Learn · updated 2026-10-22
How many parts do you need for a Cpk study?
A Cpk calculated from a sample is an estimate. With few parts it can be far from the process's real capability, so the useful question isn't “what is our Cpk?” but “what range could it really be, and is that good enough?”.
The short answer. The usual approximation (Bissell, 1990) for the 95% confidence interval on Cpk from n parts is:
Cpk ± 1.96 × √( 1/(9n) + Cpk²/(2(n − 1)) )
Halving the width takes about four times the parts. For Cpk 1.33: about 97 parts to know it within ±0.20, and 384 to know it within ±0.10.
How wide is the range?
Two-sided 95% intervals from the formula above:
| Parts (n) | Cpk 1.00 | Cpk 1.33 | Cpk 1.67 |
|---|---|---|---|
| 10 | 0.49 to 1.51 | 0.68 to 1.98 | 0.87 to 2.47 |
| 30 | 0.72 to 1.28 | 0.97 to 1.69 | 1.22 to 2.12 |
| 50 | 0.78 to 1.22 | 1.05 to 1.61 | 1.33 to 2.01 |
| 100 | 0.85 to 1.15 | 1.13 to 1.53 | 1.43 to 1.91 |
| 150 | 0.87 to 1.13 | 1.17 to 1.49 | 1.47 to 1.87 |
| 300 | 0.91 to 1.09 | 1.22 to 1.44 | 1.53 to 1.81 |
So the common “30 parts” study at Cpk 1.33 gives a range of 0.97 to 1.69: the same data fits a process that barely clears 1.0 and one that is comfortably capable. Quality Magazine's published table gives the same widths (Cpk 1.2: ±0.15 at 150 parts, ±0.10 at 300, ±0.08 at 450, ±0.06 at 1,000), and LimitLine's numbers match it.
What can you claim?
For a customer requirement like “Cpk ≥ 1.33”, the honest number is the one-sided lower bound: Cpk − 1.645 × √( 1/(9n) + Cpk²/(2(n − 1)) ). A measured 1.33 from 30 parts lets you claim at least 1.03 with 95% confidence.
To show Cpk ≥ 1.33 you need margin above it. If the process really is at 1.67, about 37 parts will show it; at 1.50, about 117. If the process is at 1.33 or below, no number of parts will show 1.33: that needs a better process, not more data.
Before the sample size matters
- The process must be stable. Plot a control chart first: with special causes there is no single Cpk to estimate.
- Spread the parts out. 50 parts from one hour show less variation than the process really has. Sample across runs, shifts, lots and operators.
- The formula assumes roughly normal data. For skewed data, use a non-normal capability method (Capability+ in LimitLine).
Sources
- A. F. Bissell (1990), “How Reliable Is Your Capability Index?”, Applied Statistics 39(3), 331–340
- Quality Magazine, “Adding confidence to your capability estimates” (published table of Cpk confidence limits)
- NIST/SEMATECH e-Handbook of Statistical Methods, §6.1.6 What is Process Capability?