Process Capability (Cp)

Cp compares the width of the tolerance with the width of the process: specification band over six standard deviations. A 1.000 mm band on a process with $\sigma = 0.125$ mm gives $1.000/0.750 = 1.33$, which is the target most automotive and aerospace customers write into their supplier requirements. Cp of 1.00 means the process exactly fills the tolerance with no room at all, and Cp of 2.00 is the "six sigma" condition.

The reason 1.33 became the standard rather than 1.00 is that a process sitting exactly at 1.00 produces 2,700 defects per million even when perfectly centred, and real processes are neither perfectly centred nor perfectly stable. The extra third is margin for drift.

Two things Cp cannot tell you, and both matter. It says nothing about where the process is running: a process could sit entirely outside the tolerance and still report Cp of 2.00, because Cp only measures spread. And it is meaningless on an unstable process. Capability assumes a single stable distribution, so if the control chart shows the mean wandering, the sigma you computed is a mixture of several processes and the index describes none of them. Get the chart in control first, then measure capability. Doing it the other way round is the most common misuse of the whole toolkit.