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Process Capability Index Calculator

Free process capability calculator. Compute Cp, Cpk, Pp, Ppk, Cpm. Six Sigma quality metrics, DPMO,

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

Cpk
SIX SIGMAQuality Control

Process Capability — Cp, Cpk, Pp, Ppk, Cpm, DPMO & Six Sigma Metrics

Compute capability indices from raw data or summary stats. Process visualization, Cpk gauge, DPMO, yield %. Step-by-step breakdown with interactive charts.

Z-Score →Control Limits →

Real-World Scenarios — Click to Load

Specification Limits & Data

process_capability.sh
CALCULATED
$ process_capability --usl=10.05 --lsl=9.95
Cpk
0.8296
Cp
0.8825
Ppk
0.8296
DPMO
12822.4
Pp
0.8825
Cpm
0.8716
Sigma Level
2.49
Yield %
98.72%
Interpretation: Incapable — process spread exceeds spec limits. Immediate improvement required.
Share:
Process Capability Result
Cpk = 0.830
Cp: 0.883DPMO: 12822.4Yield: 98.72%
numbervibe.com/calculators/statistics/process-capability-index-calculator

Process Distribution vs Spec Limits

LSL: 9.95Mean: 10.003USL: 10.05

Capability Indices Comparison

Target: Cpk ≥ 1.33 (capable), ≥ 2.0 (Six Sigma)

Cpk Gauge

Cpk = 0.830
Target: ≥ 1.33 capable, ≥ 2.0 Six Sigma

Calculation Breakdown

COMPUTATION
Cp (Potential)
0.8825
Cp = (USL − LSL) / (6σ) = (10.05 − 9.95) / (6 × 0.0189)
Cpu
0.8296
(USL − μ) / (3σ) = (10.05 − 10.0030) / (3 × 0.0189)
Cpl
0.9355
(μ − LSL) / (3σ) = (10.0030 − 9.95) / (3 × 0.0189)
RESULT
Cpk (Actual)
0.8296
\text{min}( ext{Cpu}, ext{Cpl})
PERFORMANCE
Pp
0.8825
(USL − LSL) / (6s)
Ppk
0.8296
\text{min}( ext{Ppu}, ext{Ppl})
Cpm (Taguchi)
0.8716
Cp / √(1 + ((μ−T)/σ)²)
Sigma Level
2.49
3 imes ext{Cpk}
DPMO
12822.4
1,000,000 imes (1 - Φ(3 imes ext{Cpk}))
Yield %
98.72%
Φ(3 imes ext{Cpk}) imes 100

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • • Cp measures potential capability — how well the process spread fits within spec limits. Does not consider centering.
  • • Cpk measures actual capability — accounts for both spread and centering. min((USL−μ)/(3σ), (μ−LSL)/(3σ)).
  • • Pp, Ppk use overall standard deviation (long-term) vs within-subgroup σ (short-term) for Cp, Cpk.
  • • Cpm (Taguchi) penalizes deviation from target T. Useful when being on-target matters more than being within spec.
  • • DPMO = Defects Per Million Opportunities. Six Sigma targets ~3.4 DPMO (Cpk ≥ 2.0).
  • • Cpk < 1.0: incapable | 1.0–1.33: marginal | ≥1.33: capable | ≥2.0: Six Sigma.

Did You Know?

🏭Motorola coined "Six Sigma" in 1986 — achieving Cpk ≥ 2.0 means only 3.4 defects per million.Source: Motorola University
🚗Automotive OEMs often require Cpk ≥ 1.33 for critical dimensions. Some require 1.67 or higher.Source: AIAG SPC Manual
💊FDA expects process capability documentation for pharmaceutical manufacturing — Cpk is a key metric.Source: FDA Guidance
📊When Cp = Cpk, the process is perfectly centered on the target. Cpk can never exceed Cp.Source: NIST Handbook
🎯Cpm was developed by Taguchi to emphasize "loss" when deviating from target, not just being within spec.Source: Taguchi, 1986
📈Pp is often lower than Cp when the process has instability over time — long-term variation is higher.Source: ASQ

Expert Tips

Cp vs Cpk

Cp assumes perfect centering. Cpk accounts for off-centering. A process can have Cp > 1 but Cpk < 1 if the mean is shifted. Always report Cpk.

Improving Cpk

Reduce variation (tighter control), center the process on target, or widen spec limits if justified. Focus on the limiting side (upper or lower).

Non-Normal Data

Cp and Cpk assume normality. For non-normal data, consider transformation or non-parametric capability indices. Always check distribution first.

Control Before Capability

Establish process stability with control charts (X̄-R, X̄-S) before capability analysis. Unstable processes make Cpk meaningless.

Cpk Interpretation Table

Cpk RangeInterpretation
< 1.0Incapable — process exceeds spec limits
1.0 – 1.33Barely capable — marginal
1.33 – 1.67Capable — meets requirements
1.67 – 2.0Highly capable
≥ 2.0Six Sigma capable — world-class

Formulas at a Glance

Cp = (USL − LSL) / (6σ)

Cpk = min((USL−μ)/(3σ), (μ−LSL)/(3σ))

Pp = (USL − LSL) / (6s)    Ppk = min((USL−x̄)/(3s), (x̄−LSL)/(3s))

Cpm = Cp / √(1 + ((μ−T)/σ)²)

DPMO = 1,000,000 × (1 − Φ(3×Cpk))

Yield % = Φ(3×Cpk) × 100

Industry Use Cases

Automotive:Bolt torque, part dimensions, paint thickness. Cpk ≥ 1.33 often required by OEMs.
Pharmaceutical:Fill weight, tablet hardness, dissolution. FDA expects process capability documentation.
Electronics:Resistor values, trace widths, solder paste volume. Tight specs drive high Cpk requirements.
Food & Beverage:Package weight, pH, moisture content. Process capability ensures consistent quality.
Medical Devices:Implant dimensions, tolerances. Regulatory requirements for capability studies.

Frequently Asked Questions

What is a good Cpk value?

Cpk ≥ 1.33 is generally considered capable. Cpk ≥ 2.0 is Six Sigma level. Cpk < 1.0 indicates the process is incapable of meeting specifications.

Why is Cpk always ≤ Cp?

Cpk accounts for centering. When the process is perfectly centered, Cpk = Cp. When off-center, Cpk is smaller. Cpk can never exceed Cp.

When to use Pp vs Cp?

Use Cp for short-term capability (within-subgroup variation). Use Pp for long-term performance (overall variation including shifts and trends).

What does DPMO mean?

Defects Per Million Opportunities. DPMO = 1,000,000 × (1 − Φ(3×Cpk)). Lower is better; Six Sigma aims for ~3.4 DPMO.

What if my process is not normally distributed?

Cp and Cpk assume normality. For non-normal data, consider transformation or non-parametric capability indices. Always check your data distribution first.

How do I improve Cpk?

Reduce variation (tighter process control), center the process on target, or widen spec limits if justified. Focus on the limiting side indicated by Cpk.

What is Cpm used for?

Cpm (Taguchi) penalizes deviation from target. Use when being on-target matters as much as being within spec — e.g., fill volume where overfill is costly.

Pp vs Cp — same formula?

Same formula structure, but Cp uses within-subgroup σ (short-term), Pp uses overall s (long-term). Pp is often lower when process has instability.

Process Capability by the Numbers

1.33
Minimum capable Cpk
2.0
Six Sigma Cpk target
3.4
DPMO at Six Sigma
6
Sigma level at Cpk=2

Disclaimer: Process capability indices assume normally distributed data. For non-normal processes, consider transformation or non-parametric methods. This tool is for educational and professional reference. Verify results for critical quality decisions. Raw data mode uses sample standard deviation (n−1).

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