Process Capability Calculator | Cp, Cpk, Ppk & Six Sigma Level
Calculate process capability indices Cp, Cpk, Pp, and Ppk from specification limits and process statistics. Computes the Six Sigma level, DPMO (defects per million opportunities), control chart limits (UCL, LCL), and the probability of a defect. Classifies the process as world-class, capable, marginal, or inadequate.
What Is the Process Capability Calculator | Cp, Cpk, Ppk & Six Sigma Level?
Process capability indices measure how well a manufacturing or business process fits within its specification limits. Cp compares the specification width (USL − LSL) to the natural process spread (6σ) — measuring potential capability assuming perfect centering. Cpk adjusts for actual centering by taking the smaller of Cpu = (USL − μ)/3σ and Cpl = (μ − LSL)/3σ, so Cpk ≤ Cp always. A Cpk of 1.0 means the ±3σ control limits just touch the specification limits (0.27% defect rate). Cpk ≥ 1.33 is the industry standard for capable, while Six Sigma processes require Cpk ≥ 2.0 (3.4 DPMO). Pp and Ppk are performance indices using the same formulas with overall process variation.
Formula
Cp = (USL − LSL) / 6σ | Cpk = min[(USL − μ) / 3σ, (μ − LSL) / 3σ]
How to Use
- 1
Enter USL (upper specification limit) — the maximum acceptable value
- 2
Enter LSL (lower specification limit) — the minimum acceptable value
- 3
Enter the process mean μ (average output of the process)
- 4
Enter the process standard deviation σ (within-subgroup short-term variation)
- 5
Click an example preset to see a named capability scenario
- 6
Click "Calculate Capability" — review Cp, Cpk, DPMO, Six Sigma level, and process classification
- 7
Check the spec-limit diagram at the bottom to see whether UCL and LCL fall within spec
Enter the upper and lower specification limits, process mean, and standard deviation, then click Calculate Capability.
Example Calculation
USL=110, LSL=90, μ=104, σ=2 (off-center process). Spec width=20, 6σ=12. Cp=20/12=1.67 (excellent potential). But Cpu=(110-104)/(3×2)=1.0 and Cpl=(104-90)/(3×2)=2.33, so Cpk=min(1.0,2.33)=1.0 (marginally capable). The process is off-center toward USL, wasting most of its potential capability.
Understanding Process Capability | Cp, Cpk, Ppk & Six Sigma Level
Cpk Classification Reference
| Cpk range | Classification | DPMO (approx.) | Sigma level | Action |
|---|---|---|---|---|
| ≥ 2.00 | World-class (Six Sigma) | < 3.4 | 6σ | Maintain current process |
| ≥ 1.67 | Excellent | < 64 | 5σ | Monitor for drift |
| ≥ 1.33 | Capable | < 1,350 | 4σ | Routine monitoring |
| ≥ 1.00 | Marginally capable | < 2,700 | 3σ | Improvement recommended |
| ≥ 0.67 | Incapable | < 66,800 | 3σ | Urgent process improvement |
| < 0.67 | Highly incapable | > 66,800 | <3σ | Immediate corrective action |
Capability Index Formulas
| Index | Formula | Measures | Key point |
|---|---|---|---|
| Cp | (USL − LSL) / 6σ | Potential capability | Ignores process centering |
| Cpu | (USL − μ) / 3σ | Upper one-sided index | How far μ is from USL |
| Cpl | (μ − LSL) / 3σ | Lower one-sided index | How far μ is from LSL |
| Cpk | min(Cpu, Cpl) | Actual capability | Cpk ≤ Cp always |
| Pp | (USL − LSL) / 6σ_overall | Performance (long-term) | Uses total variation |
| Ppk | min(Ppu, Ppl) | Actual performance | Ppk ≤ Pp, Ppk ≤ Cpk |
Industry Applications
- ›Automotive manufacturing — suppliers are often required to demonstrate Cpk ≥ 1.67 (AIAG PPAP standard).
- ›Semiconductor fabrication — gate oxide thickness, doping concentration, and line width all require Six Sigma capability.
- ›Pharmaceutical production — FDA process validation requires demonstrated process capability for drug dosage and purity.
- ›Medical devices — ISO 13485 quality management systems use Cpk to monitor critical dimensions.
- ›Electronics assembly — solder joint heights, component placement accuracy tracked with Cpk control charts.
Frequently Asked Questions
What is the difference between Cp and Cpk?
Cp measures potential capability assuming perfect centering — it ignores where the mean is. Cpk measures actual capability including centering. A centered process has Cp = Cpk; any off-center shift makes Cpk < Cp.
What Cpk is needed for Six Sigma?
Six Sigma quality (3.4 DPMO) corresponds to Cpk ≈ 1.5 with the classic 1.5σ long-term shift assumption, or Cpk = 2.0 for a statically centered process with ±6σ fits within spec.
What is DPMO?
Defects Per Million Opportunities — the expected number of defective units per million produced, derived from the probability that a unit falls outside the specification limits using the normal distribution.
What are UCL and LCL?
Upper and Lower Control Limits are set at μ ± 3σ. They define the expected natural variation range (99.73% of data). They are not the same as spec limits — a capable process has UCL < USL and LCL > LSL.
What is the difference between Cpk and Ppk?
Cpk uses within-subgroup (short-term) variation σ̂_within; Ppk uses total (long-term) variation σ̂_total. When there is between-subgroup variation (process drift, batch effects), Ppk < Cpk, revealing a gap between short-term and long-term performance.
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