The Cpk ratio (pk = process kurtosis, a measure of peakedness) measures where the specification limits sit compared to the production spread.

The Cpk ratio is the absolute value of the Z-score of the nearest specification limit from the process center, compared to 3 standard deviations. The formula is

Cpk =

Z (d.n.s.) is the Z score of the distance to the nearest specification limit .

Using the example from the review of capability, the nearest specification limits are 25.0 and 29.0. Since 29.0 is closer to the grand average of 27.8,

We want a Cpk of at least 1, so 100% of production is within specification. An ideal Cpk is 1.33, which means the product is within specification on both sides, with at least one standard deviation to spare.

A process must be under statistical control before capability can be determined.

A capable process must have a Cpk 1. A process that is in statistical control does not assure capability because capability is derived from process control and specifications.

The Cpk is useful as a means of comparison between processes. It does not give the percent out of specification. For example, if improvements to a process raised the Cpk from 0.31 to 0.91, that would be a sign of significant progress toward a higher goal of about 1.33.

The best way to obtain the percent out of specification it to make a frequency chart and histogram of many randomly chosen individual measurements. Next mark the specification limits on the histogram or frequency chart, then add up the number of individuals out of specification. SPC software Cpk tools can misrepresent the percent of production out of specification if they infer a normal distribution based on sample measures from skewed data.