# Capability Calculations Methods

Three measures of process capability are presented here. These are the Cp, Cpk, and Cpm.

## Cp

Cp measures the spread of the process distribution, compared against the specification range. The natural tolerance is defined as the middle 99.73% of the process distribution in long-term studies, and the middle 99.994% in short-term studies. For a normal distribution, this range is plus or minus 3 standard deviations for the long-term, and 4 for the short-term. Here is a diagram showing the Cp calculation.

## Cpk

Cpk is concerned with the closeness of the distribution to the specification limits, and the threat of producing nonconforming product. K, in the formula below would be 3 for long-term studies, and 4 for short term studies. Z is the z-score corresponding to the proportion outside either specification.

## Cpm

Cpm is concerned with the variability from target. Its derivation is aligned with the Taguchi Loss Function, which says that losses in a manufacturing process increases by the square of the deviation from target. Economic losses are inversely related to this measure.