Home / Quality & Six Sigma

Process capability (Cp and Cpk)

Enter the specification limits and process measurements to see whether the process is capable, how many parts per million will fall out of spec and what reducing variation or centering is worth.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Preliminary estimate
Specification

Use the same unit as the measurement (mm, g, bar…). No unit conversion is applied here.

Process data
See what was read

Subgroup 1: short-term variation from the moving range. Subgroups of 2 to 10: from the average range R̄/d₂.

Cost of defects
Proposed improvement
Economic analysis
—Process capability (Cpk)
—

Histogram with normal curve and limits

Distribution of the measurements, fitted normal curve and specification limits.

Tap the chart to see the values.

Measurements in production order

Each measurement with the mean and the specification limits. Trends and jumps indicate special causes.

Tap the chart to see the values.

Out-of-spec PPM versus Cpk

Centered process, log scale. Points: today and with the improvement.

Tap the chart to see the values.

Project payback

Cash flow of the improvement: investment in year 0 and annual savings escalated at the rate entered, discounted at the MARR.

Tap the chart to see the values.

The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Cp = (USL − LSL) ÷ 6σ_within; Cpk = min(USL − μ, μ − LSL) ÷ 3σ_within
σ_within = R̄ ÷ d₂ (subgroups) or MR̄ ÷ 1.128 (individuals); Pp and Ppk with overall standard deviation s
Cpm = (USL − LSL) ÷ 6√(s² + (μ − target)²)
PPM = [Φ((LSL − μ)/s) + 1 − Φ((USL − μ)/s)] × 10⁶; sigma level = Φ⁻¹(1 − PPM/10⁶) + 1.5
Anderson-Darling: A² adjusted by (1 + 0.75/n + 2.25/n²), p-value from D’Agostino and Stephens

Assumptions and limits

  • Normal distribution and a process in statistical control; without it the indices do not predict future performance.
  • PPM and savings use the overall (long-term) standard deviation. The 1.5σ shift in sigma level is a Six Sigma convention.
  • The measurement system must be adequate (gage R&R ≤ 10% of tolerance, MSA) so the measured variation belongs to the process.

Standards and technical documents

  • ISO 22514-2:2017: Statistical methods in process management — Capability and performance — Part 2: Process capability and performance of time-dependent process models
  • ISO 7870-2:2023: Control charts — Part 2: Shewhart control charts
  • AIAG. Statistical Process Control (SPC) Reference Manual, 2nd ed., 2005
  • Montgomery, D. C. Introduction to Statistical Quality Control, 8th ed. Wiley, 2019
  • D’Agostino, R. B.; Stephens, M. A. Goodness-of-Fit Techniques. Marcel Dekker, 1986

U.S. regulations

  • NIST Handbook 133: Checking the Net Contents of Packaged Goods (statistical lot acceptance)
  • 21 CFR Part 820 (Quality Management System Regulation, aligned with ISO 13485): statistical techniques for medical devices

Frequently asked questions

What is the difference between Cp and Cpk?

Cp measures only the width of variation relative to the tolerance, as if the process were centered. Cpk accounts for where the mean is: if it drifts from target, Cpk drops even with small variation.

What Cpk is acceptable?

The usual minimum is 1.33 (about 63 PPM when centered). Critical or safety characteristics require 1.67. Six Sigma corresponds to a short-term Cpk of 2.0.

Why is Ppk lower than Cpk?

Ppk uses overall variation, including between subgroups over time. A large gap indicates drift, lot changes or adjustments: the process is not stable.