Six Sigma
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 manyother manufacturing companies. GE Aircraft Engines operates at nine-sigmalevels 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 processeswith 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 settledfor 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 MicrosoftandMotorola to reduce the number of product defects. It can also beapplied to other processes in which controlling variation is agoal.Organizations such as the International Charter also include principlesfrom it in their BusinessCertification (www.icharter.org/certification/) programmes such asIC9700 (www.icharter.org/certification/ic9700) for large companies, and to a lesser extentIC9200 (www.icharter.org/certification/ic9200) which is for small businesses.
Recent developments suggest a movement to adapt the open source approach,which has garnered great popularity in informationtechnology, 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 evolutionis treqna.com.
Contents
1 Why six?
2 DMAIC
3 DMADV
4 See also
5 External links
Why six?
Anyone looking at a table of probabilities for the normal (Gaussian)distribution will wonder what six-sigma has to do with3.4 defects permillion things. Only one billionth of the normal curve lies beyond sixstandard deviations, or two billionths ifyou count both too-high andtoo-low values. Conversely, a mere three sigma corresponds to just 2.6problems in a thousand, whichwould seem a good result in manybusinesses.
The answer has to do with practical considerations for manufacturingprocesses. (The following discussion is based loosely onthe treatmentby Robert V.Binder in a discussion of whether six-sigma practices can apply to software [1] (www.rbsc.com/pages/sixsig.html).) Suppose that the toleranceforsome manufacturing step (perhaps theplacement of a hole into which apin must fit) is 300 micrometres, andthe standard deviation for theprocess of drilling thehole is 100 micrometres. Only a part which is 3standard deviations away from the mean (in either directiom) will be outof spec;this is about 1 part in 400. But in a manufacturing process,the average value of a measurement is likely to drift overtime;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 samedirection) will be in error: about 3.3% ofthe output, This is a high defect rate.
If you set the tolerance to six sigma, then a drift of 1.5 sigma inthe 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, thisis 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 dointhe long term (when all variables have the chance to express themselves), so there is usually a difference between estimate so capability based on long term and short term data. But Wheeler arguesthat the present version of the shift is indefensible.
First, the common practice is to add 1.5 "sigmas" to the result of asigma 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 inthe long term, you should be subtracting, not adding, because you aretrying to account for variation that is expected, but not yet seen. Forexample, if the short-term failure rate is 3.4 parts per million, thisshould be cited, not as six-sigma, but as three-sigma, reflectingtheactual long-term failure rate. Conversely, if you have long termdata, you have already captured the long term shifts, and thereis noreason to add or subtract anything. The data speak for themselves.
Second, there is no basis for saying that the true value is 1.5.InWheeler's view, there are much more credible ways ofproviding designmargin. It has been suggested that one of the early practitioners of sixsigma invented or adopted the 1.5 sigma shift purely for marketingreasons. It was unrealistic to expect toreduce defect to the few partsper billion level, and hedidn't want to sell a program named "4.5Sigma", so a 1.5 sigma shiftwas necessary, to get an attractive name.
However, according to original training material and a handout dated1985 from Motorola, Six Si gma is actually a Cpk of 1.5and 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 every100 would go through the entiremanufacturing process without a defect’ and thus, we can see that for aproduct to be builtvirtually defect-free, it must be designed to acceptcharacteristics which are significantly more than +/- 3 sigma away fromthemean.
'A design specification width of +/- 6 Sigma and a process width of+/- 3 Sigma yields a Cp of 12/6 = 2. However, the processmean canshift. When the process mean is shifted with respect to design mean,the Capability Index, (Cp), is adjusted with afactor k, and becomesCpk.' 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 detectablewith a samplesize of 4, prompting investigation of an "out ofcontrol" process.(Interesting coincidence, but irrelevant to the calculation ofcapability indices.)
There is another reason for six sigma: a manufactured itemprobablyhas more than one part, and some of the parts will have to fittogether, which means that the total error in two or more parts must bewithin tolerance. If each step is done to three-sigmaprecision, an itemwith 100 parts will hardly ever be defect-free. Withsix-sigma, even anobject with 10,000 parts can be made defect-free 96% of the time.
Clearly, many things on which people rely (services, softwareproducts, etc.) are not manufactured by machine tools to particularmeasurements. In these cases, "six sigma" has nothing to do withstatistical distributions, but refers to a goal ofvery few defects permillion, by analogy to a manufacturing process. The usefulness of theanalogy is controversial among thoseconcerned with quality innon-manufacturing processes.
DMAIC
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. |
DMADV
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
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