Process capability indices answer one question: does a stable process's normal spread of output actually fit inside the specification it is supposed to meet? Four numbers get reported — Cp, Cpk, Pp, and Ppk — and most of the confusion around them comes from not knowing that the four are answering two genuinely different questions, not four versions of the same one.
Capability indices only mean something once a control chart has shown the process is stable. Running a capability study on a process with unresolved special causes produces a number that doesn't describe any single, real process — it describes an average of at least two different processes tangled together.
Open the Process Capability Analyzer Read the SPC & Control Charts Guide
Why Process Capability Matters
Turns Spread Into a Decision
A control chart shows a process is stable. Capability turns that stability into an answer: will this process, as it runs today, produce parts that meet the print?
Separates Two Failure Modes
A capable process can still be poorly centered, and a well-centered process can still be too spread out. Cp and Cpk together tell you which problem you actually have.
Sets a Common Language With Customers
Automotive, aerospace, and medical device customers routinely require a minimum Cpk on critical characteristics before accepting a supplier's process.
Exposes Gaps Between "Should" and "Does"
Comparing Cpk to Ppk on the same data reveals how much of the process's real-world spread comes from shifts and drift that a short study never saw.
Core Terms
| Term | Meaning |
|---|---|
| USL / LSL | Upper and lower specification limits — the customer or drawing requirement, not a statistical calculation. |
| Within-subgroup sigma | An estimate of short-term, common-cause-only variation, calculated from subgroup ranges (R-bar/d2). Used for Cp and Cpk. |
| Overall sigma | The standard deviation of every individual data point in the study, capturing shifts and drift between subgroups as well as within them. Used for Pp and Ppk. |
| Cp | Potential capability: how wide the specification is relative to short-term process spread, ignoring centering. |
| Cpk | Actual short-term capability: Cp adjusted for how well the process is centered between the spec limits. |
| Pp / Ppk | The same two calculations, using overall sigma instead of within-subgroup sigma — long-term performance instead of short-term potential. |
Cp vs. Cpk vs. Pp vs. Ppk: The Real Difference
These four indices split along two independent lines: which sigma they use, and whether they account for centering. Knowing both lines is the entire trick to never confusing them again.
| Ignores centering | Accounts for centering | |
|---|---|---|
| Within-sigma (short-term) | Cp | Cpk |
| Overall sigma (long-term) | Pp | Ppk |
The Formulas
σwithin is estimated from subgroup data as R-bar / d2, using the same subgroup range data an X-bar/R chart already collects. σoverall is simply the standard deviation of every individual reading in the study, ignoring subgroup boundaries entirely.
| Subgroup size (n) | d2 |
|---|---|
| 2 | 1.128 |
| 3 | 1.693 |
| 4 | 2.059 |
| 5 | 2.326 |
| 6 | 2.534 |
| 7 | 2.704 |
| 8 | 2.847 |
| 9 | 2.970 |
| 10 | 3.078 |
The Process Capability Analyzer accepts either summary inputs (mean, within-sigma, overall-sigma) or raw subgroup data and runs all four indices directly, so the hand calculation below is worth doing once to see where the numbers actually come from.
Worked Example: Ridgeline Precision Machining, Continued
This continues the same bore-diameter process from the SPC & Control Charts worked example: a 25.000 mm target diameter with a print tolerance of ±0.030 mm, so USL = 25.030 mm and LSL = 24.970 mm. The X-bar/R chart confirmed the process is in control apart from the one investigated and corrected tool-wear event at subgroup 14, so a capability study is appropriate.
- Grand average X̄ = 25.002 mm, R-bar = 0.018 mm, subgroup size n = 5, so d2 = 2.326.
- σwithin = R-bar / d2 = 0.018 / 2.326 = 0.00774 mm.
- Cp = (25.030 − 24.970) / (6 × 0.00774) = 0.060 / 0.0464 = 1.29.
- Cpu = (25.030 − 25.002) / (3 × 0.00774) = 1.21. Cpl = (25.002 − 24.970) / (3 × 0.00774) = 1.38.
- Cpk = min(1.21, 1.38) = 1.21.
- The overall sigma across every individual reading (including the subgroup 14 excursion) is σoverall = 0.0091 mm, higher than σwithin because it captures that one real shift the within-subgroup estimate never sees.
- Pp = 0.060 / (6 × 0.0091) = 1.10. Ppu = 1.03, Ppl = 1.17, so Ppk = 1.03.
Cpk (1.21) is higher than Ppk (1.03) on the exact same process, and the gap is not a calculation error — it's the honest cost of the tool-wear event. Cpk describes what the process is capable of when nothing unusual happens; Ppk describes what actually happened, excursion included. Both numbers are correct at once, and reporting only Cpk to a customer would overstate what the process really delivered that week.
Interpreting the Numbers
| Cpk / Ppk | Interpretation |
|---|---|
| Below 1.00 | Not capable. The process's own spread does not reliably fit inside the specification. |
| 1.00 - 1.33 | Marginal. Meets spec on average but with little margin for drift. |
| 1.33 - 1.67 | Generally considered capable; the common minimum for many customer requirements. |
| Above 1.67 | Excellent; often the target for safety-critical or high-consequence characteristics. |
What to Do When Cpk Is Low
Check Centering First
Compare Cp to Cpk. If Cp is healthy and Cpk isn't, shift the process mean toward the middle of the tolerance before touching variation.
Reduce Variation Second
If Cp itself is low, centering won't fix it — the spread has to come down, usually through tighter process control, better tooling, or reduced input variation.
Verify the Measurement System
A high measurement-system contribution to observed variation makes a perfectly capable process look incapable. Check Gage R&R before chasing a process that may not be the real problem.
Confirm Stability Held
If new out-of-control points appear after the study, the capability number is already stale. Go back to the control chart before trusting the index.
Common Mistakes
Running Capability on an Unstable Process
A control chart with unresolved out-of-control points has no single distribution to summarize with one number.
Reporting Cpk When Ppk Was Asked For
Many customer requirements specifically call for Ppk to capture real long-term performance, not the more flattering short-term Cpk.
Assuming Normality Without Checking
All four formulas assume a normal distribution. Skewed data (common with one-sided characteristics like flatness or runout) needs a different capability approach entirely.
Too Few Data Points
A capability estimate from a handful of subgroups carries wide uncertainty even when the arithmetic is correct.
Quick Reference
Before Calculating
- Control chart confirms the process is stable.
- Measurement system has been verified (Gage R&R).
- Data has been checked for approximate normality.
- Specification limits are the real customer/drawing requirement, not a target.
Reporting
- State whether the figure is Cpk (short-term) or Ppk (long-term).
- Report Cp/Pp alongside Cpk/Ppk so centering problems are visible.
- Note the sample size and study duration the index is based on.
- Re-run the study after any confirmed, stabilized process change.
Sources and Further Reading
- Douglas C. Montgomery, Introduction to Statistical Quality Control.
- AIAG Statistical Process Control (SPC) Reference Manual.
- AIAG-VDA FMEA Handbook (for capability requirements in PPAP contexts).
- ASQ Certified Quality Engineer Body of Knowledge.