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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.

5 min readBeginner
Cpk = -0.42

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 )
When the process mean crosses a spec limit, the numerator goes negative -- and so does Cpk.

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
mm
Frequency
Cpk
0.90
Cpu (USL)
0.91
Cpl (LSL)
0.90
Process is capable and centered
The mean is centered between LSL and USL. Both numerators in the Cpk formula are positive. The process fits well within spec.

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
mm
Frequency
Cpk
0.18
Cpu (USL)
0.18
Cpl (LSL)
1.62
Process is NOT capable
The mean (25.08) is close to the USL (25.10). The numerator (USL - Mean = 0.02) is tiny. Cpk dropped even though the XmR chart shows no out-of-control signals. This is the classic trap: a process can be STABLE but NOT CAPABLE.
Key Insight

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
mm
Frequency
Cpk
-0.32
Cpu (USL)
-0.32
Cpl (LSL)
3.38
Process mean is OUTSIDE specification!
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 = -0.32
The mean has crossed PAST the USL. Now (USL - Mean) is negative, making Cpu negative. Since Cpk = min(Cpl, Cpu), the Cpk is negative. MORE THAN HALF of all parts are out of spec.

What 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

Tool wear

Gradual drift that wasn't caught by SPC monitoring

Wrong setup

Operator loaded incorrect program or offset

Material change

New lot has different properties than expected

Measurement error

Gage out of calibration or wrong gage used

Spec error

Wrong specification limits entered in the system

What To Do When You See Negative Cpk

  1. Stop production -- if Cpk is deeply negative (e.g., below -0.5)
  2. Verify the data -- are the spec limits correct? Is the gage calibrated?
  3. Check the XmR chart -- did you see a shift? When did the drift start?
  4. Run a root cause analysis -- use a structured tool to find the root cause Fishbone | 5 Whys
  5. Adjust the process -- re-center, replace tool, correct offset
  6. Re-measure -- confirm Cpk is back above 1.33
  7. Document -- the corrective action for future reference CAPA Tool

Try It Yourself

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