# What Is the Six Sigma Curve?

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Six sigma is a business philosophy developed in the 1980s to provide exceptional quality to the customer by producing products that are defect-free and made exactly the same every time. The term refers to a process that is so precise that all variations in the critical characteristics of a product – for instance, the diameter of a ball bearing – fall within six sigma of the mean (average) of the process. The six sigma curve is a visual plot of process measurements that shows how widely a process varies.

## Understanding Sigma

Sigma is the Greek character used by mathematicians to represent the standard deviation of a sample. The standard deviation is often referred to as the "average of the averages." It is calculated by finding the average, or mean, of a set of values, then finding the difference of each value from the mean, also called the deviation. Each deviation is squared and finally the average of those squares is calculated. That number is the standard deviation of the sample.

## Understanding the Normal Distribution

A sample is said to be normally distributed if, when graphed, it falls into a bell curve, so named because of its shape. While many samples are normally distributed, if a sample is large enough – 30 or more data points – it can be assumed that the data is normally distributed. This is important, because the six sigma curve and its underlying calculations are based on a normally distributed sample.

## The Six Sigma Curve

Statistically, 68.2% of a normally distributed sample falls within plus or minus one sigma of the mean. So if your mean is 30 and your standard deviation is two, 68.2 of 100 observations will fall between the values 28 and 32. By adding another sigma, you achieve 95.44%. That is, 95.44% of the observations would fall between 26 and 34. And almost all observations, 99.73%, fall within plus or minus three standard deviations from the mean, in other words between 24 and 36 in the example above. Each deviation adds less to the total percentage than the one before it.

By the time you reach six sigma, however, 99.99966% of the observations in your sample fall within six standard deviations from the mean. When this is the case, your process demonstrates exceptional quality control. Another way to say this is that for every 1 million observations, only 3.4 fall outside of the calculated six sigma limits. If you look at the bell curve representing the sample of your process observations, only an infinitesimal amount of observations will show outside the limits of plus or minus six sigma. Practically speaking, this is as stable as a process can be.

## Tips & Warnings

Six sigma means plus or minus six standard deviations from the mean. In other words, the spread between the minimum value, or lower control limit, and the maximum value, or upper control limit, is actually 12 sigma. Don't make the mistake of only calculating plus or minus three standard deviations, which is a total spread of only six standard deviations.

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