About the Process Capability (Cp, Cpk) Calculator
Process capability indices tell you how well a stable process fits inside its specification limits. Cp compares the width of the tolerance with the natural spread of the process (six standard deviations); Cpk also accounts for how far the process mean sits from the nearer limit. Pp and Ppk are the same ratios calculated with the overall (long-term) standard deviation instead of the within-subgroup (short-term) one.
Enter the lower and upper specification limits and either summary statistics — the process mean, the within (short-term) sigma and the overall sigma — or paste individual measurements and let the calculator estimate them. For raw data, the overall sigma is the sample standard deviation and the within sigma is the average moving range divided by d₂ = 1.128, the usual method for individual measurements.
It is intended for quality engineers, machinists, Six Sigma practitioners and suppliers preparing a PPAP or capability study. The indices assume the process is in statistical control and roughly normally distributed; check a control chart first, because capability numbers from an unstable process are not meaningful.
With the default inputs, the cpk is 1.067. Change any value above to recalculate instantly.
How to use the process capability (cp, cpk) calculator
- 1Enter the lower and upper specification limits.
- 2Choose whether to type summary statistics or paste raw measurements.
- 3Enter the mean and the within and overall standard deviations, or paste your data in time order.
- 4Optionally enter a target value for Cpm.
- 5Read Cpk and Ppk, the expected PPM out of spec and the capability rating.
Formula and method
Cp is the ratio of the tolerance width to six within-subgroup standard deviations: it shows what the process could achieve if perfectly centred. Cpk takes the distance from the mean to the nearer specification limit and divides by three sigma, so it drops when the process drifts off centre. Pp and Ppk use the overall standard deviation of all the data, which includes between-subgroup shifts, so they describe actual long-term performance.
Cpm (the Taguchi index) also penalises distance from a target value. The expected parts per million out of specification use the normal distribution with the overall mean and sigma: PPM = [Φ((LSL − μ)/σ_o) + 1 − Φ((USL − μ)/σ_o)] × 10⁶. For pasted data the within sigma is the average moving range of consecutive values divided by d₂ = 1.128.
- USL, LSL
- Upper and lower specification limits
- μ
- Process mean
- σ_w
- Within-subgroup (short-term) standard deviation
- σ_o
- Overall (long-term) standard deviation
- T
- Target value (defaults to the spec midpoint)
Worked examples
Shaft diameter 10.00 ± 0.10 mm, mean 10.02
The tolerance is 0.20 mm. Cp = 0.20 ÷ (6 × 0.025) = 1.333, but the mean is 0.08 from the USL, so Cpk = 0.08 ÷ 0.075 = 1.067. With the overall sigma of 0.03, Ppk = 0.08 ÷ 0.09 = 0.889, and about 3,860 parts per million would fall outside the limits, almost all above the USL. Cpm is 0.92 because the mean is off the 10.00 target.
Well-centred fill weight process
The process is centred at 505 g between 495 and 515 g, so Cp equals Cpk: 20 ÷ (6 × 2) = 1.667. Long-term, Ppk = 10 ÷ 7.5 = 1.333, which predicts about 63 PPM out of spec (32 on each side).
Raw measurements pasted in order
The ten values average 5.007 with a sample standard deviation of 0.0221, giving Ppk = (5.1 − 5.007) ÷ (3 × 0.0221) = 1.40. The average moving range is 0.0344, so within sigma = 0.0344 ÷ 1.128 = 0.0305 and Cpk is only 1.02 — the zig-zag between consecutive parts inflates short-term variation.
Frequently asked questions
What is the difference between Cp and Cpk?+
Cp measures only spread: tolerance width ÷ six sigma. Cpk also accounts for centring by using the distance from the mean to the nearest spec limit ÷ three sigma. Cpk is always less than or equal to Cp, and equals it only when the process is perfectly centred.
What is the difference between Cpk and Ppk?+
Cpk uses the within-subgroup (short-term) standard deviation and shows what the process can do; Ppk uses the overall standard deviation of all data and shows what it actually did, including shifts between subgroups. A big gap means the process is not stable.
What is a good Cpk value?+
A Cpk of 1.33 (a 4-sigma process) is the most common minimum requirement, and 1.67 is often required for new or safety-critical characteristics. A Cpk of 2.0 corresponds to six sigma. Below 1.0 the process spread extends past at least one specification limit, so a normal process will produce more than about 1,350 PPM beyond that limit.
How many parts per million does a Cpk of 1.33 produce?+
For a centred, normal process, Cpk 1.33 means the nearest limit is 4 sigma away, giving about 32 PPM per side or 63 PPM in total. Cpk 1.0 gives about 2,700 PPM, and Cpk 1.67 about 0.6 PPM.
Do I need normally distributed data for Cpk?+
The PPM estimate and interpretation assume normality and statistical control. For skewed data, transform it (e.g. Box-Cox) or use a non-normal capability method, and always confirm stability with a control chart before reporting capability.