One would have to live in a vacuum not to have heard about Six Sigma (Define, Measure, Analyze, Improve, Control = DMAIC - pronounced "di-may'-ik").  The term has been around long enough and is so pervasive today that anyone in the business world has been exposed to it in varying degrees.  However, most people do not really understand Six Sigma; they have either been misinformed or not exposed to it at all.

First, Six Sigma is not as much about the Six (or the Sigma, for that matter) as it is about, for purposes of this discussion, manufacturing excellence.  It is important, however, that one be at least conversant in the nomenclature of Six Sigma.  Let us first discuss Sigma.

In order to understand Sigma, we must crack open our old statistics textbooks and grasp the most basic principles of this subject.  We all understand the concept of an average, which in statistical terms is called the “mean.”  Take any set of data, add them and divide by the number of data points, and we have the mean; pretty simple.

The mean, though, only tells us one thing: where our data is centered.  It does not tell us how “spread” is that data about the mean.  You may at this juncture be wondering why we would even care; good question.

If all we calculate is the mean, we have described what is happening with our data, but are left short in being able to predict what will happen when more data is collected.  Example: the mean of the sample dataset 1, 2, 3, 4, 5, 6, 7, 8, 9 is 5 (grab a calculator and check it out).  If you were asked the probability of choosing a 5 from the next dataset from this population, what would you say?  The data, obviously, are too dispersed about the mean.  Conversely, the mean of 4, 5, 5, 4, 6, 5, 5, 6 ,5 is also 5 (again, check for yourself).  Were you asked the same question regarding this dataset, you might be inclined to say the chances of choosing a 5 was “pretty good;” in fact, the chances of choosing a 4, 5, or 6 might be couched as “really good.”

Enter the statistical concept of Sigma, or standard deviation.  Here we are concerned with how far each data point in the dataset is from the calculated mean.  To calculate Sigma (for our data, which is probably a sample from a larger population) we:

1.)  Calculate the difference between each data point and the mean and square each result,

 why do we square them?

...then we...

2.)  Sum all these squared values,

3.)  Divide by the number of data points minus 1.

why minus 1?

...finally we take this result and...

4.) Calculate the square root.

why the square root?

That number we have calculated is Sigma, or the sample standard deviation.  In our first example dataset above, Sigma is 2.738; in the second .707.  These numbers are in the same unit of measure as the data, whether inches, density/square meter, fluid ounces, whatever.  We may then use the combination of the mean and Sigma to effect all number of statistical calculations.  Notice how large is the first sample Sigma versus the second, which signifies the first as much more dispersed about the calculated mean of 5.

But What About the Six (in Six Sigma)?

The six comes from a quality standard currently reached for in business.  Simply put, if you are trying to achieve anything (especially manufacture something), you are shooting for a target in the output of your process and you have tolerances about that target.  However, those targets and tolerances are often missed, which we call “out of specification,” “rejects,” and whole host of other nasty words to placate ourselves, our employers, and worse yet, our customers.

If your process is such that the target you desire and the mean you are actually achieving (calculated) are equal (or “close enough”), and your tolerances are able to be located 6 Sigma to either side of the target (6 times what was calculated), then you have a “Six Sigma process.”  There is actually nothing sacred about the 6: it could be 6.1 (which is even better), 6.2, 7, whatever; today’s “accepted goal” is six (it depends upon you, your process, and your requirements). Also, although beyond the scope of this discussion, Six Sigma also accounts for your process drifting about, as it naturally will via the laws of physics.  In simple terms, we attempt to achieve this quality by reducing the Sigma or widening the tolerances, or both.