Gauge Capability: Cg and Cgk
Indice
What a capability estudo answers
R&R do sistema de medição and gauge capability are often confused because both produce a verdict about a sistema de medição. They compare against different things, and that difference determoines quando each is appropriate.
| Study | Compares medição variação against | Use quando |
|---|---|---|
| R&R do sistema de medição | The variação of the peças sampled, or optionally the tolerância | Several operadores use the gauge and you need to separate operador effects from gauge effects. |
| Gauge capability | A fixed referência fraction of the tolerância | One operador or an automated gauge, or you want a quick verdict against a specific tolerância without a full estudo. |
A capability estudo uses repeated medições of a single calibrado referência peça by one avaliador, conventionally at least 25 readings, though 50 is common. Because there is only one peça and one avaliador, it says nothing about reprodutibilidade, and it does not need to.
Cg: is the gauge precise enough?
Cg compares the spread of the gauge against a referência fraction of the tolerância. It considers only scatter, and ignores onde the readings are centred.
Cg
Cg = (0.2 × T) ÷ (6 × s)
onde T is the total tolerância width and s is the padrão deviation of the repeated readings on the referência peça.
Read the denominator as the natural spread of the gauge: six padrão deviations covers about 99.73 percent of its readings. The numerator is the budget you are allowing the gauge, being 20 percent of the tolerância. 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 processo capability index. Cp compares the tolerância to the processo spread; Cg compares a fraction of the tolerância to the gauge spread. The gauge is being treated as a processo whose output is medições.
Where the 0.2 comes from
The 0.2 factor is a decision, not a derivation. It encodes the judgement that a sistema de medição should consume no more than 20 percent of the tolerância, which is the same threshold that appears in R&R do sistema de medição as the boundary between aceitável and marginal in many acceptance schemes.
The reasoning behind it is that medição variação eats into the tolerância available for the processo. If the gauge consumes 20 percent, the processo still has the large majority of the tolerância to work within, and the risk of misclassifying a peça 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 referência valor. Cgk adds the viés penalty, in the same way that Cpk adds a centring penalty to Cp.
Cgk
Cgk = (0.1 × T − | x̄ − xref | ) ÷ (3 × s)
onde x-bar is the average of the readings and x-ref is the referência valor of the master, so the absolute difference is the viés.
The viés 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 como much capability the viés is consuming. With zero viés, Cgk equals Cg exactly.
Worked example
Illustrative dados. Thirty repeated readings of a 25 mm master on a peça with a 0.100 mm tolerância.
| Quantity | Value |
|---|---|
| Total tolerância 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 tolerância. | Accept and record the estudo. |
| Cg passes but Cgk fails | Precision is adequate; a viés 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 tolerância, 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 variação 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 tolerância.
The 10 to 1 rule
resolution ≤ T ÷ 10
With a 0.100 mm tolerância, 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 variação, repeated readings return the same displayed valor regardless of the real differences between them.
This produces a specific and dangerous failure. The padrão 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 scomoing only two or three distinct valors.
Common pitfalls
- Reporting Cg without Cgk. The pair only tells the full story together, and Cg alone conceals viés by construction.
- Comparing a Cg computed with a 0.2 factor against a limit intended for a 0.1 factor. Always state which referência fraction was used.
- Using an uncalibrado peça as the referência. Cgk is measured against the referência valor, so an unknown master valor makes the viés termo significadoless.
- Treating a capability estudo as a complete MSA. It uses one avaliador and one peça, so it says nothing about reprodutibilidade and nothing about behaviour across the medir range.