What is process capability analysis?
Process capability compares the natural variation of a process with the tolerance its customers require. A capability index summarizes that comparison in one number, so you can decide whether a process is ready for production, whether it needs 100% inspection, or where to focus improvement. Capability only means something for a stable process, so check stability first with a control chart, and make sure the measurement system is adequate with a Gage R&R study.
Cp, Cpk, Pp and Ppk explained
| Index | Formula | What it tells you |
|---|---|---|
| Cp | (USL − LSL) / 6σwithin | Potential capability if the process were perfectly centred |
| Cpk | min(USL − x̄, x̄ − LSL) / 3σwithin | Short-term capability including centring |
| Pp | (USL − LSL) / 6σoverall | Long-term potential performance |
| Ppk | min(USL − x̄, x̄ − LSL) / 3σoverall | Actual long-term performance, what the customer receives |
| Cpm | (USL − LSL) / 6·√(s² + (x̄ − T)²) | Capability around a target value (Taguchi) |
Process capability example
The example analyses 125 seal strength measurements from a pouch sealer, in 25 subgroups of 5, against a specification of 12 to 22 N/15 mm. Within subgroups the process is capable: Cp = 1.85 and Cpk = 1.41. Over the whole period it is only marginal: Pp = 1.62 and Ppk = 1.23, with about 107 PPM expected out of specification. The gap between Cpk and Ppk shows that the mean moves between subgroups, and Cp well above Cpk shows the process runs high in the tolerance. The data passes the normality test (p = 0.11). The priorities: stabilize the mean between subgroups, then centre the process.
Common pitfalls
- Unstable process: capability indices predict nothing if the process is out of control.
- Too little data: a Cpk from 30 values can easily be off by ±0.3.
- Non-normal data: expected PPM can be wrong by orders of magnitude in the tails.
- Poor measurement system: gauge variation inflates σ and lowers the indices.
- Mixing Cpk and Ppk: state which one you report; customers often ask for Ppk at launch and Cpk in production.
How to use this Process Capability Analysis tool
- Enter the specification. Type the lower and upper specification limits, and the target if there is one.
- Paste the measurements. Paste values in production order and set the subgroup size (1 for individual values).
- Read the indices. Compare Cp and Cpk (short-term) with Pp and Ppk (long-term) and the expected PPM.
- Check normality and stability. Look at the normality test and the gap between Cpk and Ppk before you draw conclusions.
- Explore what-ifs. Drag the specification lines on the chart to see how the indices would change.
- Export the report. Export the capability histogram, indices and data to PDF or Excel.
Frequently asked questions
What is the difference between Cp, Cpk, Pp and Ppk?
Cp and Pp compare the width of the tolerance with the spread of the process (6σ); they ignore where the process is centred. Cpk and Ppk also account for centring: they measure the distance from the mean to the nearest specification limit in units of 3σ. Cp and Cpk use the within-subgroup (short-term) standard deviation; Pp and Ppk use the overall (long-term) standard deviation.
What is a good Cpk value?
A Cpk of 1.33 or higher is the most common requirement (about 63 parts per million out of specification). Many automotive and medical device customers require 1.67 for critical characteristics, and Six Sigma quality corresponds to a Cpk of 2.0. Below 1.0 the process produces a noticeable share of nonconforming parts.
Why is my Ppk lower than my Cpk?
Ppk uses the total variation over the whole period, including shifts and drifts between subgroups; Cpk uses only the variation within subgroups. A large gap means the process is not stable over time. Use a control chart to find and remove the special causes.
How is the within-subgroup standard deviation estimated?
For subgroups of 2 to 10 values, the tool uses the average range divided by d2 (R-bar/d2). For individual values (subgroup size 1), it uses the average moving range divided by 1.128.
Does my data need to be normal?
The indices and the expected PPM assume a normal distribution. The tool runs an Anderson-Darling normality test and warns when the p-value is below 0.05. Non-normal data may come from mixed populations, a skewed process or a boundary at zero; investigate before you rely on the numbers.
How many data points do I need?
At least 30, and preferably 100 or more (for example 25 subgroups of 4 or 5) collected over a period that includes normal process variation. With small samples the confidence interval of Cpk is wide; the tool shows it.