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Cpk Confidence Interval Calculator: How Many Samples Do You Need?

A Cpk is an estimate, and with a small sample it is a rough one. This calculator puts a confidence interval around your Cpk and tells you roughly how many parts you need before the lower bound clears the requirement. It is useful before a PPAP submission or a supplier capability review.

Your numbers

Observed Cpk

The Cpk calculated from your sample.

Sample size

parts

Number of individual measurements used.

Confidence level

Required Cpk

Customer or internal minimum, for example 1.33 or 1.67.

Your results

Lower confidence bound

1.189

Upper confidence bound

1.811

Standard error of Cpk

0.1587

Bissell approximation.

Interval half-width

0.311

Lower bound minus required Cpk

-0.141

Positive means the requirement is demonstrated at this confidence.

Approx. sample size to demonstrate requirement

166

0 means the observed Cpk is not above the requirement.

Uses a normal approximation for Cpk and assumes a stable, normally distributed process. Not a substitute for a customer specific acceptance rule.

Save results:

Confidence bounds as sample size grows

Sweeps Sample size from 10 to 300, holding your other inputs fixed.

Capability reporting from ERP data

Optional: we can outline how to feed Cpk with bounds from your inspection results.

Optional. The tool and every export work without this. No spam.

How to use it

Enter the Cpk from your study, the number of individual measurements it was based on, and the confidence level. Add your required Cpk to see whether the lower bound clears it. The last output estimates the sample size needed for the lower bound to reach the requirement if the true Cpk equals your observed figure. Use the chart to see how fast the interval narrows as n grows.

Use the number of individual readings, not subgroups
Choose 95 percent unless the customer specifies otherwise
Check the process is stable first, a control chart before capability

The method

The standard error uses the widely cited Bissell approximation: SE = sqrt(1/(9n) + Cpk^2 / (2(n-1))). The interval is Cpk plus or minus z times SE, with z of 1.645, 1.96 or 2.576 for 90, 95 and 99 percent. Exact intervals use a non-central chi-square distribution, but the approximation is accurate enough for planning when n is above about 30 and the data are roughly normal. The sample size output solves the lower-bound equation for n.

Worked example

With the defaults, a Cpk of 1.50 from 50 parts gives a standard error of about 0.17 and a 95 percent interval of roughly 1.17 to 1.83. The lower bound is below a 1.33 requirement even though the point estimate looks comfortable. The sample size output shows you need several times more parts to demonstrate 1.33 at that confidence. This is why a 30-piece capability study often looks better than the process really is.

Common mistakes

Teams quote a single Cpk without n. Others use subgroup counts instead of the number of measurements, which understates the uncertainty. Non-normal data, drifting means and mixed cavities or machines all make the interval optimistic. Treat the result as a minimum level of doubt, not the whole story. When the requirement is Cpk 1.67, the sample needed to prove it is large, which is why many customers specify a lot-by-lot approach instead.

Frequently Asked Questions

How many samples do I need for a reliable Cpk?

At least 30 for a rough estimate, and often 100 or more to demonstrate a requirement such as 1.33 with 95 percent confidence when your observed Cpk is only slightly above it. The calculator estimates this for your numbers.

Is the lower bound the number I should report?

Many customers accept the point estimate, but the lower confidence bound is the honest figure for decisions. If the lower bound clears the requirement you have strong evidence; if it does not, you have an estimate only.

Does this work for Ppk?

The same approximation is commonly used for Ppk, since both are computed from the same kind of data. For Ppk the long-term standard deviation is used and the interval will reflect that sample.

Why does the interval widen when Cpk is higher?

The second term in the standard error grows with Cpk squared, because a higher Cpk depends on a very small estimated sigma, and a small sample estimates sigma imprecisely.

If you want Cpk with confidence bounds computed straight from your ERP or QMS inspection results, we can scope a private, read-only report.

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