In industrial quality control, once a process is in control, indices are often computed to measure the quality of the items produced (and thus the capability of the process); specifically, the extent to which the items that are produced fall within allowable engineering tolerances. Given a sample of a particular size, we can estimate the standard deviation of the respective quality characteristic of interest (e.g., piston ring diameters); we can then produce a histogram of the distribution of the characteristic of interest (piston ring diameters).

If the distribution of the quality characteristic is normal, we can make inferences concerning the proportion of items (piston rings) within specification limits (methods for non-normal distributions are also available; namely the so-called percentile method).

Common indices for process capability are Cp, Cr, and Cpk. All of these indices basically reflect the ratio of the engineering tolerances (process range) to the ± 3 sigma limits around the nominal specifications. For computational details, see Process Capability Indices; see also, Process Performance.