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

• Clearly define what is being measured and the conditions under which the measurements are made.
• Specify the instruments and techniques used for the measurement.

• Example of Temperature measurement process: How to Measure Temperature in Experiments with Best Methods

• Example of Pressure measurement process: Measurement of Fluid Pressure: Principles and Devices

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_cuc​) is given by: