Section 13. qxd

six
sigma
refers to six standard deviations. Likewise, 
three sigma
refers to
three standard deviations. In probability and statistics, the standard
deviation is the most commonly used measure of statistical disper-
sion; i.e., it measures the degree to which values in a data set are
spread. The standard deviation is defined as the square root of the
variance, i.e., the root mean square (rms) deviation from the average.
It is defined in this way to give us a measure of dispersion.
Assuming that defects occur according to a standard normal distrib-
ution, this corresponds to approximately 2 quality failures per million
parts manufactured. In practical application of the six sigma methodol-
ogy, however, the rate is taken to be 3.4 per million.
Initially, many believed that such high process reliability was impos-
sible, and 
three sigma
(67,000 defects per million opportunities, or
DPMO) was considered acceptable. However, market leaders have
measurably reached six sigma in numerous processes.
Table 13.5.6
Surface-Roughness Ranges of Production Processes
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