# Uncertainty budgets and meeting 4:1 TUR for digital calipers and micrometer

#### caliperCalibration

##### Registered
Hello,

I am working on coming up with uncertainty budgets for the calibration of a 6 inch digital caliper with a resolution of 0.0005 inches and a 1 inch digital micrometer with a resolution of .000005.

The goal in the end is to have our calibrations comply with ANSI/NCSL Z540-3 when it states "the test uncertainty ratio shall be equal or greater than 4:1"

So far, I have the following factors in my uncertainty budget, with values for measuring a 1 inch gage block at 72 degrees Fahrenheit.

- Uncertainty due to resolution: 238 μin for caliper, 23.8 μin for micrometer
- Uncertainty from the gage blocks used in calibration: 16 μin for both
- Uncertainty due to thermal expansion and contraction: 14.6 μin for both (this includes the uncertainty of thermometer reading, CTE, and nominal length. I based my method for calculating this on what I could find in the GUM about coming up with a mathematical model).
All of these uncertainties are expanded uncertainties with a 95% level of confidence.
- Uncertainty due to reproducibility and repeatability: I plan to use the results of a G R&R for this, haven't completed it yet.

I have combined the first three contributors listed above using the root sum of the squares method to obtain a value of 239 μin for the caliper and 35 μin for the micrometer.

I am using tolerance values of 0.001 inches for the caliper and 0.0001 inches for the micrometer, which I believe is what is specified by the manufacturer.

The problem that I am facing is that the micrometer calibration currently has a TUR of 2.82, and although the caliper is currently giving me a TUR of 4.17, I suspect that when the results of the G R&R are included, it could also be lower than 4.

With results like these, I am left with two main questions that I hoping to get some help with:

1) Do my uncertainties budget and associated values seem reasonable?
2) Most perplexing to me, how would anyone be able to calibrate, to a TUR 4:1, a micrometer with a resolution of 0.00005 in and a tolerance of 0.0001 both specified by the manufacturer? The uncertainty due to resolution would take up 23.8 μin, which would give a TUR of 4.2. Although that would be okay on its own, it leaves barely any room for any other source of uncertainty.

I am new to the concept of uncertainty, so any help would be greatly appreciated!!

Thanks!