Cp and Cpk are related. Really?

Process capability analysis plays an important role in quality. It helps determine whether the process is capable of consistently producing parts conforming to customer requirements. Cp and Cpk are the two most popular capability indices used to find process capability. Cp and Cpk are related to each other. Whenever I say this most people around me are surprised, some think I am insane. But it is true. Cp and Cpk are related by the equation. Refer to chapter 6 in the NIST/SEMATECH e-handbook of Statistics Handbook

Cpk = (1-k) Cp
where k is the distance between the process mean and the midpoint of specification range.



where
m = midpoint of the specification range or tolerance
mu = process mean
USL and LSL – upper and lower specification limits.

k has a value between 0 and 1.
When k is 0, Cpk is equal to Cp.
When k is less than 1, Cpk < Cp

That is why Cpk ≤ Cp.