KEVOS® MAKEOS · Quality
Gauge Repeatability and Bias Check (Type 1 Study: Cg, Cgk, Bias t-Test)
From repeated readings of a reference master, is this gauge repeatable and accurate enough for the tolerance, and is its bias statistically significant?
Type 1 gauge study from repeated readings of one reference master by one operator: the tolerance, bias (mean minus reference), the potential capability Cg from a share of the tolerance against a spread of standard deviations, the capability with bias Cgk, the percentage of tolerance taken by repeatability and by repeatability with bias, a two-sided t-test of the bias (confidence interval of the mean, as the two-sample t-test tool’s t distribution), and the gauge resolution as a share of the tolerance, against your minimum capability and largest resolution share.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of repeated readings | readings | Number of readings of the master (studies commonly use 25 to 50). |
| Mean of the readings | Average of the repeated readings, in the unit of the tolerance. | |
| Standard deviation of the readings | Sample standard deviation of the readings. | |
| Reference value of the master | Calibrated value of the reference master, from its certificate. | |
| Lower specification limit | Lower limit of the characteristic’s tolerance. | |
| Upper specification limit | Upper limit of the characteristic’s tolerance. | |
| Gauge resolution (smallest step) | Smallest step the gauge displays. | |
| Acceptance settings | ||
| Share of tolerance used for Cg | % | Share of the tolerance the gauge spread may use (20 % is Minitab’s default). |
| Spread in standard deviations | σ | Number of standard deviations taken as the gauge spread (6 covers about 99.73 %). |
| Minimum Cg and Cgk | Minimum Cg and Cgk your quality system requires. | |
| Largest resolution as a share of tolerance | % | Largest gauge resolution allowed as a share of the tolerance, from your quality system. |
| Significance level for the bias test | choice | Chance of calling a bias significant when there is none. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of repeated readings
- What it is
- The number of times the reference master was measured in the study, all by the same operator under the same conditions.
- Units and format
- Enter a number in readings: readings. The form accepts 3 readings to 1000 readings. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 readings as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More readings make the bias test more sensitive; Cg and Cgk do not change.
- Get it right
- Remove and replace the master between readings so the study includes handling, not just repeated display values.
What this means: Mean of the readings
- What it is
- The average of all the repeated readings of the master, in the same unit as the tolerance, compared with the master’s reference value to find the bias.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.0002 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moving it away from the reference value raises the bias, lowering Cgk.
- Get it right
- Keep every reading in the average; discarding readings that look odd hides real gauge problems.
What this means: Standard deviation of the readings
- What it is
- The sample standard deviation of the repeated readings, the scatter of the gauge when measuring the same master again and again.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0008 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cg and Cgk fall in proportion as the scatter rises.
- Get it right
- Use the sample standard deviation (divide by n − 1) of the readings themselves, not of their ranges.
What this means: Reference value of the master
- What it is
- The calibrated value of the reference master or setting standard, taken from its calibration certificate, which the gauge readings are compared with.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The bias is the mean less this value, so a change here moves Cgk and the bias test.
- Get it right
- Use the certificate value, not the nominal size; ideally the master sits near the middle of the tolerance.
What this means: Lower specification limit
- What it is
- The lowest acceptable value of the characteristic the gauge will check, the lower end of the tolerance the gauge spread is compared with.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9.98 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower limit widens the tolerance, raising Cg and Cgk.
- Get it right
- For a one-sided tolerance with a natural zero, such as flatness, enter 0.
What this means: Upper specification limit
- What it is
- The highest acceptable value of the characteristic the gauge will check, the upper end of the tolerance.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.02 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher limit widens the tolerance, raising Cg and Cgk.
- Get it right
- It must be above the lower limit, in the same unit as the readings.
What this means: Gauge resolution (smallest step)
- What it is
- The smallest change in reading the gauge can display, its resolution, compared with the tolerance to judge whether the gauge can see small differences.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0001 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the resolution check; Cg and Cgk do not change.
- Get it right
- Use the display step actually shown, for example 0.001 mm on a micrometer with a 0.001 mm digit.
Acceptance settings
What this means: Share of tolerance used for Cg
- What it is
- The share of the tolerance that the gauge spread may take up, the numerator of Cg; Minitab’s type 1 study uses 20 % by default.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cg and Cgk rise in proportion to it.
- Get it right
- Use the share your quality system or customer specifies; change it only with their agreement.
What this means: Spread in standard deviations
- What it is
- The number of standard deviations of the readings taken as the gauge’s spread, the denominator of Cg; six standard deviations cover about 99.73 % of normal readings.
- Units and format
- Enter a number in σ: σ. The form accepts 1 σ to 12 σ. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 σ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Cg and Cgk fall in proportion as the spread multiplier rises.
- Get it right
- Some systems use 4 or 5.15; use the value your quality system specifies.
What this means: Minimum Cg and Cgk
- What it is
- The smallest Cg and Cgk your quality system accepts for a capable gauge, the pass line for both capability indices.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.33 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line for Cg and Cgk.
- Get it right
- Take it from the customer or your quality manual; this tool does not set a value.
What this means: Largest resolution as a share of tolerance
- What it is
- The largest gauge resolution you accept as a share of the tolerance, the pass line for the resolution check.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.01% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line for resolution.
- Get it right
- Take it from your quality system; a gauge that cannot resolve small steps hides real variation.
What this means: Significance level for the bias test
- What it is
- The risk accepted of calling the gauge biased when its true bias is zero, used as the threshold for the p-value of the bias t-test.
- Units and format
- Choose one of 3 options from the list: 0.10; 0.05; 0.01.
- Example
- The form opens with “0.05” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Only changes whether the bias is reported as significant.
- Get it right
- 0.05 is usual; a smaller value demands stronger evidence before calling the bias real.
Method and formulas
- Tolerance T = USL − LSL; bias = x̄ − x_ref.
- Cg = (K × T) ÷ (L s); Cgk = (K × T ÷ 2 − |bias|) ÷ (L s ÷ 2); share of tolerance for repeatability = L s ÷ T and with bias = K ÷ Cgk.
- Bias test: t = bias ÷ (s ÷ √n) with n − 1 degrees of freedom; p from the t distribution (two-sided); significant when p < α.
- Example: Cg = 1.6667 and Cgk = 1.5833; the bias of 0.0002 has p = 0.22335.
Limitations
- One master at one point of the range, one operator: a type 1 study shows repeatability and bias only, not reproducibility between operators or linearity across the range.
- Readings assumed independent and roughly normal; drift during the study inflates the standard deviation.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Accept a new gauge or CMM program for a characteristic
- Check a gauge after repair or recalibration
- Decide whether bias needs correcting
Who it is for
- Quality engineers
- Metrology technicians
- Production supervisors
What you get
- Tolerance, bias and t-test
- Cg and Cgk
- Share of tolerance used
- Resolution share and the decision
Interpreting the result
- A gauge with good Cg but poor Cgk is repeatable but offset: correcting the bias (re-mastering or an offset) can be enough.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–129. Topic reference; no source tables or recommended settings are reproduced.
- Minitab, Methods and formulas for Type 1 Gage Study — https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/gage-study/type-1-gage-study/methods-and-formulas/methods-and-formulas/
- VDA Volume 5 (Verband der Automobilindustrie), capability of measurement processes: the source of the type 1 study; consult the current edition.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · Library collection
Measurement system analysis: making sure your gauges can tell good parts from bad
What it covers: Every accept, reject and adjust decision trusts a measurement. How to check bias, repeatability and reproducibility, run a gauge R&R study, judge the result and fix a weak system.
Method explained here · KEVOS® original book
How good is the gauge?
In Accept or Reject by the Numbers
What it covers: Judge a gauge three ways: a Type 1 study of repeatability and bias with the KEVOS® gauge check, the test uncertainty ratio, and the money a better gauge would save in wrong decisions.
Method explained here · KEVOS® original book
Measuring conductivity reliably
In Eddy-Current Inspection by the Numbers
What it covers: Edge distance, curvature, lift-off and probe condition in conductivity readings, a Type 1 gauge study on a reference standard, and an uncertainty budget for the acceptance band.
Method explained here · KEVOS® original book
Accuracy classes and whether a scale is good enough
In Strain Gauges and Load Cells by the Numbers
What it covers: How to read a load cell's OIML accuracy class and error limits, when trade rules apply, and how a gauge study and error budget show whether a scale can weigh to a tolerance.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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