Six Sigma

Perspective on Six Sigma as a Metric

Six Sigma was coined by Motorola in the 1980s. The Greek letter sigma (σ) represents the variability in a process as measured by its standard deviation. The conceptual perspective of the term Six Sigma is that it is desirable for a process to be operating such that the specification limits, which govern customer requirements on a selected quality characteristic, are located 6 standard deviations away from the mean value of the characteristic. It is assumed that the probability distribution of the quality characteristic (X) is normal, and its density function is given by

where μ and σ represent the process mean and standard deviation, respectively. When the assumption of normality of distribution of the quality characteristic can be justified, using standard normal tables, it can be shown that the proportion of nonconforming product is 0.002 ppm. The tail area under the normal curve, above or below the appropriate specification limit, is 0.001 ppm on each side. Figure 1 demonstrates this concept.

The above interpretation of Six Sigma as a metric applies in a static situation. However, Motorola wanted to account for drifts in the process in the long run. An assumption was made that the drift in the process mean would be no more than 1.5 standard deviations from its original location. This assumption implies that a system of statistical process control will be in place for detecting when a process goes “out of control.”

Figure 1 Process Distribution With Specification Limits at 6 Standard Deviations From Mean

A process could go out of control because of special causes. These special causes are not part of the system as designed but could occur as a result of the use of a wrong tool, an improper raw material, or an operator error. Identification of special causes is typically accomplished through the use of control charts. Special causes could cause a shift in the process mean or an increase in the process standard deviation. Common causes, on the other hand, are inherent to the system. A process can be redesigned to reduce the impact of the common causes, but they can never be eliminated completely. A process with only common causes is said to be in statistical control.

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