DAY 14 — Standard Uncertainty

What is standard uncertainty?

Measurement uncertainty expressed as a standard deviation

Why is standard uncertainty needed?

It provides a common basis for expressing individual uncertainty components before they are combined

Can uncertainty information come in different forms?

Yes

What are examples of uncertainty sources requiring evaluation as standard uncertainties?

Repeated measurements calibration certificates manufacturer specifications resolution environmental effects previous data reference data and other relevant information

What is the Type A standard uncertainty formula?

uA = s divided by the square root of n

What does s represent in the Type A formula?

Experimental standard deviation

What does n represent?

Number of observations

What does uA represent?

Standard uncertainty of the estimated mean

What example repeated temperature readings are shown?

100.10 100.12 100.09 100.11 and 100.10 °C

What standard deviation is approximately obtained in the example?

s approximately 0.011 °C

What standard uncertainty is approximately obtained in the example?

uA approximately 0.005 °C

Is s equal to s divided by square root of n?

No

What does Type B standard uncertainty use?

Information other than statistical analysis of repeated observations

What are examples of Type B information?

Calibration certificates manufacturer specifications resolution environmental information previous data and reference data

What must Type B information be interpreted using?

An appropriate probability distribution

What is a rectangular distribution used for?

Values that are equally likely within known limits ±a

What is the rectangular distribution formula?

u = a divided by the square root of 3

What example is given for a rectangular distribution?

±0.10 °C

What standard uncertainty results from ±0.10 °C using a rectangular distribution?

Approximately 0.058 °C

Does ±0.10 °C automatically mean a rectangular distribution?

No

What is a normal distribution used for?

Situations where the available information supports a normal-distribution model

What is the normal distribution formula shown?

u = U divided by k

What example expanded uncertainty is given for the normal distribution?

U = ±0.20 °C with k = 2

What standard uncertainty results from 0.20 °C divided by 2?

Approximately 0.102 °C according to the infographic's stated example

What is the specifically stated 95% normal coverage factor shown?

k = 1.96

Is k exactly 2 for a specifically stated 95% normal coverage interval?

No

What is a triangular distribution used for?

When values near the center are more likely than values at the limits

What is the triangular distribution formula?

u = a divided by the square root of 6

What example is given for a triangular distribution?

±0.12 °C

What standard uncertainty results from ±0.12 °C using a triangular distribution?

Approximately 0.049 °C

Can the same limit produce different standard uncertainties?

Yes

What standard uncertainty does ±0.10 °C produce under a rectangular distribution?

Approximately 0.058 °C

What standard uncertainty does ±0.10 °C produce under a normal model with k=2?

0.050 °C

What standard uncertainty does ±0.10 °C produce under a triangular distribution?

Approximately 0.041 °C

What does the quick comparison show about distributions?

Different distribution assumptions produce different standard uncertainties from the same limit

What is the common process for converting information to standard uncertainty?

Identify the contributor understand the available information choose a justified model or distribution convert to standard uncertainty check units and assumptions and include it in the uncertainty budget

What should be done first when evaluating a contributor?

Identify the contributor

What should be done after identifying the contributor?

Understand the available information

What should be done before calculating standard uncertainty?

Choose a justified model or distribution

What should be checked after converting to standard uncertainty?

Units and assumptions

Where should the evaluated standard uncertainty be included?

In the uncertainty budget

What is standard uncertainty compared with combined standard uncertainty?

Standard uncertainty describes an individual component while combined standard uncertainty results from combining individual components according to the measurement model

What is expanded uncertainty?

A larger uncertainty value used for reporting when required

What is the expanded uncertainty formula?

U = k × uc

What does k represent in expanded uncertainty?

Coverage factor

What does uc represent?

Combined standard uncertainty

Why is the distribution assumption important?

It affects how information is converted into standard uncertainty

What are calibration red flags for standard uncertainty?

Assuming every specification uses square root of 3

Does every specification use the square root of 3?

No

Is every Type B component rectangular?

No

Does ±0.10 °C automatically equal standard uncertainty?

No

Does 95% always mean k=2?

No

Are s and s√n the same?

No

Does a calculator result prove that the uncertainty model is correct?

No

What should the calibrator do instead of starting with the formula?

Start with the information and measurement model

What questions should the calibrator ask about the available information?

What information is available

What is the main lesson of Day 14?

Standard uncertainty puts different uncertainty contributors on a common basis so they can be appropriately combined