Process capability analysis compares how much a process naturally varies with how much variation the specification allows. You collect measurements from a stable process, estimate its mean and spread, and express the fit against the upper and lower specification limits as an index, usually Cp and Cpk. If the index is high enough, the process can hold the tolerance. If it is not, you know whether the problem is spread, centering, or both.
This guide covers what a capability study measures, the conditions that must be true before you run one, the formulas with a worked example, the difference between capability and performance indices, and how to turn the numbers into action on the shop floor.
TL;DR
- Process capability analysis compares a process's inherent variation with its specification limits. Cp shows spread against tolerance. Cpk adds centering.
- Check stability first. Capability describes a process in statistical control, and indices from an unstable process do not predict future output.
- Cp = (USL − LSL) / 6σ. Cpk = the smaller of (USL − μ) / 3σ and (μ − LSL) / 3σ.
- Cp and Cpk use within-process variation. Pp and Ppk include the extra variation from special causes, so report them under their own names.
- An index is an estimate. Sample size and confidence intervals decide how much weight a single number deserves.
Table of Contents
- What a process capability study measures
- Capability versus stability
- Conditions to meet before you collect data
- Calculating Cp and Cpk
- How to read the numbers
- Cp, Cpk, Pp and Ppk: which one are you reporting?
- Running a capability study step by step
- Using capability results to improve the process
- Our perspective: capability data is only as good as its traceability
- Where QA-Report fits
- FAQ
- Sources
What a process capability study measures
A capability study answers one question: can this process produce parts inside the tolerance, consistently? ASQ describes process capability analysis as the statistical comparison of a process's inherent variability with its specification limits. For continuous data, the comparison is usually summarized with Cp and Cpk.
The study does not tell you whether a particular lot passed inspection. Inspection looks at the parts you made. Capability looks at the process that makes them and predicts how it will behave. A lot can pass 100% inspection from a process that barely holds tolerance, and you would not know how close you were to scrapping parts until the next shift drifted.
That is why customers in aerospace, automotive and medical device work ask for capability data alongside dimensional results. It is evidence that conformance is repeatable, not accidental. If you submit PPAP packages, our practical guide to PPAP in manufacturing explains where capability evidence fits. The specific minimums are set by your customer, so confirm them in the customer-specific requirements.
Capability versus stability
These two ideas are often mixed up, and mixing them produces misleading numbers.
- Stability (statistical control) asks whether the process behaves predictably, with no detectable special-cause patterns, shifts or trends.
- Capability asks whether the spread of that controlled process fits within the specification.
ASTM E2281 defines process capability as the natural or inherent behavior of a stable process operating in statistical control, and it says control should be evaluated before capability. In practice, that means you plot a control chart first. If the chart shows points outside limits, runs, or trends, you fix those causes before you calculate an index you intend to rely on.
Think of it as numbering the answers before you have the questions. A Cpk computed on an unstable process looks like an answer, but it has nothing solid behind it.
Conditions to meet before you collect data
The formulas are simple. The validity of the result depends on the setup.
- Define the characteristic. Pick one dimension or feature from the drawing, with its nominal and tolerance limits. Capability is calculated per characteristic, not per part.
- Confirm the measurement system. If gauge variation consumes a large share of the tolerance, your "process" spread is partly measurement noise. Verify the gauge or CMM routine first.
- Sample from a stable process. ASQ states that sampling from a stable system is essential for meaningful estimates of future performance.
- Check the distribution. NIST notes that Cp, Cpk and Cpm assume normally distributed data. ASQ warns that Cp and Cpk are highly sensitive to this assumption.
- Collect enough data. NIST describes about 50 independent observations as a general indication of a sufficiently large sample for many capability-index estimates.
What if the data are not normal?
Some characteristics are naturally skewed or bounded. Flatness, runout, position and surface finish cannot go below zero, so their distributions are rarely symmetric. ASQ says that for stable but non-normal data you can transform the data or use an alternative distribution such as Weibull or lognormal. Do not feed skewed data into the normal formula and report the result as if nothing were wrong.
Independent observations
Fifty parts measured in sequence from one setup, one operator and one tool are not the same as fifty independent observations of the process over time. Decide in advance how you will sample (consecutive pieces for short-term capability, subgroups over days or tool changes for longer-term views) and write it in the study plan, so a reviewer can see what the number represents.
Calculating Cp and Cpk
The indices rest on four quantities: the process mean μ, the standard deviation σ, the lower specification limit LSL and the upper specification limit USL. In a real study you replace μ and σ with the sample mean and sample standard deviation, as NIST's handbook describes.
- Cp = (USL − LSL) / (6σ)
- Cpk = min[(USL − μ) / (3σ), (μ − LSL) / (3σ)]
Cp compares the width of the tolerance with the width of the process (six standard deviations). It ignores where the process is centered. Cpk measures the distance from the mean to the nearer limit, in units of three standard deviations, so it penalizes an off-center process.
A worked example
This example is illustrative, not real production data. A bore has a specification of 10.00 mm ± 0.05 mm, so LSL = 9.95 and USL = 10.05. From a stable sample, the mean is 10.01 mm and the standard deviation is 0.012 mm.
| Quantity | Calculation | Result |
|---|---|---|
| Tolerance width | 10.05 − 9.95 | 0.10 mm |
| Process spread (6σ) | 6 × 0.012 | 0.072 mm |
| Cp | 0.10 / 0.072 | 1.39 |
| Upper side | (10.05 − 10.01) / (3 × 0.012) | 1.11 |
| Lower side | (10.01 − 9.95) / (3 × 0.012) | 1.67 |
| Cpk | smaller of the two sides | 1.11 |
The spread is comfortably narrower than the tolerance, so Cp looks strong at 1.39. But the mean sits 0.01 mm above nominal, closer to the upper limit, and Cpk falls to 1.11. The gap between Cp and Cpk is the diagnosis: this process has a centering problem, not a spread problem. An offset correction on the machine would raise Cpk toward Cp without any investment in a tighter process.
How to read the numbers
NIST's guidance on assessing process capability says a process is capable if virtually all possible values fall within the specification limits, and that a Cp above 1.0 means the specifications cover almost all process observations. It also explains that Cpk is lower than Cp whenever the distribution is not centered between the limits.
A useful reading pattern:
- Cp and Cpk both high and close together: spread is small and the process is centered. Keep monitoring.
- Cp high, Cpk much lower: the process is precise but off target. Adjust the mean.
- Cp low, Cpk low: the process is too variable for the tolerance. Reduce variation, or review whether the tolerance is realistic.
- Cpk below 1.0 on a stable process: expect a meaningful share of parts outside the limits.
You will often hear a Cpk of 1.33 quoted as a pass mark. That is a customer or industry requirement, not a law of statistics, and different customers set different minimums for new and ongoing production. Use the number written in your contract, drawing notes or customer-specific requirements, not a number from a forum thread.
Treat the index as an estimate
A Cpk calculated from 30 parts is a statistic, not the process's true capability. ASQ recommends considering confidence intervals because capability indices are point estimates. A Cpk of 1.40 from a small sample may have a lower confidence bound under 1.0. Report the sample size beside every index, and when a decision rides on the number, collect more data or show the interval.
Cp, Cpk, Pp and Ppk: which one are you reporting?
ASTM E2281 identifies Cp and Cpk as capability indices and Pp and Ppk as performance indices. The performance indices use a variability estimate that includes additional components due to special causes. The standard's scope covers all four normal-distribution indices, attribute-data methods, and further measures such as Cpm and rolled throughput yield.
| Index | What it describes | Variation used |
|---|---|---|
| Cp | Spread against tolerance, ignoring centering | Inherent, stable-process variation |
| Cpk | Spread and centering against the nearer limit | Inherent, stable-process variation |
| Pp | Spread against tolerance over the observed period | Overall variation, including special causes |
| Ppk | Spread and centering over the observed period | Overall variation, including special causes |
In plain terms: Cp and Cpk say what the process can do when it is running as designed. Pp and Ppk say what it actually did over the data you collected, including tool changes, material lots and shifts. A big gap between Cpk and Ppk means special causes are inflating your variation, which is a stability problem to chase before any capability target. We cover how to present both in Cpk vs Ppk: what quality engineers need to report.
Running a capability study step by step
- Choose the characteristic and record the drawing revision, nominal, LSL and USL.
- Verify the measurement system for that characteristic.
- Write the sampling plan: subgroup size, frequency, number of parts, and which sources of variation (operators, tools, lots) the sample should cover.
- Collect the measurements, keeping part or serial numbers and time order so traceability stays intact.
- Plot a control chart and look for special causes. Resolve them and recollect if needed.
- Test the distribution. If it is non-normal, transform the data or fit a suitable distribution before calculating indices.
- Calculate Cp and Cpk, and Pp and Ppk where the contract asks for them, with the sample size.
- Interpret the result against the required minimum and decide on an action: continue, recenter, reduce variation, or revisit the tolerance with design engineering.
- File the study with the inspection records, so an auditor can follow the chain from drawing to measurement to index.
Step 4 is where manual workflows break down. Measurements pasted between CMM output, spreadsheets and PDF reports lose the link between a result and its drawing characteristic. When that link breaks, the capability number has no defensible origin.
Using capability results to improve the process
ASTM presents capability indices as aids for continuous improvement, for comparing products and processes, and for identifying management actions to reduce common-cause variation. The point is to act on them. A practical sequence:
- Rank characteristics by Cpk and start with the lowest. Fixing one dimension at 0.9 usually returns more than polishing one at 1.8.
- Compare Cp with Cpk to decide between a recentering action and a variation-reduction project.
- Feed rejected and reworked quantities back to the process owner by operation, not just by part number. Our guide to quality control in manufacturing covers how to stop rework from hiding the real cause.
- Re-run the study after each change, with the same plan, so before and after are comparable.
- Keep capability in the wider quality system. Our manufacturing QA guide shows how capability data connects to inspection planning and corrective action.
Our perspective: capability data is only as good as its traceability
We build inspection software for machine shops and quality teams in aerospace, automotive and medical device production, and the pattern we see most is not bad statistics. It is broken lineage. The Cpk in the report cannot be tied back to a ballooned characteristic on a specific drawing revision, measured on a specific part from a specific batch. When a customer or auditor asks where the number came from, the team spends days rebuilding the answer from spreadsheets.
Our view is that the capability calculation should be the last, easy step in a chain that is already clean. Balloon the drawing once. Link every balloon to its measured result. Import the CMM data rather than retyping it. Flag out-of-tolerance values at the moment of entry. Keep batch and serial tracking attached to each result. When those steps are systematic, the statistical summary is a by-product, not a project.
The second thing we would tell any quality manager: report which index you are quoting, how many parts it rests on, and what sampling plan produced it. A Cpk without that context invites an argument. A Cpk with it ends one.
— Michael Chen
Where QA-Report fits
QA-Report is a cloud-based inspection and reporting platform. It links ballooned drawing dimensions to measured results, flags out-of-tolerance deviations, imports CMM data, and produces statistical summaries and PDF reports for FAI, dimensional and PPAP work. Batch and serial tracking keeps each result tied to the parts it came from, which is the foundation a capability study needs.
You can start with the free drawing ballooning tool, then compare plans on the pricing page: Free is $0 per month, Basic is $49.99 per month and PRO is $149.99 per month. On-Premise and Enterprise Solutions are available for organizations with data confidentiality or scale requirements, with pricing on request. If your capability evidence feeds customer submissions, see our overview of APQP and PPAP software.
FAQ
What is a capable process Cpk?
A process is capable when virtually all of its output falls inside the specification limits. For a stable, roughly normal process, a higher Cpk means more room between the process spread and the nearer limit. The minimum acceptable value is set by your customer or internal standard, so check the requirement for each characteristic.
How many parts do I need for a capability study?
NIST gives about 50 independent observations as a general indication of a large enough sample for many capability-index estimates. Smaller samples can be used, but the index becomes less certain, so quote the sample size and consider a confidence interval. Sampling across tool changes and material lots gives a more honest picture than 50 consecutive parts.
What is the difference between process capability and process performance?
Capability (Cp, Cpk) describes the inherent variation of a stable process. Performance (Pp, Ppk) uses the overall variation seen in the data, including special causes. If Ppk is well below Cpk, the process is being disturbed by something outside its normal behavior.
Can I run a capability analysis on non-normal data?
Yes, but not with the standard normal formulas applied blindly. ASQ says stable non-normal data can be transformed, or analyzed with an alternative distribution such as Weibull or lognormal. Document the method you chose in the study report.
Is a process capability study the same as an inspection report?
No. An inspection report records measured values on specific parts. A capability study uses many such measurements to estimate how the process will behave. Good inspection records make the study possible, because the study depends on traceable, correctly mapped measurements.
Sources
- ASQ: What is Process Capability? Capability Estimates and Studies
- NIST/SEMATECH e-Handbook: 6.1.6. What is Process Capability?
- NIST/SEMATECH e-Handbook: 3.4.6. Assessing Process Capability
- ASTM E2281: Standard Practice for Process Capability and Performance Measurement