http://www.qualityadvisor.com/library/six_sigma_inside_story.php

You hear the expression "six sigma" all the time; it’s one of those terms that you think you understand and don’t want to ask questions about for fear of showing your ignorance, right?

Indeed, the expression has become a popular term that people equate with quality. Motorola in particular has become known for six sigma quality. But long before Motorola developed its six-sigma quality program, manufacturers were using quality indices that correspond to sigma levels. These indices carried specific meanings in terms of process capability. Some organizations actually achieved six-sigma capability levels in their processes. The six sigma capability achieved by manufacturers differs from Motorola’s six-sigma quality program, even though the language may seem nearly identical. Just as a pint isn’t really a pound the world around, no more does six sigma always mean six sigma.

Confused? Many manufacturers are required to produce a product with a specified Cpk value. This Cpk level, among other things, is used by the customer to determine whether a particular supplier will continue to be on that customer’s list of approved suppliers. For many organizations to survive, they need to meet or exceed this specified Cpk value or quality level.

Cpk values are related to sigma levels (there’s that term again). The higher the Cpk, the better a process should be. Where the sigma comes in is that, for example, a process capability (or Cpk) of 1.0 is roughly equivalent to a capability level of 3 sigma, commonly called three sigma capability. That is, the mean plus and the mean minus three standard deviations should be the point at which the closest specification lies. This is 3 sigma capability, but it is more commonly referred to as Cpk = 1.0. Cpk values can easily be determined using SPC software such as SQCpack and CHARTrunner.

With 3 sigma capability (Cpk=1.0), a process will produce approximately 99.73% good product (from an optimist’s point of view) or .27% bad product (for a pessimist). To some, this represents an unacceptably high level of poor products. High quality standards dictate four standard deviations between the mean and the closest specifications. In other words, the variation was reduced so that instead of three sigmas between the closest specification, four sigmas could fit. This equates to a Cpk = 1.33. At this level, the process will produce approximately 99.9937% good product or .0063% bad product-a figure that is still too high for some. The table below shows Cpk values along with various quality levels and the parts per million that are defective or Dpm - defects per million (many textbooks refer to this as Ppm defect rate): Cpk

Cpk / Quality level / Dpm
1.00 / 3 sigma / 2,700.000
1.33 / 4 sigma / 63.000
1.66 / 5 sigma / 0.570
2.00 / 6 sigma / 0.002

So at a six sigma capability level, a process will produce very few defects. This level represents a Cpk value of 2.0, it is more commonly referred to as six sigma capability.

Motorola’s six sigma quality refers to 3.4 defects per million. However, the table above shows that a six sigma capability level equates to only .002 defects per million. The difference is caused by an anticipated shift in the mean. Motorola anticipates that the process may shift by as much as 1.5 sigmas to the left or right of the process average, generating at most 3.4 Dpm. In other words, the average will shift slightly from one time-period to another. Proponents of Motorola’s six sigma program assert that it is reasonable to expect a shift in the mean by as much as 1.5 sigmas. While you may or may not agree with this assumption, this is one basis by which the 3.4 Dpm is determined. To learn more about the Motorola six sigma program, visit the Motorola web site.

For those who are sticklers for accuracy in terminology, six sigma should be reported as either "six sigma quality" or "six sigma capability." The two terms are not precisely interchangeable, as we have seen.