SIX SIGMA FUNDAMENTALS - Software Design for Six-Sigma: A Roadmap for Excellence - page 158

LSL USL

-6 σ

+6 σ

-6 -4 -2 0 2 4 6

FIGURE 7.9 Highly capable pocess.

deviation. If the process cannot be measured in real numbers, then we convert the
pass/fail, good/bad (discrete) into a yield and then convert the yield into a sigma
value. Several transformations from discrete distributions to continuous distribution
can be borrowed from mathematical statistics.
If the process follows a normal probability distribution, 99.73 % of the values will
fall between the

± 3 σ limits, where σ is the standard deviation, and only 0.27 % will

be outside of the ± 3 σ limits. Because the process limits extend from -3 σ to + 3 σ ,

the total spread amounts to 6 total variation. This total spread is the process spread

and is used to measure the range of process variability.
For any process performance metrics, usually there are some performance speci-
fication limits. These limits may be single sided or two sided. For the A/P process,
the specification limit may be no less than 95 % accuracy. For receipt of material
into a plant, it may be two days early and zero days late. For a call center, we may
want the phone conversation to take between two minutes and four minutes. For each
of the last two double-sided specifications, they also can be stated as a target and as
a tolerance. The material receipt could be one-day early

σ

± 1 day, and for the phone

conversation, it could be three minutes 1 minute.

If we compare the process spread with the specification spread, we can usually
observe three conditions:

±

Condition I: Highly Capable Process (see Figure 7.9). The process spread is
well within the specification spread.

6 σ< (USL − LSL)

The process is capable because it is extremely unlikely that it will yield
unacceptable performance.