Home » Categories » Statistics » Capability » Capability Analysis (from Practical Tools for Continuous Improvement)

ST: 4.6.2. Calculate Cpk

Revision Date: 2005-09-07

Cpk takes into account the center of the data relative to the specifications, as well as the variation in the process. Cpk is simple to calculate. The smaller of the two Z values is selected. This is known as Z min . When Zmin has been selected, it is divided by 3. The formula is:

The Z values for the example are Zupper of 2.00 and Zlower of 5.00, therefore Zmin is 2.00. Cpk for the example is:

If the Cpk formula is written in full, it becomes more apparent how Cpk works.

This is the smaller of:

Graphically this can be drawn for the example as follows:

The diagram clearly shows that the overall average is too close to the upper specification. By taking the smaller of the two Z values, Cpk is always looking at the worst side, where the specification is closest to the overall average. Since it is looking only at half the picture, instead of dividing by 6 as in Cp, it is divided by 3.

 A Cpk value of one indicates that the tail of the distribution and the specification are an equal distance from the overall average, as shown below:

  A Cpk of less than one, as in the example, means that some of the data is beyond the specification limit. A Cpk greater than one indicates that the data is within the specification. The larger the Cpk, the more central and within specification the data.

Previous   Next

 The above article is an excerpt of the "Capability Analysis" section of Practical Tools for Continuous Improvement Volume 1 Statistical Tools.

Attachments Attachments
There are no attachments for this article.
Related Articles RSS Feed
ST: 3 When is it used
Viewed 2300 times since Fri, Nov 9, 2007
ST: 4.5.3. Determining the total percentage outside the specifications
Viewed 2556 times since Fri, Nov 9, 2007
ST: 4.6.4. Calculate Cpu and Cpl
Viewed 8631 times since Wed, Nov 14, 2007
ST: 4.5. Calculate how much data is outside the specifications
Viewed 2574 times since Fri, Nov 9, 2007
ST: 4.7. Analyze the Results
Viewed 1967 times since Fri, Nov 9, 2007
ST: 4.3. Determine the location of the tails for the distribution
Viewed 2245 times since Fri, Nov 9, 2007
ST: 2 What does it look like
Viewed 2107 times since Fri, Nov 9, 2007
ST: 4.1. Sketch the distribution
Viewed 2150 times since Fri, Nov 9, 2007
ST: 4.6.1. Calculate Cp
Viewed 6444 times since Fri, Nov 9, 2007
ST: 4.5.2. Find the percentage below the lower specification
Viewed 2224 times since Fri, Nov 9, 2007