What is Cpk and what does it measure?

Cpk measures process capability accounting for centering: how well output fits within spec limits given where the mean sits. It is the minimum of (USL - Mean) / (3 x Sigma) and (Mean - LSL) / (3 x Sigma). In the example, min(1.11, 1.67) = 1.11. The lower value wins because the mean of 10.01mm leans toward the USL of 10.05mm, so the upper side has less margin.

How do I calculate Cpk from process data?

Get Mean and Sigma from a stable data run, and USL and LSL from the drawing. Compute both ratios and take the smaller. With USL 10.05, LSL 9.95, Mean 10.01, Sigma 0.012: upper = 0.04 / 0.036 = 1.11, lower = 0.06 / 0.036 = 1.67, so Cpk = 1.11. Confirm the process is in statistical control first, or Sigma and the resulting Cpk are unreliable.

What is a good Cpk value?

1.33 is the usual minimum for a capable process, roughly 63 defects per million. 1.67 is preferred for safety-critical or high-volume features. Below 1.0 the process yields out-of-spec parts. The example's 1.11 is marginally capable but not comfortable, and the off-center mean at 10.01mm means the upper spec is the risk. Aim to reach at least 1.33 before releasing to production.

My Cpk is low but the spread looks fine. Why?

The process is probably off-center. Cpk penalizes a mean that drifts toward one limit even when Sigma is small. In the example, spread supports a lower ratio of 1.67, but the mean at 10.01mm pulls the upper ratio down to 1.11, which becomes Cpk. Recenter the mean toward 10.00mm and both ratios balance near 1.39, raising Cpk without reducing variation.

What is the difference between Cp and Cpk?

Cp is (USL - LSL) / (6 x Sigma) and ignores where the mean sits, measuring only tolerance versus spread. Cpk uses the mean's actual position and takes the worse side. In the example Cp = 0.10 / 0.072 = 1.39, but Cpk is only 1.11 because the mean leans toward USL. When Cp exceeds Cpk, the process is off-center and centering it will recover capability.

Do USL, LSL, Mean, and Sigma all need the same units?

Yes. Every term must share one unit, since the formula subtracts limits from the mean and divides by Sigma. The example uses millimeters throughout: USL 10.05, LSL 9.95, Mean 10.01, Sigma 0.012mm. Mixing millimeters and microns, or using spec tolerances in one unit and data in another, corrupts the ratios. Convert everything to a single consistent unit before computing Cpk.

Quality and Inspection

Process Capability Cpk Formula

Cpk measures how well a process fits within its specification limits while accounting for where the process mean sits relative to center. Use it when validating a new process, reviewing supplier capability, or setting control chart action limits.

Formula

Cpk = min((USL - Mean) / (3 x Sigma), (Mean - LSL) / (3 x Sigma))

Variables

USL: Upper specification limit
LSL: Lower specification limit
Mean: Process mean (average of measured values)
Sigma: Process standard deviation from actual process data

Understanding the Process Capability Cpk Formula

Cpk tells you how much room a process has inside its spec limits while penalizing off-center behavior. It takes the smaller of two distances from the mean to each spec limit, each divided by 3 sigma, so it captures both spread and location. In the example the process mean of 10.01mm sits above center between LSL 9.95 and USL 10.05, so the upper ratio (1.11) is worse than the lower (1.67). Cpk = min(1.11, 1.67) = 1.11, driven by the nearer limit.

Compute Mean and Sigma from actual process data, ideally a stable run of 30-plus in-control measurements, not spec values or guesses. USL and LSL come from the drawing. Keep units consistent, here millimeters throughout. Calculate both ratios: (USL - Mean) / (3 x Sigma) and (Mean - LSL) / (3 x Sigma), then take the minimum. Verify the process is in statistical control first, because an unstable process makes Sigma meaningless and any Cpk you compute unreliable.

Read Cpk against standard thresholds: 1.33 is the common minimum for a capable process (about 63 DPMO), 1.67 is preferred for critical dimensions, and below 1.0 the process produces out-of-spec parts. At 1.11 the example is marginally capable but the mean drifts toward USL, so watch the upper side. Recentering the mean from 10.01 to 10.00mm would balance both ratios near 1.39 and lift overall capability without touching the process spread at all.

Worked Example

A machined dimension has USL = 10.05mm, LSL = 9.95mm. Process mean is 10.01mm. Sigma is 0.012mm.

Upper ratio = (10.05 - 10.01) / (3 x 0.012) = 0.04 / 0.036 = 1.11
Lower ratio = (10.01 - 9.95) / (3 x 0.012) = 0.06 / 0.036 = 1.67
Cpk = min(1.11, 1.67) = 1.11

Result: Cpk = 1.11 (capable, but monitor the upper side closely)

Common Mistake

Confusing Cp and Cpk. Cp measures the ratio of tolerance to process spread but ignores centering. Cpk adjusts for where the mean sits. A process can have a good Cp but a poor Cpk if it is off-center. Always use Cpk when centering matters.

Frequently Asked Questions

What is Cpk and what does it measure?: Cpk measures process capability accounting for centering: how well output fits within spec limits given where the mean sits. It is the minimum of (USL - Mean) / (3 x Sigma) and (Mean - LSL) / (3 x Sigma). In the example, min(1.11, 1.67) = 1.11. The lower value wins because the mean of 10.01mm leans toward the USL of 10.05mm, so the upper side has less margin.
How do I calculate Cpk from process data?: Get Mean and Sigma from a stable data run, and USL and LSL from the drawing. Compute both ratios and take the smaller. With USL 10.05, LSL 9.95, Mean 10.01, Sigma 0.012: upper = 0.04 / 0.036 = 1.11, lower = 0.06 / 0.036 = 1.67, so Cpk = 1.11. Confirm the process is in statistical control first, or Sigma and the resulting Cpk are unreliable.
What is a good Cpk value?: 1.33 is the usual minimum for a capable process, roughly 63 defects per million. 1.67 is preferred for safety-critical or high-volume features. Below 1.0 the process yields out-of-spec parts. The example's 1.11 is marginally capable but not comfortable, and the off-center mean at 10.01mm means the upper spec is the risk. Aim to reach at least 1.33 before releasing to production.
My Cpk is low but the spread looks fine. Why?: The process is probably off-center. Cpk penalizes a mean that drifts toward one limit even when Sigma is small. In the example, spread supports a lower ratio of 1.67, but the mean at 10.01mm pulls the upper ratio down to 1.11, which becomes Cpk. Recenter the mean toward 10.00mm and both ratios balance near 1.39, raising Cpk without reducing variation.
What is the difference between Cp and Cpk?: Cp is (USL - LSL) / (6 x Sigma) and ignores where the mean sits, measuring only tolerance versus spread. Cpk uses the mean's actual position and takes the worse side. In the example Cp = 0.10 / 0.072 = 1.39, but Cpk is only 1.11 because the mean leans toward USL. When Cp exceeds Cpk, the process is off-center and centering it will recover capability.
Do USL, LSL, Mean, and Sigma all need the same units?: Yes. Every term must share one unit, since the formula subtracts limits from the mean and divides by Sigma. The example uses millimeters throughout: USL 10.05, LSL 9.95, Mean 10.01, Sigma 0.012mm. Mixing millimeters and microns, or using spec tolerances in one unit and data in another, corrupts the ratios. Convert everything to a single consistent unit before computing Cpk.