Process Capability Cp / Cpk Contract Specification Calculator

Check process capability before agreeing to delivery terms

A mean dimension inside a drawing’s limits does not show the spread of repeated production or how far the process is off center.
A supplier’s report and a customer’s contract may also refer to different specifications or estimation methods.
This worksheet helps small manufacturing business owners and quality staff compare the arithmetic before confirming a quotation or delivery conditions.

Enter two-sided limits, a verified mean and verified process standard deviation to calculate Cp, Cpk and headroom on both sides.
Optional contract targets and reported indices reveal the direction and size of differences.
Save a TXT worksheet with assumptions and evidence for a quality review before accepting rework or return conditions.

Use the same characteristic, period and units

Distinguish overall sample s from within-process σ

Raw measurement mode summarizes the mean and overall sample standard deviation s, using n−1 in the variance denominator.
Overall s may include changes across times or subgroups, so the tool does not silently treat it as within-process σ.
Ask the quality analyst how subgroups and the estimator were chosen.

Identical observations produce s=0, which does not establish zero future variation.
Review resolution, rounding and sampling.
Verified within σ must be positive; zero cannot produce an infinite capability index.

Cp, Cpk and specification headroom formulas

Cp compares specification width with process spread without directly accounting for the mean’s position.
Cpk uses the smaller headroom relative to three standard deviations.
Moving the mean toward one limit can therefore lower Cpk while Cp remains unchanged.
The center offset is the mean minus the midpoint of the two limits.

Lower headroom is μ−LSL; upper headroom is USL−μ.
A negative headroom means the mean is beyond that limit, and negative Cpk is preserved.
A mean exactly at a limit produces zero headroom and Cpk=0.
Indices are dimensionless; mean, headroom and deviations use the selected common unit.

Compare a report in five steps

1. Confirm both limits and units for the same characteristic in the current drawing and contract.
   Do not mix a revised specification with an older report.
   
2. Enter a verified mean and source sample count, or paste 2–10,000 raw measurements.
   Separate raw values with whitespace or semicolons and omit commas.
   
3. Select the deviation method.
   For verified within-process σ, enter the positive value and document the source; this tool does not estimate σ from subgroups.
   
4. Enter the agreed target and reported indices, then check only assumptions you have verified.
   Leave unresolved conditions unchecked for follow-up.
   
5. Review difference signs and both headrooms, then save the TXT worksheet.
   Editing an input clears the previous result, so recalculate before saving an updated worksheet.
   

Individual numeric fields accept signed decimals and correctly grouped thousands separators.
Commas are rejected in raw measurement lists to prevent ambiguity between separators and thousands grouping.
An invalid token rejects the list rather than silently discarding an observation.

Worked example: equal Cp, different Cpk

Use LSL 8, USL 20 and verified σ 2, consistent with the NIST example’s numbers.
All dimensions share a unit; these are arithmetic illustrations rather than recommended product dimensions or targets.
The table displays up to six decimal places.

Theoretical out-of-spec rates require verified assumptions

The secondary normal-tail estimate requires a verified normal model, stability, independent representative observations, a suitable measurement system, verified within σ and a method note.
The formula is Φ((LSL−μ)/σ)+Φ((μ−USL)/σ), adding both tails separately.
It does not assume that one Cpk value describes both tails equally, and applies no 1.5σ shift.

The centered mean 14 example gives about 2,699.796 ppm in total; mean 16 gives about 22,781.803 ppm.
These are model calculations, not measured shipment defect rates.
The numerical approximation has an absolute total error of about ≤0.15 ppm.
Very small results carry a precision warning and do not guarantee zero defects.

The observed out-of-spec count instead counts raw values strictly below LSL or above USL.
Values exactly on a limit are inside for this descriptive count.
Confirm contractual endpoint and measurement-uncertainty rules separately.
Observed counts cannot be recovered from summary input alone.

Use the results for improvement and renegotiation

• A large Cp/Cpk gap: review centering and collection periods.
  Before changing machine settings, inspect control charts and the actual measurement history for causes.
  
• A report difference: compare specification revisions, units, deviation estimators, overall versus subgroup variation, averaging scope and rounding.
  Establish comparable conditions before concluding that the other party made an error.
  
• A negative target difference: the calculated index is below the entered target.
  Review sampling uncertainty and contractual decision procedures before arranging additional measurements, improvement or revised terms.
  

Checkboxes record your independent review; they are not automated statistical tests.
Even with every condition checked, the result remains an arithmetic comparison under stated assumptions and calls for quality review.
Do not treat its status as shipment approval or product safety certification.

Record sampling and measurement limitations

Small samples create uncertainty in the estimated mean, deviation and indices.
The screen warns below 100 observations; reaching 100 does not guarantee adequate precision.
NIST discusses roughly 50 independent observations in general guidance and n≥100 for capability studies in another context.
Neither is a universal statutory contract minimum.

Pooling molds, machines or material lots, or counting repeat measurements of one part as independent products, changes the interpretation.
Review temperature, tool wear, shift changes, selection and rounding.
Nonnormal distributions, subgroup estimation, confidence intervals, one-sided limits and lot acceptance probabilities require separate analysis.
This tool does not replace statutory net-quantity inspection or MES investment analysis.

Frequently asked questions