DAY 20 — UNCERTAINTY CASE STUDY

What is an uncertainty case study?

A practical example showing how the uncertainty process fits together from the measurement result to the final reported uncertainty

What process is illustrated in the uncertainty case study?

Measurement result → uncertainty budget → combined uncertainty → expanded uncertainty → reporting

What is the reference value in the illustrative temperature-calibration example?

100.00 °C

What is the UUT indication in the illustrative temperature-calibration example?

100.12 °C

How is the error calculated in the case study?

Error = UUT indication − Reference value

What is the calculated error in the case study?

Error = 100.12 − 100.00 = +0.12 °C

What contributors are included in the uncertainty budget?

Reference standard repeatability resolution and environment

What is the standard uncertainty of the reference standard?

0.050 °C

What is the standard uncertainty of repeatability?

0.040 °C

What is the standard uncertainty of resolution?

0.030 °C

What is the standard uncertainty of environment?

0.020 °C

What sensitivity coefficients are assumed in the example?

The sensitivity coefficients are cᵢ = 1

What is assumed about the input quantities in the example?

The input quantities are uncorrelated

Why must uncertainty contributors be relevant to the actual measurement?

Because possible contributors must be relevant to the actual measurement

What warning is given about including uncertainty effects?

Do not automatically include every possible effect

What formula is shown for combining uncorrelated uncertainties?

u_c = √Σ(cᵢuᵢ)²

What is the value of each sensitivity coefficient in this example?

cᵢ = 1

How is the combined standard uncertainty calculated?

u_c = √(0.050² + 0.040² + 0.030² + 0.020²)

What intermediate value is obtained under the square root?

0.0054

What is the combined standard uncertainty in the case study?

u_c = 0.0735 °C

What coverage factor is used for the expanded uncertainty example?

k = 2

How is expanded uncertainty calculated?

U = k × u_c

What is the unrounded expanded uncertainty?

U = 2 × 0.0735 = 0.147 °C

What is the expanded uncertainty for presentation to 2 significant digits?

U = 0.15 °C

What illustrative result is reported?

Error = +0.12 °C ± 0.15 °C

What expanded uncertainty is stated in the reported result?

U = 0.15 °C

What coverage factor is stated in the reported result?

k = 2

What must be stated about coverage probability?

Coverage probability must be stated and supported by the uncertainty evaluation

What does ±0.15 °C represent in this case?

It is the expanded measurement uncertainty for the example

What does ±0.15 °C not represent?

It is not the error not the tolerance not the MPE and not automatically a PASS/FAIL limit

What should the technician review before reporting the result?

The measurement model input quantities standard uncertainties sensitivity coefficients correlation combined uncertainty coverage factor and reporting and rounding

What should be checked regarding the measurement model?

The measurement model should be reviewed

What should be checked regarding input quantities?

The relevant input quantities should be reviewed

What should be checked regarding standard uncertainties?

The standard uncertainties should be reviewed

What should be checked regarding sensitivity coefficients?

The sensitivity coefficients should be reviewed

What should be checked regarding correlation?

Correlation should be reviewed

What should be checked regarding combined uncertainty?

The combined uncertainty should be reviewed

What should be checked regarding the coverage factor?

The coverage factor should be reviewed

What should be checked regarding reporting and rounding?

Reporting and rounding should be reviewed

What mistake is identified when measured values are used directly as standard uncertainties?

Measured values should not be used as standard uncertainties without evaluation

What mistake involves counting the same effect more than once?

Double-counting one effect is a red flag

What warning is given about using k = 2?

Do not use k = 2 without considering coverage

What warning is given about rounding?

Do not round before calculations are complete

What is wrong with reporting uncertainty without stating k?

Reporting uncertainty without stating k is identified as a red flag

What is wrong with declaring PASS/FAIL without an applicable specification and decision rule?

It is identified as a red flag

What is the main takeaway from the case study?

The calibration result is not just “UUT = 100.12 °C”

What questions should a complete uncertainty evaluation answer?

What is the result how was it determined what contributes to its uncertainty and how was the uncertainty evaluated and reported

What does the GUM reference address in the case study?

Uncertainty evaluation

What does ILAC P14:09/2020 address in the case study?

Calibration uncertainty and reporting

What does VIM3 — JCGM 200:2012 address in the references?

Terminology

What technical challenge is given for u_c = 0.0735 °C and k = 2?

What is the expanded uncertainty?

What is the answer to the technical challenge?

The expanded uncertainty is 0.147 °C or 0.15 °C for presentation

What question does the witty challenge ask about a result of +0.12 °C ± 0.15 °C?

If the result is +0.12 °C ± 0.15 °C can you just stamp PASS immediately and why or why not?