Process capability measures how well a process can produce output inside its specification limits. The process capability definition most quality engineers use is this: you compare the natural spread of a stable process, usually six standard deviations, to the width of the tolerance the customer allows, then express the result as an index such as Cp or Cpk. A Cpk of 1.33 or higher is the common benchmark for a capable process.
Put simply, the index answers one question: how much room does the process have before it makes a bad part? A high number means the process fits easily inside the limits. A low number means defects are coming, even if the process looks steady on a control chart.
This article covers why capability matters, how to calculate and read Cp and Cpk, how they differ from Pp and Ppk, and how to run a study that gives numbers you can trust. At Lean Six Sigma Experts, we have helped businesses improve their operations since 2011, and we teach process capability in our Six Sigma Online Training.
Why process capability matters
Process capability matters because it tells you whether a process can meet the customer’s requirements before bad output reaches the customer. Inspection finds defects after the fact. A capability index predicts them.
Voice of the process versus voice of the customer
A control chart shows what your process does. Its limits come from your own data, so they are the voice of the process. Specification limits come from the customer or the drawing, so they are the voice of the customer. Control limits and specification limits are unrelated until a capability study connects them.
That is why a process can be perfectly in control and still ship defects. If its natural spread is wider than the tolerance, every stable day produces scrap.
A process can be in control and still be incapable.
What the number changes in practice
The index tells you what to fix, and it keeps you from spending money on the wrong thing. Read the pattern of Cp and Cpk together:
- Low Cp: the spread is too wide. Reduce variation with better tooling, materials, or method.
- High Cp, low Cpk: the spread fits but the process is off target. Re-center the process with an adjustment, which is usually cheaper than a new machine.
- Both high: the process is capable. You can reduce inspection and move to routine monitoring.
How to calculate and read Cp and Cpk
Cp divides the tolerance width by six standard deviations. Cpk takes the smaller of the two distances from the mean to a spec limit and divides it by three standard deviations. Both assume a stable process with roughly normal data.
The formulas
With USL as the upper spec limit, LSL as the lower spec limit, and σ as the process standard deviation:
- Cp = (USL − LSL) / 6σ
- CPU = (USL − mean) / 3σ
- CPL = (mean − LSL) / 3σ
- Cpk = the smaller of CPU and CPL
Cp ignores centering, so it shows what the process could do if you aimed it perfectly. Cpk penalizes an off-center process, so it shows what you are getting now. Cp is never lower than Cpk, and the two match only when the mean sits exactly midway between the limits. If a characteristic has only one spec limit, use just the matching one-sided index.
A worked example
Say a shaft diameter must fall between 9.90 mm and 10.10 mm. Your data show a mean of 10.02 mm and a standard deviation of 0.03 mm.
| Measure | Calculation | Result |
|---|---|---|
| Cp | 0.20 / (6 × 0.03) | 1.11 |
| CPU | (10.10 − 10.02) / 0.09 | 0.89 |
| CPL | (10.02 − 9.90) / 0.09 | 1.33 |
| Cpk | smaller of CPU and CPL | 0.89 |
Cp of 1.11 looks acceptable. Cpk of 0.89 says otherwise. The upper limit is only 2.67 standard deviations from the mean, so about 0.4% of parts, roughly 3,800 per million, exceed 10.10 mm. Move the mean to 10.00 and Cpk rises to 1.11 with no change in variation.
How to read a Cpk value
A Cpk of 1.33 means the nearest spec limit sits four standard deviations from the mean. For a centered, normal process that is about 63 defects per million. Many customers treat 1.33 as the minimum for a capable process.
| Cpk | Nearest limit | Defects per million (centered, normal) | Reading |
|---|---|---|---|
| 1.00 | 3σ | about 2,700 | Marginal, expect scrap |
| 1.33 | 4σ | about 63 | Capable, common minimum |
| 1.67 | 5σ | about 0.6 | Highly capable |
| 2.00 | 6σ | about 0.002 | Six Sigma level, short term |
Below 1.00, the process is not capable. Some customers set their own minimums, often 1.33 or 1.67 for critical characteristics, so check the requirement before you judge a result. The familiar 3.4 defects per million figure assumes a 1.5 sigma long-term shift, so it is not the same as the Cpk 2.00 row.
Cp tells you what the process could do, and Cpk tells you what it does.
Cp, Cpk, Pp and Ppk: what separates them
The difference is the standard deviation. Cp and Cpk use short-term, within-subgroup variation, while Pp and Ppk use overall, long-term variation across all the data. The formulas are otherwise identical.
Short-term and long-term variation
| Index | Variation used | What it describes |
|---|---|---|
| Cp, Cpk | Within subgroups | Potential capability of a stable process |
| Pp, Ppk | All data combined | Actual performance over the period studied |
Within-subgroup sigma is usually estimated from a control chart, for example with the average range divided by a constant. Overall sigma is the plain standard deviation of every measurement.
What a gap between Cpk and Ppk tells you
If Ppk is clearly lower than Cpk, the process drifts or shifts between subgroups. Tool wear, shift changes, and material lots are the usual causes. The short-term spread is fine, but something moves the mean over time.
For a new process or a first customer approval with limited data, report Ppk. For a stable process you monitor continuously, report Cpk and track Ppk beside it.
A wide gap between Cpk and Ppk means the process is unstable, not just wide.
How to run a capability study that holds up
A capability study holds up when you confirm the process is stable and the measurement system is sound before you calculate anything. A neat index from bad data is worse than no index.
A step-by-step checklist
- Pick one characteristic with a defined spec limit, such as a diameter, fill weight, or cycle time.
- Validate the measurement system with a gauge R&R study. Measurement error inflates your measured variation.
- Collect data under normal conditions. Gather at least 30 values and 100 or more where you can, because small samples make the index unreliable.
- Check stability on a control chart. If points signal special causes, fix those first.
- Check normality. If the data are clearly skewed, use a transformation or a non-normal capability method.
- Calculate Cp, Cpk, Pp, and Ppk, and compare them to the customer’s requirement.
- Act on the pattern. Reduce variation, re-center, or keep monitoring.
Where capability fits in DMAIC
In a DMAIC project, you run a capability study in the Measure phase to set the baseline. You run it again in the Control phase to prove the improvement held. Without the first number, you cannot show what changed.
Our Six Sigma Online Training covers process capability alongside DMAIC, Pareto analysis, and SIPOC. Our Green Belt course goes further into the statistical techniques behind the Measure phase.
Run the capability study twice, once to set the baseline and once to prove the fix.
Putting the definition to work
Process capability compares what your process naturally does to what the customer allows. Cp shows the potential, Cpk shows the current result including centering, and Pp and Ppk show how the process behaved over the whole period. Treat 1.33 as a common floor, check stability and measurement quality first, and let the pattern of the indices tell you whether to cut variation or re-center.
If you want help running a capability study on your own process, or training your team to do it, contact Lean Six Sigma Experts to talk it through.