Operations & Quality Engineering Lab

Process Capability (Cp, Cpk) Lab

Calculate Cp, Cpk, Pp, Ppk process capability indices, Six Sigma DPMO defect rates, and centering shifts.

Capability Model Six Sigma Standards SPC Theory FAQ

Engineering Presets

Load calibrated manufacturing processes.

Step 1: Specification Limits & Process Data

Tolerance Boundaries & Statistical Variations

Minimum acceptable customer threshold.
Ideal design engineering center.
Maximum allowable engineering limit.
Actual average output of production run.
Subgroup variation (R-bar/d2) for Cp & Cpk.
Total sample standard deviation for Pp & Ppk.
Actual Capability (Cpk)
1.63
World Class
Potential Capability (Cp)
2.08
10% off-center
Defect Rate (DPMO)
0.48 DPMO
99.9999% Yield
Overall Performance (Ppk)
1.48
6.38σ (with shift)

Step 2: Six Sigma Quality Standards

Industry Capability Benchmarks

Capability Index (Cpk) Quality Rating Expected Defect Rate (DPMO) Process Yield (%) Sigma Level (Long Term)
Cpk < 1.00 Incapable (Severe defects & rework) > 2,700 DPMO < 99.73% < 3.0σ
1.00 ≤ Cpk < 1.33 Marginally Capable (Bare minimum) 63 – 2,700 DPMO 99.73% – 99.99% 3.0σ – 4.0σ
1.33 ≤ Cpk < 1.67 Good / Standard Quality (ISO benchmark) 0.6 – 63 DPMO 99.994% – 99.9999% 4.0σ – 5.0σ
Cpk ≥ 1.67 Six Sigma / World Class (Aerospace & Medical) < 0.6 DPMO (3.4 @ 2.0) > 99.9999% ≥ 6.0σ

Statistical Quality Control

Understanding Cp vs. Cpk and Centering

Process capability analyzes whether an engineering or service process can consistently produce outputs within customer-defined specification limits.

  • Cp (Potential Capability): Measures the spread of the process ($6sigma$) relative to the allowable tolerance band ($USL - LSL$). It shows what capability is possible if the process is perfectly centered.
  • Cpk (Actual Capability): Penalizes the index if the process mean ($mu$) drifts away from nominal toward one of the spec limits. $C_{pk} = C_p(1 - k)$.
  • Pp vs. Ppk (Long Term): Uses the overall sample standard deviation to account for tool wear, raw material variation, and operator shifts over time.

Connect defect prevention with overall equipment health in the OEE Lab.

Mathematical Quality Formulas

Essential capability formulas

Cp = (USL − LSL) ÷ (6σ)

Cpk = min[ (USL − μ)/(3σ), (μ − LSL)/(3σ) ]

Centering Shift k = |μ − Target| ÷ [ (USL − LSL)/2 ]

DPMO = [ P(Z > Z_upper) + P(Z < Z_lower) ] × 1,000,000

Pp = (USL − LSL) ÷ (6s_overall)

Analyze defect prevention costs in the Cost of Quality Lab.

FAQ

Process capability questions

What is the difference between Cp and Cpk?

Cp measures potential capability by comparing tolerance width (USL − LSL) to 6σ process spread, assuming perfect centering. Cpk measures actual capability by accounting for how close the process mean is to the nearest specification limit.

What Cpk values represent acceptable process quality?

Cpk < 1.0 indicates an incapable process with significant defects (>2,700 PPM). 1.33 is standard industry threshold for capable processes (63 PPM). 1.67 to 2.0 represents world-class Six Sigma quality (≤ 3.4 DPMO with 1.5σ shift).

How do Cp/Cpk differ from Pp/Ppk?

Cp and Cpk use within-subgroup variation (R-bar/d2 or S-bar/c4) reflecting short-term inherent capability. Pp and Ppk use total sample standard deviation (s), capturing long-term variation including batch-to-batch shifts.

Why is the 1.5 sigma shift used in Six Sigma calculations?

In long-term production, processes experience subtle drifts in mean due to tool wear, temperature, and material lots. Motorola established a standard 1.5σ shift, meaning a 6.0σ short-term process produces 3.4 DPMO long-term (4.5σ).

Can I export process capability metrics and defect rates to CSV?

Yes. You can export complete capability indices (Cp, Cpk, Pp, Ppk), Z-scores, DPMO defect estimates, yield %, and centering statistics as a UTF-8 CSV spreadsheet with formula injection defense or print an executive SPC certificate.

Is this tool certified ISO/IATF statistical quality auditing advice?

No. This tool provides educational SPC and operations management models for business training without formal ISO or IATF regulatory compliance certifications.

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