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Questions and Answers
What is the difference between the measured value and the true value of a measurement called?
What is the difference between the measured value and the true value of a measurement called?
Which of the following represents the true value of a measured variable?
Which of the following represents the true value of a measured variable?
What is the formula for absolute error, represented by δx, in a measurement?
What is the formula for absolute error, represented by δx, in a measurement?
What is the formula for relative error, represented by εx, in a measurement?
What is the formula for relative error, represented by εx, in a measurement?
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If the true value of a measurement is 100°C and the measured value is 100.1°C, what is the absolute error?
If the true value of a measurement is 100°C and the measured value is 100.1°C, what is the absolute error?
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What is the main reason for dynamic errors in temperature measurement?
What is the main reason for dynamic errors in temperature measurement?
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Which of the following is NOT a factor contributing to dynamic errors in temperature measurement?
Which of the following is NOT a factor contributing to dynamic errors in temperature measurement?
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Why does introducing a sensor into a system cause a change in the object's temperature?
Why does introducing a sensor into a system cause a change in the object's temperature?
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What is the term used to describe the time it takes for a measurement system to respond to changes in the measured variable?
What is the term used to describe the time it takes for a measurement system to respond to changes in the measured variable?
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Which of these factors directly influences the error in temperature measurement?
Which of these factors directly influences the error in temperature measurement?
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Why is it important to consider the temperature of the object being measured when analyzing dynamic errors?
Why is it important to consider the temperature of the object being measured when analyzing dynamic errors?
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What is the primary objective of using a computational tool like Excel in this context?
What is the primary objective of using a computational tool like Excel in this context?
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What is the main goal of sensitivity analysis in this context?
What is the main goal of sensitivity analysis in this context?
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What is the term used to describe the time it takes for a temperature sensor to stabilize at the measured temperature?
What is the term used to describe the time it takes for a temperature sensor to stabilize at the measured temperature?
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Which dynamic error occurs when a system initially exceeds the final steady-state value?
Which dynamic error occurs when a system initially exceeds the final steady-state value?
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What is the definition of a lag error?
What is the definition of a lag error?
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Which dynamic error is characterized by a system's output being dependent on both current and past inputs?
Which dynamic error is characterized by a system's output being dependent on both current and past inputs?
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What scenario best illustrates the concept of overshoot in temperature measurement?
What scenario best illustrates the concept of overshoot in temperature measurement?
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Which of the following is an example of hysteresis error in temperature measurement?
Which of the following is an example of hysteresis error in temperature measurement?
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Which of the following is NOT a type of dynamic error?
Which of the following is NOT a type of dynamic error?
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Which dynamic error is most closely associated with the concept of 'time delay' in a system's response?
Which dynamic error is most closely associated with the concept of 'time delay' in a system's response?
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What is indicated by a high precision in a measurement instrument?
What is indicated by a high precision in a measurement instrument?
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Which of the following is associated with random errors?
Which of the following is associated with random errors?
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What term is used to describe the difference between the measured value and the true value?
What term is used to describe the difference between the measured value and the true value?
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How is uncertainty expressed in measurements?
How is uncertainty expressed in measurements?
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Which statement is true regarding accuracy and precision?
Which statement is true regarding accuracy and precision?
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Which factor can cause systematic errors?
Which factor can cause systematic errors?
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What does uncertainty express regarding a measurement?
What does uncertainty express regarding a measurement?
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What is the relationship between standard deviation and precision?
What is the relationship between standard deviation and precision?
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What does a low standard deviation indicate about repeated measurements?
What does a low standard deviation indicate about repeated measurements?
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What percentage of values falls within a bound of ±2σ for a normal distribution?
What percentage of values falls within a bound of ±2σ for a normal distribution?
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Which of the following statements about standard deviation is true?
Which of the following statements about standard deviation is true?
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What does high standard deviation in repeated measurements suggest?
What does high standard deviation in repeated measurements suggest?
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What is the standard uncertainty associated with a measurement based on its mean and standard deviation for normally distributed data?
What is the standard uncertainty associated with a measurement based on its mean and standard deviation for normally distributed data?
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Which of the following is NOT a reason why standard deviation is useful in metrology?
Which of the following is NOT a reason why standard deviation is useful in metrology?
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Which statement about the standard deviation and precision is accurate?
Which statement about the standard deviation and precision is accurate?
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When considering a normal distribution, what portion of measurements does ±3σ encompass?
When considering a normal distribution, what portion of measurements does ±3σ encompass?
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What does the mean value represent in a dataset?
What does the mean value represent in a dataset?
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Which function in Excel calculates the average?
Which function in Excel calculates the average?
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What does a low standard deviation indicate about a dataset?
What does a low standard deviation indicate about a dataset?
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How is the range of a dataset calculated?
How is the range of a dataset calculated?
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If a dataset has a high standard deviation, what does that signify?
If a dataset has a high standard deviation, what does that signify?
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What shape does a frequency distribution curve typically take when values are clustered around the mean?
What shape does a frequency distribution curve typically take when values are clustered around the mean?
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In the calculation of standard deviation, what does 'n - 1' represent?
In the calculation of standard deviation, what does 'n - 1' represent?
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What does the standard deviation measure in a set of data?
What does the standard deviation measure in a set of data?
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Which Excel function would you use to calculate the standard deviation of a dataset?
Which Excel function would you use to calculate the standard deviation of a dataset?
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What can be misleading when analyzing the spread of data using range alone?
What can be misleading when analyzing the spread of data using range alone?
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If the average flue gas flow rate is calculated to be 185.2 m³/h, what does this value represent?
If the average flue gas flow rate is calculated to be 185.2 m³/h, what does this value represent?
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Which statement is true regarding a frequency distribution curve?
Which statement is true regarding a frequency distribution curve?
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Why might a single outlier affect the interpretation of the range?
Why might a single outlier affect the interpretation of the range?
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Flashcards
True Value
True Value
The actual or exact value of a measured variable.
Measured Value
Measured Value
The best value obtained from a measurement process.
Absolute Error
Absolute Error
The difference between the measured value and the true value.
Relative Error
Relative Error
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Error in Measurement
Error in Measurement
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Dynamic Error
Dynamic Error
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Response Time
Response Time
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Sensitivity Analysis
Sensitivity Analysis
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Error Factors
Error Factors
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Immersion Length (L)
Immersion Length (L)
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Thermal Equilibrium
Thermal Equilibrium
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Assumptions in Analysis
Assumptions in Analysis
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Compounding Errors
Compounding Errors
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Lag Error
Lag Error
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Overshoot
Overshoot
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Undershoot
Undershoot
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Hysteresis Error
Hysteresis Error
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Transient Conduction
Transient Conduction
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Steady-state Value
Steady-state Value
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Standard Deviation
Standard Deviation
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Confidence Interval
Confidence Interval
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Normal Distribution
Normal Distribution
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68-95-99.7 Rule
68-95-99.7 Rule
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Measurement Uncertainty
Measurement Uncertainty
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High Standard Deviation
High Standard Deviation
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Low Standard Deviation
Low Standard Deviation
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Standard Uncertainty
Standard Uncertainty
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Random Error
Random Error
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Precision
Precision
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Systematic Error
Systematic Error
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Accuracy
Accuracy
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Uncertainty
Uncertainty
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Environmental Changes
Environmental Changes
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Measurement Bounds
Measurement Bounds
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Mean Value
Mean Value
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Average Calculation
Average Calculation
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Flow Rate Example
Flow Rate Example
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Range
Range
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Variance
Variance
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Data Distribution
Data Distribution
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Frequency Distribution Curve
Frequency Distribution Curve
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Temperature Measurement Example
Temperature Measurement Example
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Excel Average Function
Excel Average Function
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Excel Standard Deviation Function
Excel Standard Deviation Function
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Individual Measurements
Individual Measurements
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Quantifying Spread
Quantifying Spread
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Study Notes
Metrology Applied to Energy and Environmental Engineering
- Metrology is the science of measurement, applied to energy and environmental engineering.
- Error and uncertainty are crucial concepts in metrology.
- Measurements rarely equal the true value, the difference is the error.
- True value (X) or μ
- Measured (best) value (Xbest)
- Absolute error δx = |Xbest − X|
- Relative error εx = |Xbest − X| / Xbest
Types of Errors
- Measurement blunders (big mistakes)
- Systematic (bias) errors
- Dynamic errors
- Random errors
Measurement Blunders (Big Mistakes)
- These errors come from inadequacies in calibration, data acquisition system or loss of information.
- They occur due to issues with sensor placement or miscalibration.
- Data from blunders should be disregarded.
Systematic Errors - Bias
- Bias error is a consistent offset between the average indicated value and the true value.
- Repetition of measurements does not remove bias error.
- Bias error can be estimated by calibration, by concomitant methodology, or by inter-laboratory comparisons.
- Corrections for bias error must be incorporated into data.
- Example of Defects of the Instrument: uncalibrated instruments, wrong working conditions, and instrument-surveyor interaction (parallax error).
- Example of Instrument-Medium of Interest Interaction: using an immersed sensor and protection tubes (thermowells) for temperature measurements.
- Example of Cylindrical Fin: a conduction path between the support and the transducer affecting temperature measurement.
Estimation of Systematic Errors
- The level of bias error can only be estimated by comparison.
- Corrections for bias error should be incorporated into the data
- If there’s a 0.5°C overestimation in calibration for example, all results should be adjusted accordingly.
- The uncertainty associated with the calibration remains and propagates to the uncertainty in the result.
Dynamic Errors
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Dynamic error is the difference between the true value and the reading of the device, when the measured quantity is changing
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Also, response time: the speed the measurement system reacts to changes in the measured variable.
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Lag Error: the time delay between input changes and the system’s response.
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Overshoot and Undershoot: when a system initially exceeds or falls short of its final value
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Hysteresis Error: output depends on both current and past inputs.
Statistical Background – Average Value
- An average provides an estimate of the true value
Statistical Background - Quantify the Spread of Data
- One way to quantify spread is the range: the difference between the highest and lowest values
- The standard deviation (s or σ) indicates how much the readings typically differ from the average.
Statistical Background - Data Distribution
- Data distribution or the frequency distribution curve shows the number of occurrences of data with the same value.
- The Curve shows the spread of data or the frequency distribution.
Normal Distribution (Gaussian Distribution)
- For normally distributed data, the probability density function is used to determine the frequency of a specific range of values.
Standard Deviation in Metrology
- In metrology, the standard deviation is important for quantifying spread in data, and defining confidence intervals for measurements.
- A low standard deviation means consistent results.
- A high standard deviation indicates inconsistency and systematic errors, or other influences.
- Standard deviation is directly proportional to the width of the variation, and therefore used to characterize the uncertainty of a measurement.
Independent Uncorrelated Variables
- A function of several independent and uncorrelated variables. Examples are temperature sensor on either side to measure a flow meter.
Statistical Mean and Standard Deviation of a Function
- The uncertainty in the outcome of function that depends on multiple variables can be evaluated by total differential calculations.
Numerical Examples
- Provide example calculations to demonstrate the methods. These demonstrate error propagation and different scenarios.
Conclusion
- A variety of methods are available for quantifying measurement errors and uncertainties for metrology.
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Description
This quiz covers the application of metrology in energy and environmental engineering, focusing on errors and uncertainty in measurements. Participants will learn about different types of errors, including blunders and systematic errors, as well as methods to evaluate measurement accuracy.