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Statistical Basics and Six Sigma Metrics 407

11.4.2 Process Capability Indices

Capability indices are simplified measures that quickly describe the relationship
between the variability of a process and the spread of the specification limits.

The Capability Index C p
The equation for the simplest capability index C is the ratio of the speci-
p
fication spread to the process spread, the latter represented by six standard
deviations or 6s.

C = USL − LCL
p 6s

we assume that the normal distribution is the correct model
When using C p
for the process.
The capability index C can be translated directly to the percentage or pro-
p
portion of nonconforming product outside specifications, if the mean of the
process performance is at the center of the specification limit.

When C = 1.00, approximately 0.27 percent of the parts are outside the
p
specification limits (assuming that the process is centered on the midpoint
between the specification limits) because the specification limits closely
match the process UCL and LCL. We say this is about 2700 parts per million
(ppm) nonconforming.

= 1.33, approximately 0.0064 percent of the parts are outside the
When C p
specification limits (assuming the process is centered on the midpoint between
the specification limits). We say this is about 64 ppm nonconforming. In this
case, we would be looking at normal curve areas beyond 1.33 × 3s =±4s
from the center.

When C = 1.67, approximately 0.000057 percent of the parts are outside
p
the specification limits (assuming the process is centered on the midpoint
between the specification limits). We say this is about 0.6 ppm nonconforming.
In this case, we would be looking at normal curve areas beyond 1.67 × 3s =
±5s from the center of the normal distribution.

The Capability Index C pk
The major weakness in C is that, for many processes, the mean per-
p
formance is not equal to the center of the specification limit; also many