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Six SigmaSix 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 operates at Nine Sigma levels of quality. 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. 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.
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 [1].) 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. Then only about 1 part in 400 will be out of spec. But in a manufacturing process, the average value of a measurement is likely to drift over time, and the drift can be 1.5 standard deviations in either direction. At any time, 6.6% of the output will be off by 1.5 sigma in each direction. Thus, when the process has drifted by 150 micrometres, 6.6% of the product will be off by 150 + 150 or 300 micrometres, and therefore out of spec. 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 is very problematic, to say the least. Dr. Donald J Wheeler, one of the most respected authorities on the subject, bluntly labels it as "goofy". Yes, in the short term, processes do exhibit less variation than they do in the long term, so, yes, there is usually a difference between estimates of capability based on long term (all variables have opportunity to express themselves) and short term (they don't) data. But, if you think about it for a moment, the present version of the shift is indefensible. First, 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, you are saying that the process is better than what the data indicate that it is. 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. You should be derating, not inflating, your estimate. 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 factual basis for saying that the true value is 1.5. Why not 1? Why not 2? 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.) When many parts have to fit together, tolerances actually work in the favor of the manufacturer. It is quite possible to make six sigma assemblies out of three sigma parts, since it is highly unlikely that all parts will simultaneously be at one extreme of the tolerance range. Intelligently allocating variation is called "Statistical Tolerancing", and is a useful part of Design for Six Sigma. Clearly, many things on which people rely (services, software products, etc.) 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. DMAICBasic methodology to improve existing processes
DMADVBasic methodology of introducing new processes.
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