Is it possible to determine the Cpk value from Cp and Cr values?

[dbulak]

Is it possible to determine the cpk value just by having the cp and cr values?

[Atul Khandekar]

I'm not sure there is a relationship. Cr is defined as the reciprocal of Cp (Cr = 1/Cp). These are two ways of comparing the total tolerance with total (6Sigma) process spread. Process centering is not considered.

[The Taz!]

The Cpk will equal the Cp IF and ONLY IF you are dead on target. This is a rare case. Cr is your % of B/P tolerance consumed by the process (Inverse of Cp). Helpful index, but you need to take process center location into account to determine Cpk.

Cp does not take process location into account and is a process capability index assuming you can center the process to obtain a reasonable Cpk. A process with a Cp of 4.0 will produce 50% rejects if centered on one of the tolerance limits.

Hope this helps. . .

[Darius]

dbulak you said.

Is it possible to determine the cpk value just by having the cp and cr values ?

Atul is right, Cr = 1/Cp and as Taz said Cp= Cpk if centered on target (Cpk is always less or equal to Cp).

The question is if you hace specs and mean also, if such the case,

Cp = (USL - LSL) / (6 * Sigma) or Sigma = (USL - LSL) / (6 * Cp)

Cpk = min ( USL - mean, mean - LSL) / (3 * Sigma)
Cpk = min ( USL - mean, mean - LSL) / [3 * (USL - LSL) / (6 * Cp)]
Cpk = min ( USL - mean, mean - LSL) * (2 * Cp) / (USL - LSL)

If only specs are available, you could use target insteed of mean, I readed somewhere in the Milstd hanbooks (but always document the asumptions ie. on target).

Cpk = min ( USL - target, target - LSL) * (2 * Cp) / (USL - LSL)

[Rob Nix]

Originally Posted by dbulak

Is it possible to determine the cpk value just by having the cp and cr values?

The short answer then, to dbulak's question, is NO. If all you know is cp / cr, you cannot determine the cpk. If you get one more metric - the mean - then you have enough to determine cpk (assuming you know the USL/LSL and std devs).