Distinguish process spread from off-center performance

Verify the reference conditions

Obtain upper and lower specification limits from the study or engineering requirement. Establish that the measurement process is stable over the reference interval and that the dispersion estimate represents the intended process. A capability calculation using an unstable mixture can give a precise-looking but misleading summary.

Compare two distances

Cp divides the specification width by six standard deviations. Cpk uses the smaller distance from the mean to a specification limit, divided by three standard deviations. A symmetric spread can fit inside the specification width while its center lies close to one limit. When the mean is outside the allowed interval, Cpk can be negative.

Hypothetical example

Suppose an assay simulator has an acceptable output range from 90 to 110 units, mean 106 and standard deviation 2. Cp is 20/12, about 1.67. The upper distance gives 4/6 and the lower distance gives 16/6, so Cpk is approximately 0.67. Shifting the mean to 100 while holding dispersion fixed would raise Cpk to 1.67.

Record the source of the specifications, the sample used for the standard deviation and evidence supporting stability. These are estimated indices. Translating them to an expected fraction outside limits requires a defensible distributional model. A favorable index by itself cannot certify a measurement system.

Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 6.1.6. What is Process Capability?.

Two-sided process capability indices · Download the specification limit provenance sheet