Can Cpk Be Negative? Yes -- Here's What It Means
Interactive visual explanation of how Cpk can be negative. Learn what it means when your process mean drifts outside spec limits, with live XmR charts and histograms.
Yes. It means your process average has drifted OUTSIDE the specification limits.
Quick Refresher: What Is Cpk?
Cpk measures how far your process center is from the nearest specification limit, relative to the process spread. It uses the minimum of the upper and lower capability indices.
Cpk = min( (USL - Mean) / 3σ, (Mean - LSL) / 3σ )Cpk 0.90 A Process That's On Target
This bore diameter process is centered at 25.00 mm with spec limits LSL = 24.90 and USL = 25.10. The process is stable and well within spec.
XmR Control Chart
Distribution
Cpk 0.18 Drifting Toward the Spec Limit
Same process, but the mean has drifted to 25.08 mm -- close to the USL of 25.10. The XmR chart may still show statistical control, but capability has dropped sharply.
XmR Control Chart
Distribution
A stable XmR chart does NOT mean the process is capable. Stability means the process is predictable. Capability means it meets spec. You need BOTH.
Cpk -0.32 The Negative Cpk -- Mean Outside Spec!
Now the process mean has crossed past the USL to 25.12 mm. The control chart may still look stable (control limits are based on process variation, not spec limits), but the capability index has gone NEGATIVE.
XmR Control Chart
Distribution
Step-by-Step Calculation
Cpu = (USL - Mean) / (3 x sigma)
Cpu = (25.10 - 25.12) / (3 x 0.016)
Cpu = -0.02 / 0.048
Cpu = -0.32What Does Negative Cpk Mean In Practice?
| Cpk Range | What It Means | Action |
|---|---|---|
| > 1.33 | Process is capable and centered | Monitor with SPC |
| 1.00 - 1.33 | Marginally capable | Investigate, reduce variation |
| 0 - 1.00 | Not capable, but mean is within spec | Reduce variation and/or re-center |
| < 0 | Mean is OUTSIDE spec limits | STOP -- immediate correction needed |
- If Cpk is less than 0, your average product does not meet the specification
- More than 50% of your production is out of spec
- This is not a statistical subtlety -- it's a production emergency
Common Causes of Negative Cpk
Gradual drift that wasn't caught by SPC monitoring
Operator loaded incorrect program or offset
New lot has different properties than expected
Gage out of calibration or wrong gage used
Wrong specification limits entered in the system
What To Do When You See Negative Cpk
- Stop production -- if Cpk is deeply negative (e.g., below -0.5)
- Verify the data -- are the spec limits correct? Is the gage calibrated?
- Check the XmR chart -- did you see a shift? When did the drift start?
- Run a root cause analysis -- use a structured tool to find the root cause Fishbone | 5 Whys
- Adjust the process -- re-center, replace tool, correct offset
- Re-measure -- confirm Cpk is back above 1.33
- Document -- the corrective action for future reference CAPA Tool
Try It Yourself
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