Process Capability Index, Cpk


Cpk is a short term process index that numerically describes the "within subgroup" or "potential" capability (Ppk is long term indicator) of a process assuming it was analyzed and stays in control.

It's an option (along with z-score and PPM or DPMO) when describing process baseline measurement in the MEASURE phase or in the CONTROL phase. As with all the process capability indices, the process must be in control before assessing capability.

Use time-series and SPC charts to determine process control. If the process is out of control (i.e. still rising with upward trend), then assessing the current process is unlikely to reflect the long term performance.

Cpk Calculation

The Cp is the best a process can perform if that process is centered on the midpoint. The Cp is commonly referred to as the process entitlement because, when centered, it represents the best performance possible.

The addition of "k" in Cpk quantifies the amount of which a distribution is centered, in other words it accounts for shifting. A perfectly centered process where the mean is the same as the midpoint will have a "k" value of 0.

The minimum value of "k" is 0 and the maximum is 1.0. A perfectly centered process will have Cp = Cpk.

Both Cpk and Ppk relate the standard deviation and centering of the process about the midpoint to the allowable tolerance specifications.

An estimate for Cpk = Cp(1-k).

and since the maximum value for k is 1.0, then the value for Cpk is always equal to or less than Cp.

Cpk will never exceed the Cp

Similar to Ppk, the Cpk capability index is only a function of the standard deviation and mean of the data, not a nominal (target) value that may be historical or provided by the customer. The Cpm capability calculation accounts for a nominal value.

Cpk also requires input from the customer for the lower specification limit (LSL) and upper specification limit (USL).

There are two calculations from the formula providing two values for Cpk. Select the MINIMUM value as the Cpk and to serve as the baseline value. This minimum value must be equal to or greater than the minimum acceptability level.

Unlike Cp (and Pp), the Cpk (and Ppk) index can be calculated using unilateral or bilateral tolerances. If only one specification is provided (unilateral) the use the value that involves that specification limit.

In such case, there will not be a minimum (or maximum), just calculate using the formula that has a specification and use it for the Cpk value.

  • Cp is a measure of variation only.
  • Cpk is a measure of location and variation.
  • Cp will never be a negative number.
  • Cpk can be a negative number.

The standard Cpk level is 2.0 for a process in six sigma quality control . The most relevant acceptability levels for Cpk depends on your customer - the Voice of the Customer.

Read more about the process capability indices, their meanings, and relationships.

Once again, the Cpk can not be used if the:

  1. data is not a bell-shaped normal distribution
  2. control chart is not in control and free from special cause.

It is recommended to have at least 25 subgroups and preferably a each subgroup having >1 data point. The greater the subgroups size the higher likelihood the special cause variation is detected and that it exist if it is detected.  

Think about it this way, if a subgroup size is 5 and all five data points show an average that is vastly different from the averages of the other subgroups (that also have 5 data points) then there is a strong chance that the subgroup was measured under a "unique" or special condition. 

Relationship of Capability Indices


Additional Visual Aids

Relationships of Cp, Pp, Cpk, Ppk

Recommended Video for Cpk and Cp

Cpk and Cp are the two most commonly used capability indices in statistics. This is a video that we recommend to help grasp the similarities, differences, application, and calculations. 

Converting from Cpk to a Z-score

With a normally distributed set of data an approximation of Z from Cpk and vice versa can be made in substituting and solving within these two formulas.

What is the Cpk approximated from a 6 sigma performance?

Substituting the Z formula in Cpk (USL) and plugging in 6 for Z from the given data gives:

Relating Cpk to sigma (Z)

A Cpk of 2 corresponds to approximately 6 sigma (short term) performance or 4.5 sigma (long term) if applying the shift.

The Z in the above formula refers to a short term sigma, short term Z.

Click here to learn more about z-scores.

Capability Study Module - Download

This module provides lessons with statistical capability studies. Understanding the basic meaning and applications for capability studies is necessary for any level of a Six Sigma Project Manager.

Click here to purchase 'Capability Study' and view others subjects that are available.

Sigma / DPMO / Cpk Conversion Table

Sigma, Cpk, DPMO Conversion Table

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