# Six Sigma Versus Three Sigma

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The following is an excerpt on Six Sigma implementation and the Six Sigma steps from The Six Sigma Handbook: Fourth Edition by Paul Keller and Thomas Pyzdek (McGraw-Hill, 2014).

The traditional quality model of process capability differed from Six Sigma in two fundamental respects:

- It was applied only to manufacturing processes, while Six Sigma is applied to all important business processes.
- It stipulated that a "capable" process was one that had a process standard deviation of no more than one-sixth of the total allowable spread, where Six Sigma requires the process standard deviation be no more than one-twelfth of the total allowable spread.

These differences are far more profound than one might realize. By addressing all business processes, Six Sigma not only treats manufacturing as part of a larger system, it removes the narrow, inward focus of the traditional approach. Customers care about more than just how well a product is manufactured. Price, service, financing terms, style, availability, frequency of updates and enhancements, technical support, and a host of other items are also important. Also, Six Sigma benefits others besides customers. When operations become more cost-effective and the product design cycle shortens, owners or investors benefit too. When employees become more productive their pay can be increased. The broad scope of Six Sigma means that it provides benefits to all stakeholders in the organization.

The second point also has implications that are not obvious. Six Sigma is, basically, a process quality goal, where sigma is a statistical measure of variability in a process. As such it falls into the category of a process capability technique. The traditional quality paradigm defined a process as capable if the process natural spread, plus and minus Three Sigma, was less than the engineering tolerance. Under the assumption of normality, this Three Sigma quality level translates to a process yield of 99.73%. A later refinement considered the process location as well as its spread and tightened the minimum acceptance criterion so that the process mean was at least four sigma from the nearest engineering requirement. Six Sigma requires that processes operate such that the nearest engineering requirement is at least Six Sigma from the process mean.

One of the most significant contributions from Motorola was to change the discussion of quality from one where quality levels were measured in percent (parts-per-hundred), to a discussion of parts-per-million or even parts-per-billion. Motorola correctly pointed out that modern technology was so complex that old ideas about "acceptable quality levels" could no longer be tolerated. Modern business requires near perfect quality levels.

One puzzling aspect of the "official" Six Sigma literature is that it states that a process operating at Six Sigma will produce 3.4 parts-per-million (PPM) non-conformances. (See Converting DPMO & Sigma Level). However, if a special normal distribution table is consulted (very few go out to Six Sigma) one finds that the expected non-conformances are 0.002 PPM (2 parts-per-billion, or PPB). The difference occurs because Motorola presumes that the process mean can drift 1.5 sigma in either direction. (This assumption is further discussed in Chap. 7. See also Six Sigma 1.5 Sigma Shift). The area of a normal distribution beyond 4.5 sigma from the mean is indeed 3.4 PPM. Since control charts will easily detect any process shift of this magnitude in a single sample, the 3.4 PPM represents a very conservative upper bound on the non-conformance rate.

In contrast to Six Sigma quality, the old Three Sigma quality standard of 99.73% translates to 2,700 PPM failures, even if we assume zero drift. For processes with a series of steps, the overall yield is the product of the yields of the different steps. (See throughput yield). For example, if we had a simple two step process where step #1 had a yield of 80% and step #2 had a yield of 90%, then the overall yield would be 0.8 x 0.9 = 0.72 = 72%. Note that the overall yield from processes involving a series of steps is always less than the yield of the step with the lowest yield. If Three Sigma quality levels (99.73% yield) are obtained from every step in a ten step process, the quality level at the end of the process will contain 26,674 defects per million! Considering that the complexity of modern processes is usually far greater than ten steps, it is easy to see that Six Sigma quality is not optional; it is required if the organization is to remain viable.

The requirement of extremely high quality is not limited to multiple-stage manufacturing processes. Consider what Three Sigma quality would mean if applied to other processes:

· Virtually no modern computer would function.

· 10,800,000 healthcare claims would be mishandled each year.

· 18,900 US Savings bonds would be lost every month.

· 54,000 checks would be lost each night by a single large bank.

· 4,050 invoices would be sent out incorrectly each month by a modest-sized telecommunications company.

· 540,000 erroneous call details would be recorded each day from a regional telecommunications company.

· 270,000,000 (270 million) erroneous credit card transactions would be recorded each year in the United States.

With numbers like these, it is easy to see that the modern world demands extremely high levels of error free performance. Six Sigma arose in response to this realization. See other Example Sigma Levels.

See also:

What does the term "Six Sigma" stand for

Six Sigma vs. Control Charts based on 3 Sigma Limits

Learn more about the Lean Six Sigma principles and tools
for process excellence in Six Sigma
Demystified (2011, McGraw-Hill) by Paul Keller,
in his online Lean Six Sigma DMAIC short course (**$249**), or his
online Green Belt certification course (**$499**).