Six Sigma: The Classic Bell Curve

As we covered in our introductory article (“A Six Sigma Primer”) <link to Vol 2. #22>, Motorola was the company that developed and first adopted Six Sigma; however, the principle on which it's based dates back to the early 1800s. German mathematician, Carl Gauss, first introduced the concept of the bell curve. The bell curve is the basis for mapping and measuring variation, and measuring variation is the foundation of Six Sigma.

Before reviewing how a bell curve is created, let's review variation. Simply defined, variation is a deviation from expectation. If you're manufacturing widgets, your goal is to have every widget be exactly the same as every widget before and after it on your production line. However, every widget will probably differ ever so slightly from every other widget you manufacture. Applying Six Sigma methodology will help you define the level of acceptable variation in order to produce an acceptable widget every time. Variation is a part of life: For example, no two baseball or golf swings are exactly the same every time, no matter how much the athlete practices. Hitting a baseball or golf ball with success means limiting the acceptable variation. Limiting variation leads to success on the production line as well.

Now back to that bell curve. If you plot data on a simple x-y axis, the resulting bar chart (or histogram) will typically reveal a bell curve. Let's put theory into action with the example of school grades. On any given test, a number of students will excel and a number of students will fail. And the greatest number of students will probably earn an average grade. For example, there are 30 students in the class. Plotting their grades on a histogram will likely produce a chart that looks like this:


And when converted to a line chart, you’ll produce the classic bell curve. Once we have the bell curve, the important measurements we’ll focus on are the mean and the specification limits. The mean is represented by the peak of the curve, and the specification limits fall on either side of the mean, representing acceptable performance. (In the case of the students and the test, the specification limits would probably be set a “A” and “C”… okay, maybe “C-”.)


You set your own upper and lower specification limits for any given process and acceptable defect range, and your goal is to have any amount of deviation fall within those limits. Staying within the limits equates to no defects (in essence, acceptable deviation). Standard deviation is the statistic that indicates how tightly your variations are to the mean. Tighter variations equates to better control, hence better quality.

Quality improvements occur in any process when you reduce variation, so every widget (or baseball or golf swing) is as close as possible to the one before and after it – the perfect mean. Contact us to learn how the MPower can help you determine your standard deviation and use Six Sigma to improve your operation.