BIZOMAT MAKEOS · Quality
Guard-Banded Acceptance Decision (Uncertainty Budget, Accept, Reject or Indeterminate)
Given my gauge’s measurement uncertainty, can I accept this part from its reading, must I reject it, or is it too close to the limit to decide?
Acceptance decision for a measured part that allows for measurement uncertainty: the uncertainty budget from calibration, resolution, repeatability, Abbe error and temperature, the expanded uncertainty and test uncertainty ratio, and the guard-banded acceptance zone (as the measurement uncertainty budget tool), then the deviation of the reading from nominal compared with the guard-banded and the tolerance limits to accept, reject or flag it as indeterminate.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal size | mm | Nominal size of the feature (mid-tolerance). |
| Tolerance band (total, symmetric) | mm | Total tolerance band, placed symmetrically about the nominal. |
| Measured size | mm | Size measured on the part. |
| Uncertainty contributors | ||
| Calibration uncertainty of the gauge (expanded, k = 2) | µm | Expanded uncertainty from the gauge’s calibration certificate. |
| Resolution of the gauge | µm | Smallest step the gauge displays. |
| Repeatability (standard deviation of repeat readings) | µm | Standard deviation of repeated readings on the same part. |
| Abbe offset | mm | Distance between the measuring line and the scale line (Abbe offset). |
| Tilt of the moving element | arcsec | Possible tilt of the moving jaw or slide. |
| Length measured | mm | Length being measured. |
| Part expansion coefficient | µm/m·K | Expansion coefficient of the part. |
| Uncertainty of the temperature difference | K | Uncertainty in the temperature difference between part and gauge. |
| Coverage factor | Coverage factor for the expanded uncertainty (2 for about 95%). | |
| Least test uncertainty ratio | Least ratio of tolerance to measurement uncertainty you accept. | |
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: Nominal size
- What it is
- The nominal size of the measured feature, taken here as the middle of the tolerance band.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If the drawing tolerance is unequal, enter the mid-tolerance size, not the basic size.
What this means: Tolerance band (total, symmetric)
- What it is
- The total width of the tolerance band, from the lower to the upper limit, placed equally either side of the nominal.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.0001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider band widens the acceptance zone and raises the test uncertainty ratio.
- Get it right
- Enter the total band, not the ± value: ±0.02 mm is a 0.04 mm band.
What this means: Measured size
- What it is
- The size measured on the part with the gauge, corrected for any known gauge error.
- Units and format
- Enter a number in mm: millimetres. The form accepts -100000 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25.012 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter millimetres, the same unit as the nominal.
Uncertainty contributors
What this means: Calibration uncertainty of the gauge (expanded,…
- What it is
- The expanded uncertainty of the gauge from its calibration certificate, stated at a coverage factor of 2; the tool halves it to a standard uncertainty.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0 µm to 1000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter micrometres. If the certificate uses another coverage factor, convert to the k = 2 value first.
What this means: Resolution of the gauge
- What it is
- The smallest step the gauge display or scale can show; the tool turns it into a standard uncertainty.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0 µm to 1000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter micrometres: a 0.001 mm resolution is 1 µm.
What this means: Repeatability (standard deviation of repeat rea…
- What it is
- The standard deviation of repeated readings of the same feature with the same gauge, from a repeatability study.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0 µm to 1000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the standard deviation, not the range of the readings, in micrometres.
What this means: Abbe offset
- What it is
- The Abbe offset: the distance between the line along which the size is measured and the line of the gauge’s scale.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The Abbe error rises in direct proportion to the offset.
- Get it right
- For a micrometer it is near zero; for a caliper it is the distance from the jaws’ contact points to the beam scale.
What this means: Tilt of the moving element
- What it is
- The possible tilt of the moving jaw or slide during measurement, which with the Abbe offset causes a size error.
- Units and format
- Enter a number in arcsec: arcsec. The form accepts 0 arcsec to 3600 arcsec. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 arcsec as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter arcseconds (1° = 3600 arcsec), from the gauge specification or an estimate of slide play.
What this means: Length measured
- What it is
- The length over which thermal expansion acts in the temperature contributor, normally the measured length of the feature.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The temperature uncertainty rises in direct proportion to this length.
- Get it right
- Use the length of the feature being measured; it is used only for the temperature term.
What this means: Part expansion coefficient
- What it is
- The coefficient of thermal expansion of the part material, from the material data sheet.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 50 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.5 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter micrometres per metre per kelvin, which equals 10⁻⁶ per kelvin.
What this means: Uncertainty of the temperature difference
- What it is
- The uncertainty in the temperature difference between the part and the gauge at the time of measurement.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0 K to 50 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is the doubt in the difference between part and gauge, not the room temperature or its distance from 20 °C.
What this means: Coverage factor
- What it is
- The coverage factor that multiplies the combined standard uncertainty to give the expanded uncertainty used for guard banding.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger factor widens the guard band and narrows the acceptance zone.
- Get it right
- Use the factor your quality system or the guidance on measurement uncertainty requires.
What this means: Least test uncertainty ratio
- What it is
- The smallest test uncertainty ratio you accept: the tolerance band divided by twice the expanded uncertainty.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from your quality system or customer requirement; it is a ratio, not a percentage.
Method and formulas
- Standard uncertainties: calibration U ÷ 2, resolution ÷ √12, repeatability, Abbe and temperature errors ÷ √3; combined by root sum of squares; expanded = k × combined (as the measurement uncertainty budget tool).
- Test uncertainty ratio = tolerance ÷ 2U; acceptance zone = ±(tolerance ÷ 2 − U) about nominal.
- Accept inside the acceptance zone; reject outside the tolerance; otherwise indeterminate.
- Example: U = 5.9696 µm, so accept within ±19.03 µm; the part is 12 µm from nominal.
Limitations
- Symmetric tolerance and uncorrelated contributors.
- Simple guard band of one expanded uncertainty; your standard may use a different rule.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Decide whether a borderline part passes
- Set guard-banded acceptance limits on an inspection plan
- Show a customer how the decision was made
Who it is for
- Inspectors
- Quality engineers
- Metrologists
What you get
- Uncertainty budget, expanded uncertainty and test uncertainty ratio
- Guard-banded acceptance zone
- Accept, reject or indeterminate
Interpreting the result
- Indeterminate parts need a better measurement, not a coin toss: re-measure with a more capable gauge.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 709–735. Topic reference; no source tables or recommended settings are reproduced.
- ISO/IEC Guide 98-3 Uncertainty of measurement (GUM)
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Guard bands and the cost of errors
In Accept or Reject by the Numbers
What it covers: Set acceptance limits inside the tolerance: the one-uncertainty guard band in the BIZOMAT tool, cost-based limits from the costs of each error, sensitivity to costs, and contract rules.
BIZOMAT 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.