Many people get confused about this since the formula is

(upper specification limit - lower specification limit)/(6*sigma),

but the six here refers to three sigmas up from the centerline
and three sigmas down from the midpoint of the tolerance interval. So if the Process Capability Ratio is 1.0 that means that the distance from the upper specification limit to the lower specification limit is six sigmas, but the distance from the "Design Target" (the midpoint of the tolerance interval) to either specification limit is only three sigmas.

The Process Capability Index is one third of the number of standard deviations from the observed process mean to the nearest specification limit. If the observed process mean is exactly halfway between the upper and lower specification limits (in other words, process mean = Design Target), the Process Capability Ratio and the Process Capability are the same; otherwise the "index" is less than the "ratio."

Six Sigma Control means that the distance from the Design Target to each control line is six times the standard deviation, which means that in Six Sigma Control the distance from one control line to the other is actually TWELVE times the standard deviation. Six Sigma control corresponds to a Process Capability Ratio of 2.0

Another source of confusion is this:

- the measure of dispersion used for xbar and R control charts is the range

- the measure of dispersion used for process capability analysis is the standard deviation

Exercise 8 on page 364 is an exception, since it uses an xbar chart based on the standard deviation.