Gauge Capability: Cg and Cgk
Tabla de contenidos
What a capability estudio answers
R&R del sistema de medición and gauge capability are often confused because both produce a verdict about a sistema de medición. They compare against different things, and that difference detérminoines cuándo each is appropriate.
| Study | Compares medición variación against | Use cuándo |
|---|---|---|
| R&R del sistema de medición | The variación of the piezas sampled, or optionally the tolerancia | Several operadores use the gauge and you need to separate operador effects from gauge effects. |
| Gauge capability | A fixed referencia fraction of the tolerancia | One operador or an automated gauge, or you want a quick verdict against a specific tolerancia without a full estudio. |
A capability estudio uses repeated mediciones of a single calibrado referencia pieza by one evaluador, conventionally at least 25 readings, though 50 is common. Because there is only one pieza and one evaluador, it says nothing about reproducibilidad, and it does not need to.
Cg: is the gauge precise enough?
Cg compares the spread of the gauge against a referencia fraction of the tolerancia. It considers only scatter, and ignores dónde the readings are centred.
Cg
Cg = (0.2 × T) ÷ (6 × s)
dónde T is the total tolerancia width and s is the patrón deviation of the repeated readings on the referencia pieza.
Read the denominator as the natural spread of the gauge: six patrón deviations covers about 99.73 percent of its readings. The numerator is the budget you are allowing the gauge, being 20 percent of the tolerancia. Cg is therefore the ratio of the allowance to the requirement, and a Cg of 1.33 means the gauge spread fits into its allowance with 33 percent to spare.
Note the structure is identical to a proceso capability index. Cp compares the tolerancia to the proceso spread; Cg compares a fraction of the tolerancia to the gauge spread. The gauge is being treated as a proceso whose output is mediciones.
Where the 0.2 comes from
The 0.2 factor is a decision, not a derivation. It encodes the judgement that a sistema de medición should consume no more than 20 percent of the tolerancia, which is the same threshold that appears in R&R del sistema de medición as the boundary between aceptable and marginal in many acceptance schemes.
The reasoning behind it is that medición variación eats into the tolerancia available for the proceso. If the gauge consumes 20 percent, the proceso still has the large majority of the tolerancia to work within, and the risk of misclassifying a pieza near the specification limit stays modest. Allow the gauge 50 percent and that risk becomes severe.
Cgk: is the gauge also accurate enough?
Cg can look excellent while every reading is offset from the referencia valor. Cgk adds the sesgo penalty, in the same way that Cpk adds a centring penalty to Cp.
Cgk
Cgk = (0.1 × T − | x̄ − xref | ) ÷ (3 × s)
dónde x-bar is the average of the readings and x-ref is the referencia valor of the master, so the absolute difference is the sesgo.
The sesgo is subtracted directly from the half-allowance before dividing by the half-spread. This means Cgk can never exceed Cg, and the gap between them is a direct measure of cómo much capability the sesgo is consuming. With zero sesgo, Cgk equals Cg exactly.
Worked example
Illustrative datos. Thirty repeated readings of a 25 mm master on a pieza with a 0.100 mm tolerancia.
| Quantity | Value |
|---|---|
| Total tolerancia T | 0.100 mm |
| Reference valor of the master | 25.000 mm |
| Average of the readings | 25.004 mm |
| Bias (absolute difference) | 0.004 mm |
| Standard deviation s | 0.0025 mm |
| Cg = (0.2 × 0.100) / (6 × 0.0025) | 1.33 |
| Cgk = (0.010 − 0.004) / (3 × 0.0025) | 0.80 |
Interpreting the pair
| Pattern | What it means | Typical action |
|---|---|---|
| Cg and Cgk both at or above the limit, and close together | The gauge is both precise and well aligned for this tolerancia. | Accept and record the estudio. |
| Cg passes but Cgk fails | Precision is adequate; a sesgo is consuming the capability. | Adjust or recalibrate. This is usually correctable, because the scatter is already good enough. |
| Cg fails | The gauge scatter alone is too large for this tolerancia, regardless of alignment. | Adjustment will not help. Improve the method or fixturing, or use a more precise gauge for this characteristic. |
Resolution and the 10 to 1 rule
Before any capability index is significadoful, the gauge must be able to see the variación you are asking it to quantify. The conventional requirement is that the resolution, significado the smallest increment the gauge displays, is no more than one tenth of the tolerancia.
The 10 to 1 rule
resolution ≤ T ÷ 10
With a 0.100 mm tolerancia, this calls for a resolution of 0.010 mm or finer. The reason is that a coarse gauge quantizes the readings: if the resolution is too large relative to the variación, repeated readings return the same displayed valor regardless of the real differences between them.
This produces a specific and dangerous failure. The patrón deviation of the readings collapses toward zero, Cg becomes very large, and the gauge appears outstanding. It is not outstanding, it is blind. The tell-tale sign is repeated readings scómoing only two or three distinct valors.
Common pitfalls
- Reporting Cg without Cgk. The pair only tells the full story together, and Cg alone conceals sesgo by construction.
- Comparing a Cg computed with a 0.2 factor against a limit intended for a 0.1 factor. Always state which referencia fraction was used.
- Using an uncalibrado pieza as the referencia. Cgk is measured against the referencia valor, so an unknown master valor makes the sesgo término significadoless.
- Treating a capability estudio as a complete MSA. It uses one evaluador and one pieza, so it says nothing about reproducibilidad and nothing about behaviour across the medir range.