Determination of Uncertainty in Measurement of Pressure and Temperature

Steps in Uncertainty Calculations

  • Determining the uncertainty of pressure and temperature measurement devices involves a series of steps to assess and quantify the possible errors in measurements.
  • Determining the uncertainty in measurements involves several systematic steps to ensure accuracy and reliability. Here’s a detailed outline of the steps involved in uncertainty calculations:

Steps in Uncertainty Calculations

1. Define the Measurement Process

2. Identify Sources of Uncertainty

  • List all potential sources of uncertainty that might affect the measurement. These can include:
    • Instrument resolution
    • Calibration uncertainty
    • Environmental conditions
    • Measurement procedure
    • Operator influence
    • Drift over time

3. Quantify Individual Uncertainties

  • Manufacturer Specifications: Refer to the instrument’s manual or data sheet to find the specified uncertainties.
  • Calibration Data: Use uncertainties provided in the calibration certificate of the instrument.
  • Experimental Data: Conduct repeated measurements and statistical analysis to determine the standard deviation (repeatability).
  • Environmental Effects: Evaluate the influence of environmental conditions on the measurement.

4. Convert Uncertainties to Standard Uncertainties

  • If uncertainties are not already given as standard deviations, convert them. For example:
    • For a rectangular distribution (e.g., resolution), the standard uncertainty is the half-width divided by the square root of 3:
    • For a triangular distribution, the standard uncertainty is the half-width divided by the square root of 6:

5. Combine Standard Uncertainties

  • Combine the individual standard uncertainties using the root sum of squares (RSS) method to find the combined standard uncertainty (ucu):

6. Determine the Expanded Uncertainty

  • Multiply the combined standard uncertainty by a coverage factor (k) to obtain the expanded uncertainty (U).
  • The coverage factor depends on the desired confidence level (e.g., k=2k for approximately 95% confidence):
  • U=k⋅uc

7. Report the Uncertainty

  • Report the measurement result along with the expanded uncertainty and the confidence level.
  • For example: Measured value  at 95% confidence level

Example Calculation for Pressure Measurement

  1. Measurement Process:
    • Measuring pressure using a digital pressure gauge.
    • Conditions: room temperature, stable environment.
  2. Identify Sources of Uncertainty:
    • Instrument resolution: ±0.1 kPa
    • Calibration uncertainty: ±0.2 kPa
    • Environmental factors: ±0.05 kPa
    • Repeatability (standard deviation from repeated measurements): ±0.1 kPa
  3. Quantify Individual Uncertainties:
    • Instrument resolution (U1)
    • Calibration uncertainty (U2)
    • Environmental factors (U4)
    • Repeatability (U5)
  4. Combine Standard Uncertainties, Uc= U1 + U2,+ U2+……+Un
  5. Determine the Expanded Uncertainty:

 Identify the Sources of Uncertainty

For both pressure and temperature measurement devices, uncertainties can arise from several sources, including:

  • Instrument Resolution: The smallest change that can be detected by the instrument.
  • Calibration: Uncertainties associated with the calibration process.
  • Environmental Factors: Temperature, humidity, and other environmental conditions affecting the measurement.
  • Drift: Changes in the instrument’s performance over time.
  • Measurement Procedure: Variations introduced by the method of measurement.
  • Operator Influence: Differences in how different operators use the instrument.

 Quantify Each Source of Uncertainty

Each identified source of uncertainty needs to be quantified, usually in terms of a standard deviation. This can be done through:

  • Manufacturer Specifications: Use the instrument’s data sheet to find specified uncertainties.
  • Calibration Certificates: Refer to the calibration certificate for uncertainties associated with the calibration process.
  • Repeatability Studies: Perform repeated measurements to assess the repeatability of the instrument.

3. Combine the Uncertainties

  • Combine the individual uncertainties to obtain the overall uncertainty using the root sum of squares (RSS) method.
  • The combined standard uncertainty (ucu_c) is given by:
Formula for Uncertainty calculations
Formula for Uncertainty calculations

Expanded Uncertainty

  • To express the uncertainty with a higher level of confidence, calculate the expanded uncertainty (U) by multiplying the combined standard uncertainty by a coverage factor (kk), typically 2 for a 95% confidence level.
  • U

Example of Pressure Measurement Device

  1. Instrument Resolution: ±0.1 kPa
  2. Calibration Uncertainty: ±0.2 kPa
  3. Environmental Factors: ±0.05 kPa
  4. Repeatability: ±0.1 kPa
  5. Combined Standard Uncertainty: U=2*0.25=0.5 kPa
Examples of Pressure Uncertainty calculations
Examples of Pressure Uncertainty calculations
Type of pressure measurement methods
Type of pressure measurement methods

Example of Temperature Measurement Device

  1. Instrument Resolution: ±0.1°C
  2. Calibration Uncertainty: ±0.15°C
  3. Environmental Factors: ±0.05°C
  4. Repeatability: ±0.1°C
  5. Combined Standard Uncertainty:U=2*0.212=0.424°C
Examples of Temperature Uncertainty calculations
Examples of Temperature Uncertainty calculations
Temperature measurement Devices and its Types
Temperature measurement Devices and its Types

Conclusion

  • By following these steps, you can determine the uncertainty of pressure and temperature measurement devices, providing a quantifiable measure of the confidence in your measurements

Reference

  1. Michalski et al, Estimating uncertainty of temperature measurements

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