,

    Do u think that SPC can be implemented in defined level software companies with three sigma limits?
    i need some guidance if so yes.

    thanks,
    Vijaya

  16. marc says:

    Vijaya,

    The short answer is YES, of course! Please feel free to contact me if you would like to discuss this further.

    Marc

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  18. Tom Mellett says:

    Hi Marc,

    Might you wax philosophical or even theological about the latest Three-Sigma Bump that portends yet another new elementary particle or force? (If we can’t discover ‘em, we just invent ‘em — and that’s where 3-sigma comes in, right?)

    From today’s NY Times
    http://www.nytimes.com/2011/04/06/science/06particle.html

    Physicists at the Fermi National Accelerator Laboratory are planning to announce Wednesday that they have found a suspicious bump in their data that could be evidence of a new elementary particle or even, some say, a new force of nature.

    (. . . )
    The key phrase, everyone agrees, is “if it holds up.” The experimenters estimate that there is a less than a quarter of 1 percent chance their bump is a statistical fluctuation, making it what physicists call a three-sigma result, enough to attract attention but not enough to claim an actual discovery. Three-sigma bumps, as every physicist knows, can come and go.

    Tom Mellett
    Los Angeles, CA

  19. marc says:

    At 3 sigma and beyond, I can’t predict and neither can they. How could I or the investigators at Fermi know? Still, when you’re spending megabucks on toys like atomic accelerators, any event is worth publicizing, even if nothing more than bumps in the night. A new force of nature or a glitch in the equipment? There’s no telling. One quarter of one percent? Nonsense.

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  21. M. ALomairy says:

    Thanks Marc,

    you made the 3-sigma thing easy to understand, I was confused between 3-sigma and 6-sigma but now the difference is clear to me.

    based on the 3-sigma principal, do you think loosing hair is common cause of our men body that we shouldn’t pay attention too or an assignable cause that should be treated ;) .

  22. marc says:

    If your hair fails out when you are 18 years old, you might want look for an assignable cause. If your hair falls out when you are going on 60, it probably nothing special—just part of the ride.

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