A process capability analysis compares the natural spread of a process against its specification limits and reports the result as four indices: Cp, Cpk, Pp, and Ppk. Cp and Cpk are calculated from the within-subgroup (short-term) standard deviation, while Pp and Ppk use the overall (long-term) standard deviation.
The plain letters, Cp and Pp, describe potential capability assuming the process is perfectly centered; the k versions, Cpk and Ppk, describe actual capability because they use the distance from the process mean to the nearer specification limit. As a widely used industry rule of thumb, a Cpk of 1.33 or higher is considered capable and 1.67 or higher is considered world class.
With the free online Process Capability Calculator in SIGMADESK, you can paste a column of measurements, enter your specification limits, pick a subgroup size, and read all four indices in your browser without installing anything.
This guide walks through one complete capability study from start to finish. We load a realistic dataset, set the specification limits, choose a subgroup size, and then read the output together so you can judge whether your own process is capable.
Step 1: Open the Process Capability Calculator
Go to sigmadesk.app in your browser and open the Process Capability Calculator. The page loads with a demo dataset already in place, so you can follow along even if you do not have data of your own yet.
This example holds 150 individual measurements taken from a stable process, and each value is a single reading recorded in the order it was collected. If you want to analyze your own measurements, you can type values straight into the spreadsheet or paste a column directly from Excel.
Step 2: Set the Two Inputs That Drive the Analysis
Subgroup size
A subgroup is a small batch of parts measured together under the same conditions, and SIGMADESK uses it to estimate short-term, within-subgroup variation. For this dataset we use a subgroup size of 5, which means every 5 consecutive measurements form one subgroup.
Cp and Cpk cannot be calculated without an estimate of within-subgroup variation, so how you collect and group your data matters. Pp and Ppk need only the overall standard deviation and can be calculated from ungrouped data. The same rational subgrouping logic used for Xbar-R charts applies here, and it is described in detail in the AIAG & VDA SPC Manual.
Specification limits
The lower specification limit (LSL) is the smallest value the customer will accept, and the upper specification limit (USL) is the largest. For this example the LSL is 63 and the USL is 73, which puts the midpoint of the specification window at 68.
Step 3: Read the Histogram
The blue bars in the center show how the measurements are distributed. The dashed curve on top is the fitted normal distribution for this data, so you can see at a glance how closely the process follows a bell shape.
The two red dashed lines are the specification limits, and the shaded red zones outside them are the reject regions. The teal line in the middle is the process average. All of the data sits comfortably between the limits, which is a very good sign.
Step 4: Read the Results Panel
The panel on the right is where the real answers live. At the top, SIGMADESK gives a plain verdict: this process is labeled Capable, based on a Cpk of 1.426. Here is the full output:
- Verdict: Capable
- Mean: 67.141 | Sample size: 150
- Within standard deviation: 0.968 | Overall standard deviation: 0.973
- Cp: 1.722 | Cpk: 1.426
- Pp: 1.714 | Ppk: 1.419
Within vs. overall standard deviation
Two different standard deviations are reported, and this is the part worth slowing down for, because each pair of indices is built on one of them.
| Statistic | What it estimates | Used by |
|---|---|---|
| Within σ = 0.968 | Variation inside subgroups — short-term, best-case behavior | Cp, Cpk |
| Overall σ = 0.973 | Variation across all 150 readings — long-term reality, including drift | Pp, Ppk |
If you want the full derivations, the complete capability analysis guide covers the mathematics behind every index. This walkthrough stays on the practical side.
Cp and Cpk: Potential vs. Actual Capability
Cp measures potential capability
Cp asks a simple question: if the process were perfectly centered, how many times would its spread fit inside the specification window? It divides the specification width by six within-subgroup standard deviations, so a Cp above 1 means the spread physically fits inside the limits, and higher is better. Because Cp assumes perfect centering, on its own it can be a little too optimistic — a point the NIST/SEMATECH e-Handbook of Statistical Methods makes explicitly.
Cpk measures actual capability
Cpk accounts for how far off-center the process sits. Instead of using the full window, it measures the distance from the mean to each specification limit, divides each by three within-subgroup standard deviations, and reports the worse of the two sides.
Our Cpk of 1.426 is lower than our Cp of 1.722, and that gap is telling us something useful: the process is not perfectly centered. The average of 67.141 sits below the specification midpoint of 68, so the process leans toward the low side. Whenever Cpk is smaller than Cp, centering is your improvement opportunity — a relationship explored further in the difference between Cp and Cpk.
Pp and Ppk: The Long-Term View
Pp and Ppk answer exactly the same questions as Cp and Cpk, with one difference: they use the overall standard deviation. Pp describes long-term potential performance if the process were centered, while Ppk uses the distance from the mean to the nearer specification limit over three overall standard deviations to describe long-term actual performance.
Here Pp is 1.714 and Ppk is 1.419. These definitions follow ISO 22514-4, the international standard for process capability estimates and performance measures, and are compared side by side in our guide to capability vs. performance.
The quick way to remember all four
| Index | Standard deviation | Assumes centering? | What it tells you |
|---|---|---|---|
| Cp | Within (short-term) | Yes | Potential capability on a good day |
| Cpk | Within (short-term) | No | Actual short-term capability |
| Pp | Overall (long-term) | Yes | Potential performance over time |
| Ppk | Overall (long-term) | No | Actual long-term performance |
So Is This Process Capable?
Yes. A common industry rule of thumb is that a Cpk of 1.33 or higher means the process is capable, and 1.67 or higher is world class. Our Cpk of 1.426 clears the 1.33 mark, which is why SIGMADESK labels the process Capable, and you can translate that number into a sigma level and expected defect rate.
The overall Ppk of 1.419 tells the same story for the long term. Because the within and overall standard deviations are nearly identical, the process is behaving consistently over time with no large hidden drift. Keep in mind that capability indices are only meaningful when the process is in statistical control, so confirm stability on a control chart before trusting any Cpk number.
The Practical Takeaway
A high Cp with a lower Cpk is not a bad process — it is an off-center one. Often you can close that gap simply by nudging the process mean back toward the middle of the specification window, with no expensive rework required.
Capability is not about chasing a perfect number. It is about understanding your variation and your centering, and then knowing exactly which one to improve next.
Frequently Asked Questions
What is a good Cpk value?
A Cpk of 1.33 or higher is widely accepted as capable, and 1.67 or higher is considered world class. Many automotive customers require a Ppk of at least 1.67 for initial process studies before granting production approval. Always check the specific requirement in your customer’s contract or control plan, since the threshold is a business decision rather than a statistical law.
What is the difference between Cpk and Ppk?
Cpk uses the within-subgroup standard deviation and Ppk uses the overall standard deviation of all the data. Cpk therefore reflects short-term capability under stable conditions, while Ppk reflects actual long-term performance including drift between subgroups. When Cpk and Ppk are close, as in the example above, the process is stable over time.
Can you calculate Cp and Cpk with a subgroup size of 1?
Yes, but the short-term standard deviation must then be estimated from the average moving range divided by d2 rather than from within-subgroup ranges. This is the same approach used by an I-MR chart for individual measurements. If you do not have a defensible short-term estimate, report Pp and Ppk only.
Why is my Cpk lower than my Cp?
Cpk is lower than Cp whenever the process mean is off-center within the specification window. Cp only measures spread, while Cpk penalizes the distance from the mean to the nearer specification limit. The larger the gap between the two values, the more centering — not variation reduction — is your priority.
Does process capability analysis require normally distributed data?
The standard Cp, Cpk, Pp, and Ppk formulas assume an approximately normal distribution and a process that is in statistical control. If the data is clearly non-normal, use a distribution fit or a transformation before interpreting the indices, otherwise the predicted defect rates will be wrong. Checking the histogram and the fitted normal curve first is the fastest way to spot a problem.