Six Sigma

From Academic Kids

Six Sigma is a quality management program to achieve "six sigma" levels of quality. It was pioneered by Motorola in the mid-1980s and has spread to many other manufacturing companies. GE Aircraft Engines strives to operate at six-sigma levels of quality[1] ( It continues to spread to service companies as well. In 2000, Fort Wayne, Indiana became the first city to implement the program in a city government.

Six Sigma aims to have the total number of failures in quality, or customer satisfaction, occur beyond the sixth sigma of likelihood in a normal distribution of customers. Here sigma stands for a step of one standard deviation; designing processes with tolerances of at least six standard deviations will, on reasonable assumptions, yield fewer than 3.4 defects in one million. (See below for those assumptions.)

Achievement of six-sigma quality is defined by Motorola in terms of the number of defects per million opportunities (DPMO). That is, fewer than four in one million customers will have a legitimate issue with the company's products and service. Many people believed that six-sigma quality was impossible, and settled for three to four sigmas. However market leaders have measurably reached six sigmas in numerous processes.

It is currently used in a number of large companies, such as Microsoft and Motorola to reduce the number of product defects. It can also be applied to other processes in which controlling variation is a goal. Organizations such as the International Charter also include principles from it in their Business Certification ( programmes such as IC9700 ( for large companies, and to a lesser extent IC9200 ( which is for small businesses.

Recent developments suggest a movement to adapt the open source approach, which has garnered great popularity in information technology, to Six Sigma. By opening Six Sigma to greater participation through peer review, open source advocates hope to spread the Six Sigma philosophy. One site advocating this evolution is


Why six?

Anyone looking at a table of probabilities for the normal (Gaussian) distribution will wonder what six-sigma has to do with 3.4 defects per million things. Only one billionth of the normal curve lies beyond six standard deviations, or two billionths if you count both too-high and too-low values. Conversely, a mere three sigma corresponds to just 2.6 problems in a thousand, which would seem a good result in many businesses.

The answer has to do with practical considerations for manufacturing processes. (The following discussion is based loosely on the treatment by Robert V. Binder in a discussion of whether six-sigma practices can apply to software [2] ( Suppose that the tolerance for some manufacturing step (perhaps the placement of a hole into which a pin must fit) is 300 micrometres, and the standard deviation for the process of drilling the hole is 100 micrometres. Only a part which is 3 standard deviations away from the mean (in either direction) will be out of spec; this is about 1 part in 400. But in a manufacturing process, the average value of a measurement is likely to drift over time; the Six Sigma methodology supposes that the drift is 1.5 standard deviations in either direction. If the process has drifted that far, then a piece only 150 micrometres away from the mean (in the same direction) will be in error: about 3.3% of the output, This is a high defect rate.

If you set the tolerance to six sigma, then a drift of 1.5 sigma in the manufacturing process will still produce a defect only for parts that are more than 4.5 sigma away from the average in the same direction. By the mathematics of the normal curve, this is 3.4 defects per million.

The 1.5 sigma shift assumption is controversial: Donald J. Wheeler, one of the most respected authorities on the subject, bluntly labels it "goofy".

In the short term, processes exhibit less variation than they do in the long term (when all variables have the chance to express themselves), so there is usually a difference between estimates of capability based on long term and short term data. But Wheeler argues that the present version of the shift is indefensible.

First, the common practice is to add 1.5 "sigmas" to the result of a sigma calculation, so that a 4.5 sigma process (Cp = 1.5) magically becomes a 6.0 sigma process (Cp = 2.0). In other words, the process is claimed to be better than what the data would indicate. But if you have short term data, and are trying predict what the process would be in the long term, you should be subtracting, not adding, because you are trying to account for variation that is expected, but not yet seen. For example, if the short-term failure rate is 3.4 parts per million, this should be cited, not as six-sigma, but as three-sigma, reflecting the actual long-term failure rate. Conversely, if you have long term data, you have already captured the long term shifts, and there is no reason to add or subtract anything. The data speak for themselves.

Second, there is no basis for saying that the true value is 1.5. In Wheeler's view, there are much more credible ways of providing design margin. It has been suggested that one of the early practitioners of six sigma invented or adopted the 1.5 sigma shift purely for marketing reasons. It was unrealistic to expect to reduce defect to the few parts per billion level, and he didn't want to sell a program named "4.5 Sigma", so a 1.5 sigma shift was necessary, to get an attractive name.

However, according to original training material and a handout dated 1985 from Motorola, Six Sigma is actually a Cpk of 1.5 and a Cp of 2.0. Based on a 1200 parts/step process, and using a 3 sigma design margin, fewer than 4 units out of every 100 would go through the entire manufacturing process without a defect and thus, we can see that for a product to be built virtually defect-free, it must be designed to accept characteristics which are significantly more than +/- 3 sigma away from the mean.

'A design specification width of +/- 6 Sigma and a process width of +/- 3 Sigma yields a Cp of 12/6 = 2. However, the process mean can shift. When the process mean is shifted with respect to design mean, the Capability Index, (Cp), is adjusted with a factor k, and becomes Cpk.' The important difference here is Design vs. Process.

Nonetheless it is the case that processes drift over time due to noise factors, and a shift of +/-1.5 standard deviations is the limit at which the shift becomes detectable with a sample size of 4, prompting investigation of an "out of control" process. (Interesting coincidence, but irrelevant to the calculation of capability indices.)

There is another reason for six sigma: a manufactured item probably has more than one part, and some of the parts will have to fit together, which means that the total error in two or more parts must be within tolerance. If each step is done to three-sigma precision, an item with 100 parts will hardly ever be defect-free. With six-sigma, even an object with 10,000 parts can be made defect-free 96% of the time.

Clearly, people rely on many products -- such as software -- and services that are not manufactured by machine tools to particular measurements. In these cases, "six sigma" has nothing to do with statistical distributions, but refers to a goal of very few defects per million, by analogy to a manufacturing process. The usefulness of the analogy is controversial among those concerned with quality in non-manufacturing processes.


Basic methodology to improve existing processes

  • Define out of tolerance range.
  • Measure key internal processes critical to quality.
  • Analyze why defects occur.
  • Improve the process to stay within tolerance.
  • Control the process to stay within goals.


Basic methodology of introducing new processes.

  • Define the process and where it would fail to meet customer needs.
  • Measure and determine if process meets customer needs.
  • Analyze the options to meet customer needs.
  • Design in changes to the process to meet customers needs.
  • Verify the changes have met customer needs

See also

External links

lt:Six Sigma nl:Zes sigma ja:シックス・シグマ


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