CCT Measurement Uncertainty & Error Analysis 2 — Questions and Answers
Question 1: Systematic errors in measurement are best described as:
- Random, unpredictable deviations that cancel out with averaging
- Consistent, repeatable offsets in one direction that do not average out (Correct answer)
- Errors caused solely by the observer's reading technique
- Errors that only occur in digital instruments
Correct answer: Consistent, repeatable offsets in one direction that do not average out
Systematic errors are reproducible inaccuracies that consistently bias results in one direction and cannot be reduced by averaging — they must be identified and corrected.
Question 2: The most effective way to reduce the contribution of random errors to a measurement result is to:
- Recalibrate the instrument more frequently
- Replace all analog components with digital ones
- Take multiple measurements and compute the mean (Correct answer)
- Apply a zero offset correction factor
Correct answer: Take multiple measurements and compute the mean
Random errors are governed by statistics; taking multiple measurements and computing the mean reduces the standard uncertainty by 1/√n, where n is the number of observations.
Question 3: The resolution uncertainty contribution from a digital display device is typically estimated as:
- Half the last significant digit divided by √3 (Correct answer)
- One full last digit divided by √6
- The last digit divided by 2
- Two last digits divided by √12
Correct answer: Half the last significant digit divided by √3
For a digital display, the resolution uncertainty is half the last significant digit (±0.5 LSD), modeled as a rectangular distribution, giving a standard uncertainty of (0.5 LSD)/√3.
Question 4: What is 'expanded uncertainty' in a calibration report?
- The uncertainty before applying sensitivity coefficients
- The combined standard uncertainty multiplied by a coverage factor to provide a stated confidence interval (Correct answer)
- The maximum possible error of the instrument under all conditions
- The uncertainty contributed only by the reference standard
Correct answer: The combined standard uncertainty multiplied by a coverage factor to provide a stated confidence interval
Expanded uncertainty U = k × uc, where k is a coverage factor chosen to achieve a desired level of confidence, and is the value reported on calibration certificates.
Question 5: Hysteresis error in a measuring instrument is caused by:
- Temperature changes affecting component dimensions
- Differences in readings when approaching the same value from increasing versus decreasing directions (Correct answer)
- Electrical noise introduced by nearby equipment
- Wear on contact surfaces over time
Correct answer: Differences in readings when approaching the same value from increasing versus decreasing directions
Hysteresis is the path-dependent behavior where an instrument gives different readings for the same measurand value depending on whether the measurement was approached from above or below.
Question 6: Linearity error in an instrument refers to:
- The inability of the instrument to read below a certain threshold
- Deviation of the instrument's response from a best-fit straight line across its range (Correct answer)
- Differences between the instrument's reading and the previous reading
- Error introduced by misalignment of the sensor axis
Correct answer: Deviation of the instrument's response from a best-fit straight line across its range
Linearity error is the maximum deviation of the actual output curve from a best-fit or terminal-based straight line over the full measurement range.
Question 7: In the context of uncertainty analysis, sensitivity coefficients (∂f/∂xi) are used to:
- Convert measurements from one unit system to another
- Account for how much each input quantity influences the combined output uncertainty (Correct answer)
- Determine the minimum number of repeated measurements needed
- Establish the traceability chain to national standards
Correct answer: Account for how much each input quantity influences the combined output uncertainty
Sensitivity coefficients represent the partial derivatives of the output with respect to each input variable, weighting each component's uncertainty by its influence on the final result.
CCT Measurement Uncertainty & Error Analysis 2
Systematic errors in measurement are best described as: