How to use the process capability calculator
- Paste your data from Excel or a CSV file. Each line is one subgroup (for example 5 consecutive parts), or put all values in one column and set the subgroup size.
- Enter the lower and upper specification limits (LSL, USL). One limit is enough for one-sided characteristics. Add the target to get Cpm.
- Read the verdict first. It combines stability, normality and the required Cpk. Then check the control charts for special causes before trusting the indices.
Formulas
Short-term sigma is estimated within subgroups: σ = R̄ / d₂ for subgroup sizes 2 to 10, σ = S̄ / c₄ above 10, and σ = MR̄ / 1.128 for individual values. Long-term sigma is the sample standard deviation of all values.
Cp = (USL − LSL) / 6σ_within,Cpk = min(USL − μ, μ − LSL) / 3σ_withinPp = (USL − LSL) / 6σ_overall,Ppk = min(USL − μ, μ − LSL) / 3σ_overallCpm = (USL − LSL) / 6√(σ² + (μ − T)²)penalises distance from the target.- The 95 % confidence interval of Cpk uses the Bissell approximation.
Control charts and Nelson rules
The tool picks the chart from the subgroup size: I-MR for individuals, X-bar and R for 2 to 10, X-bar and S above 10. All eight Nelson rules can be switched on, from a single point beyond 3 sigma to runs, trends and stratification. Flagged points are shown in red and listed under the chart.
Interpreting the result
| Cpk | Expected PPM (centred) | Meaning |
|---|---|---|
| < 1.00 | > 2,700 | Not capable, parts outside tolerance are produced |
| 1.00 to 1.33 | 63 to 2,700 | Marginal, needs tight control or 100 % inspection |
| 1.33 to 1.67 | 0.6 to 63 | Capable, typical requirement for series production |
| ≥ 1.67 | < 0.6 | Highly capable, typical for new or critical processes |
If Cp is high but Cpk is low, the spread is fine and the process is just off centre: move the mean to the target. If both are low, the variation itself has to be reduced. Before blaming the process, make sure the gauge is good enough with a Gage R&R study.
Frequently asked questions
›What is the difference between Cpk and Ppk?
Cpk uses the short-term (within-subgroup) standard deviation and shows what the process could achieve if it stayed stable. Ppk uses the overall standard deviation of all values, so it also contains drift and shifts between subgroups. A large gap between Cpk and Ppk means the process is moving over time.
›What is a good Cpk value?
Cpk 1.33 is the usual minimum for an existing process, which corresponds to about 63 defective parts per million for a centred normal process. Many automotive customers ask for Cpk 1.67 for new processes or safety-relevant characteristics, and Six Sigma targets Cpk 2.0.
›How many measurements do I need for a capability study?
At least 100 individual values, for example 25 subgroups of 4 or 5, is a common rule. With fewer than 50 values the confidence interval of Cpk becomes wide, which is why the calculator shows the 95 % interval.
›Why does the tool say the process is not stable?
Capability indices only predict future performance when the process is in statistical control. If a point is outside the control limits or a Nelson rule pattern is found, a special cause is present and Cpk does not describe a single, predictable process.
›What should I do if my data are not normal?
First check whether the non-normality comes from an instability or a mix of several processes. If the characteristic is naturally skewed, for example flatness, runout or roughness, switch on the Box-Cox option. The tool finds the best lambda and calculates Ppk and expected PPM on the transformed scale.
›What is the difference between Cm/Cmk and Cp/Cpk?
Cm and Cmk are machine capability indices from a short run on one machine, usually 50 parts. They use 8 and 4 standard deviations instead of 6 and 3, as in VDA volume 4, so the requirement is typically Cmk 1.67 or higher.