What is Cpk?
Cpk (process capability index) measures how well a process fits inside its specification limits, taking into account both the spread of the process and how well it is centered. It compares the distance from the process mean to the nearest spec limit with three standard deviations:
Cpk = min( (USL − μ) / 3σwithin , (μ − LSL) / 3σwithin )
A Cpk of 1.00 means the nearest spec limit sits exactly 3σ from the mean, so roughly 1,350 PPM fall outside on that side. Each 0.33 step adds one more sigma of margin.
Cp vs Cpk vs Pp vs Ppk
| Index | Sigma used | Considers centering? | Answers |
|---|---|---|---|
| Cp | within | No | Could the process fit if it were perfectly centered? |
| Cpk | within | Yes | How capable is the process in the short term? |
| Pp | overall | No | Potential performance including drift between subgroups |
| Ppk | overall | Yes | Actual long-term performance the customer sees |
Within sigma is estimated from short-term variation: the average moving range divided by d2 = 1.128 for individual values, or the average subgroup range divided by d2(n) for subgroups. Overall sigma is the ordinary sample standard deviation of all values. When Ppk is much lower than Cpk, the process is shifting over time — look at the control chart.
How to interpret Cpk
| Cpk | Expected PPM (centered, two-sided) | Typical judgement |
|---|---|---|
| 0.67 | 44,400 | Not capable |
| 1.00 | 2,700 | Not capable / marginal |
| 1.33 | 66 | Capable — common minimum |
| 1.67 | 0.54 | Excellent — common for new or safety-critical processes |
| 2.00 | 0.002 | Six Sigma level |
Control charts and Nelson rules
Capability indices are only meaningful when the process is stable. This tool draws an I-MR chart for individual values or an X̄-R chart for subgroups of 2–10, and checks Nelson rules 1–4: a point beyond 3σ, nine points on one side of the center line, six points trending, and fourteen points alternating.
FAQ
How many data points do I need?
At least 25 subgroups or 100 individual values is the usual recommendation. Sample size matters: for a true Cpk of 1.33, the 95% confidence interval is about ±0.36 with 30 values and about ±0.20 with 100 values.
Is my data uploaded anywhere?
No. All calculations run in JavaScript inside your browser. Nothing is sent to a server, so it is safe for confidential production data.
Why are my Cpk and Ppk different?
Cpk uses within-subgroup variation; Ppk uses total variation. A gap means there is extra variation between subgroups — drift, shifts, tool wear or batch effects.
Does it handle one-sided specifications?
Yes. Enter only USL or only LSL. Cp and Pp are not defined in that case, and Cpk equals the one-sided index (Cpu or Cpl).