What are Cp and Cpk, and how are they calculated?

Cp versus Cpk

Cp says how much room the process has if its mean is centred. The specification width (USL − LSL) is compared with 6σ, the spread that covers about ±3σ around the mean of a normal process. If the mean sits away from the middle of the specification, Cp overstates capability, so Cpk is calculated as well. Cpk takes the smaller of the two distances from the mean to a limit, measured in units of 3σ. Cpk can never exceed Cp, and the two are equal only when the mean is exactly centred.

Targets such as 1.33 and 1.67 are common, but the customer or the applicable requirement sets them. They are not universal pass marks.

A hypothetical diameter measurement

Hypothetical example: LSL 9.8 mm, USL 10.2 mm, mean 10.05 mm, σ 0.05 mm.

• Cp = (10.2 − 9.8) / (6 × 0.05) = 0.4 / 0.30 = 1.33
• Cpk = min((10.2 − 10.05) / (3 × 0.05), (10.05 − 9.8) / (3 × 0.05)) = min(0.15 / 0.15, 0.25 / 0.15) = min(1.00, 1.67) = 1.00

Cp looks good, but the mean is closer to the upper limit, so Cpk drops to 1.00. Centring the mean at 10.00 would raise Cpk to 1.33, equal to Cp, with no change in spread.

Misreadings to avoid

The first mistake is computing Cp or Cpk from a process that is not in statistical control. A drifting mean means the numbers describe only the sampled period and do not guarantee future output. The second is mixing up sources of sigma: short-term within-subgroup variation gives Cp and Cpk, while overall variation across all the data gives Pp and Ppk, and the two should not be mixed in one report. The third is treating non-normal data as normal. Skewed distributions may need a transformation or percentile-based methods.

Follow-up questions