Measurement System Analysis

Repeatability Index Cg (MSA Type 1)

Evaluates the repeatability of a measurement instrument: How large is the spread of repeated measurements relative to the tolerance?

Statusvalidated

Version1.0.0

Minitab equivalentStat > Quality Tools > Gage Study > Type 1 Gage Study

Description

The repeatability index Cg compares the spread of a measurement instrument against a defined fraction of the tolerance. It is calculated from at least 25 repeated measurements on a calibrated reference part (master). Factor k₁ defines the tolerance fraction allocated to the measurement system (default: 20% per VDA 5), factor k₂ defines the spread coverage (default: 4 for 99.99%). A Cg ≥ 1.33 is considered capable. Unlike Cgk, Cg does not account for systematic deviation (bias).

Formulas

C_{g} = \frac{k _{1} \cdot T}{2 \cdot k _{2} \cdot s _{g}}

Repeatability index: ratio of the allowed tolerance fraction to the observed spread

T = U S L - L S L

Tolerance width (difference between upper and lower specification limits)

s_{g} = \frac{1}{n - 1} i = 1 \sum n (x_{i} - \overset{x}{ˉ})^{2}

Sample standard deviation of repeated measurements (Bessel's correction, n−1)

% T = \frac{2 \cdot k _{2} \cdot s _{g}}{T} \cdot 100

Tolerance usage: fraction of tolerance consumed by measurement instrument spread

Assumptions

Measurements under repeatability conditions (one operator, one instrument, one reference part)
At least 25 measurements (n ≥ 25)
Reference part is calibrated with known true value (x_ref)
Measurements are approximately normally distributed

Limitations

Cg only considers repeatability spread, not systematic deviation (bias) — use Cgk for that
Requires a calibrated reference part — MSA Type 1 is not possible without a known true value
Result depends strongly on k₁ and k₂ — comparisons are only meaningful with the same factors

References

VDA Band 5 — Prüfprozesseignung: Eignung von Messsystemen, Mess- und Prüfprozessen, Erweiterte Messunsicherheit, 3. Auflage
AIAG — Measurement Systems Analysis Reference Manual, 4th Edition (MSA-4)
Dietrich, E. & Schulze, A. — Statistische Verfahren zur Maschinen- und Prozessqualifikation, 7. Auflage, Hanser