# Cpk

Cp = Process Capability. A simple and straightforward indicator of process capability. Cpk = Process Capability Index. Adjustment of Cp for the effect of non-centered distribution. Pp = Process Performance. A simple and straightforward indicator of process performance. Ppk = Process Performance Index. Adjustment of Pp for the effect of non-centered distribution.

The "k" stands for "katayori" which means deviation, inclination or offset in Japanese. The origins of k actually go back to the 1970s in Japan. The Japanese are credited with developing the the Cp, Cpl, Cpu, Cpk, and k indexes of process capability.

So what is k? It is an index of process centering, defined as follows, where M is the middle of the tolerance, mu is the process average, USL is the upper spec limit, and LSL is the lower spec limit:

k = |M - mu| / [(USL - LSL) / 2]

k is then used as follows to compute Cpk.

Cpk = Cp (1 - k)

When the process average is centered at the middle of the tolerance, M = mu, and therefore, M - mu = 0. With k = 0, Cpk will equal Cp.

Cpk = Cp (1 - 0) = Cp

If the process average is centered anywhere else, then the absolute value of the quantity M - mu is greater than zero, making k also greater than 0. Suppose k is 0.30 for a process. Then the Cpk index for this process is only 70% of the Cp index.

Cpk =Cp (1 - 0.30) = 0.70Cp

So in one way, k measures how much potential capability is lost due to poor centering. In the above example, Cpk could be increased by 30% if we could center mu at M.

A visual animation: Process Capability - Cp vs. Cpk

Also see: Process Capability Index and Cp

Discussion thread: Ppk vs Cpk - A Good, clear explanation

Elsmar Cove forum Cp and Cpk discussion threads