Type 1 Gage Study Calculator

Use this calculator to assess a gage's repeatability and bias from repeated measurements of one reference part by one operator. Calculate Cg to evaluate repeatability relative to tolerance, and Cgk to account for systematic measurement bias as well.

How to calculate a Type 1 gage study

1. Enter the repeated readings of one reference part in a single numerical column.
2. Select Continuous data and Crossed, then select your column under Measurements. Leave Part and Operator unselected. With only a measurement column selected, the calculator performs a Type 1 study.
3. Enter the accepted value of the reference part in Reference to calculate bias and its t-test.
4. Enter the Tolerance (USL-LSL), or choose Specification limits and enter both limits, to calculate capability indices.
5. Check Study variation and Percent of tolerance. The defaults are 6 and 20%, respectively; use the settings required by your study procedure.

Example: repeated readings of a 10 mm reference

The example contains 50 simulated readings of one reference part with an accepted value of 10 mm. Load the data and select Measurement (mm). Enter 10 as the reference and 0.2 as the tolerance, corresponding to limits of 9.9 and 10.1 mm. Keep study variation at 6 and percent of tolerance at 20. The example button loads the readings; enter these study settings separately.

Compare the mean with 10 mm to assess bias, then compare Cg with Cgk. If Cgk is lower than Cg, the offset from the reference reduces the assessed capability. These simulated readings illustrate the calculation and are not a calibration record.

What do Cg, Cgk, and bias mean?

• Repeatability: the spread of repeated readings under the same conditions, summarized by the standard deviation.
• Bias: the mean reading minus the accepted reference value. Positive bias means the gage reads high; negative bias means it reads low.
• Cg: compares the allowed share of tolerance with measurement spread. Larger values indicate better repeatability relative to the chosen tolerance.
• Cgk: also accounts for bias. A gage can have consistent readings and a high Cg, yet a low Cgk if those readings are systematically off target.

For a two-sided tolerance with the default settings, Cg = (0.20 × tolerance) / (6 × standard deviation), and Cgk = (0.10 × tolerance - absolute bias) / (3 × standard deviation). Changing the settings changes the indices. Without a reference value, bias and Cgk cannot be calculated. Capability indices also require a valid tolerance.

How to interpret the results

A value of 1.33 is a common benchmark for Cg and Cgk, but acceptance depends on your procedure and application. Review both indices, the actual bias, and the measurement spread. A small p-value indicates evidence of nonzero bias; it does not by itself show that the bias is practically unacceptable. A nonsignificant result does not prove that the gage has no bias.

Required data and limitations

Use a stable reference with a known accepted value, one operator, and consistent measurement conditions. Collect enough independent repeat readings for your study procedure and avoid rounding away meaningful variation. Check for drift and unusual readings before interpreting capability.

A Type 1 study evaluates one reference value. It does not assess differences between operators or establish accuracy across the entire measurement range. Use the Gage R&R calculator to study parts and operators, or the linearity and bias study to assess bias across several reference values. For categorical inspection ratings, use attribute agreement analysis.