# Engineering Metrology Questions and Answers – Expanded Uncertainty

This set of Engineering Metrology Multiple Choice Questions & Answers (MCQs) focuses on “Expanded Uncertainty”.

1. What is the actual definition of expanded uncertainty?
a) Uncertainty of the measurement result expressed as a standard deviation
b) Quantity defining an interval about the measurement result
c) Evaluation method of uncertainty by the statistical analysis of series of observations
d) Uncertainty Evaluation method by other than the statistical analysis

Explanation: The quantity that defines an interval about the measurement outcome which can be expected to include a large portion of the distribution of values that could be attributed to the measurand.

2. What is the relation of expanded uncertainty with coverage factor and combined uncertainty?
a) Expanded uncertainty = Coverage factor * Combined uncertainty
b) Combined uncertainty = Coverage factor * Expanded uncertainty
c) Coverage factor = Combined uncertainty * Expanded uncertainty
d) Coverage factor * Combined uncertainty * Expanded uncertainty = 1

Explanation: The equation which is used to calculate expanded uncertainty is a very basic equation. To calculate expanded uncertainty, one will need to multiply a coverage factor by the combined uncertainty.

3. What is the confidence interval for the value of coverage factor ‘2’?
a) 95 %
b) 94 %
c) 95.45 %
d) 94.45 %

Explanation: Confidence interval for the value of coverage factor 2 is generally taken as 95 % but it is not the actual value. The actual value for this is 95.45 %. For 95 % confidence interval, actual ‘k’ or coverage factor is 1.96.

4. Which table is generally used to find the coverage factor?
a) Student’s T table
b) F distribution table
c) Wishart distribution table
d) Tau distribution table

Explanation: Student’s T table is generally used to find coverage factor. The values are generally found at the bottom of the table especially the last row and it is generally marked with the infinity (∞) symbol.

5. What is the value of coverage factor which is generally used in the manufacturing industry?
a) 2
b) 2.89
c) 3
d) 3.89

Explanation: In the manufacturing industry, the main aim is for a failure rate of 1 in ten thousand or a coverage factor ‘k’ of 99.99% confidence, where coverage factor = 3.89. However, Confidence intervals can be greater or smaller for different industries depending on acceptable failure rates.
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6. Which of the following option is true for given statements about expanded uncertainty and coverage factor?
Statement 1: Last calculation is the expanded uncertainty when estimating uncertainty in measurement.
Statement 2: In metrology industry, the mostly used value of the coverage factor is 2.
a) T, F
b) F, F
c) T, T
d) F, T

Explanation: In metrology industry, a typically estimate of uncertainty to 95.45% confidence and coverage factor where k=2 is used. It can vary according to requirement. Last calculation is generally the expanded uncertainty while estimating measurement uncertainty.

7. Which option is not correct about coverage factor?
a) It is a number which is generally larger than 1
b) Range – 2 to 7
c) Can be calculated by using MS excel
d) Depends on the selected coverage probability

Explanation: The coverage factor generally depends upon the probability distribution type of the output measurement quantity in the measurement model and on the selected coverage probability. Its range is generally between 2 to 3, can be more for special purposes.

8. What is the formula for relative expanded uncertainty?
a) Ur = U/| y |
b) Ur = U/y
c) Ur = U*| y |
d) Ur = U*2y

Explanation: In analogy with relative standard uncertainty Ur and relative combined standard uncertainty Uc,r the relative expanded uncertainty of a measurement result y is Ur = U/ | y |, y is not equal to zero and U is expanded uncertainty.

Sanfoundry Global Education & Learning Series – Engineering Metrology.