Measurement Uncertainty and Accuracy

Measurement Uncertainty

  • Definition of Measurement Uncertainty

    • Measurement uncertainty is defined as the doubt that exists regarding the result of a measurement.

    • Refers to the range within which the true value is expected to lie.

    • The term uncertainty is denoted by the symbol u.

Types of Measurement Uncertainty

  • Measurement uncertainty can be classified into two primary types:

    1. B Type Uncertainty

    • Applicable when only a single measurement is made without repetition.

    • Example: If a measurement is taken once, the uncertainty evaluated is B type uncertainty.

    • Determination of B type uncertainty is usually done as part of laboratory work where only one instance of measurement is made.

    1. A Type Uncertainty

    • Applicable in cases where a series of measurements are made multiple times (which may include hundreds or thousands of measurements).

    • In practice, most measurements in laboratory scenarios are often a single measurement (B type).

Calculating B Type Measurement Uncertainty

  • The formula for determining the maximum permissible error (MPE) is crucial for calculating measurement uncertainty:

    • Formula:
      ext{MPE} (Maximum Permissible Error)

    • Sometimes referred to as Limiting Error, both terms can be used interchangeably.

  • The determination of MPE may involve considering the type of meter employed for measurements (e.g., analog vs. digital).

Determining MPE Using Analog Meters

  • For analog meters, the manufacturer specifies a parameter known as Class of Accuracy, which is vital for determining MPE.

    • Class of accuracy informs the user the precision of the measurement device.

    • Example: A provided class of accuracy value is 0.5.

  • Class of Accuracy Formula for MPE in Analog Meters:

    • ext{MPE} = ext{(Class of Accuracy)} imes ext{(Range)} / 100

    • This formula expresses MPE as a percentage based on the range the meter is set to.

Analyzing the Class of Accuracy Formula

  • The two known parameters in the formula are:

    1. Class of Accuracy (provided by the manufacturer).

    2. Range (maximum measurable value determined by adjusting settings on the device).

  • The only variable is the MPE which can be calculated using known parameters.

Importance of Minimizing Measurement Uncertainty

  • From a practical standpoint, the goal is to minimize measurement uncertainty. A smaller uncertainty leads to:

    • Higher precision in measurements.

    • To minimize uncertainty individuals should strive for:

    • Small MPE values.

    • Utilize meters with lower class of accuracy, which signifies better precision.

    • For example, selecting a device with a class of accuracy 0.5 over one with 1.5 will yield more reliable results.

Reading Measurements from Analog and Digital Meters

Analog Meter Reading Procedure

  • To read from an analog meter:

    1. Identify the number of divisions on the scale where the pointer currently indicates (denote as I).

    2. The pointer should be approximated to the closest full division without estimating its fractional part (e.g., if between two divisions, round to the nearest whole).

    3. Factor in the range settings to read the corresponding measurement value properly.

  • Calculation of Measured Value for Analog Meters:

    • ext{Measured Value} = rac{ ext{Number of Divisions}}{ ext{Scale Range}} imes ext{Range}

    • Measurements expressed in volts.

Digital Meter Reading Procedure

  • Digital meters present results directly, minimizing the calculation needed:

    1. Simply read the measurement output displayed on the screen, representing the voltage in volts (e.g., 10.19 volts).

  • Calculating MPE for Digital Meters:

    • Formula structure:

    • ext{NPV} = 0.5 imes ext{RDG} + 4 imes ext{DGT}

    • Coefficients may vary based on the specific range set on the meter.

Definitions of Key Terms in Digital Meters

  • RDG (Reading): Represents the measured value given directly from the device.

  • DGT (Last Digit):

    • Refers to the decimal position for the last character shown in the reading. Actual measurement adjustments are made based on its placement, e.g., values such as 1, 0.1, and 0.001 can rely on where the decimal point is noted.

Final Steps

  • Shift focus to practical applications:

    • Group teams to practice measuring scenarios using analog and digital meters, consolidating theoretical knowledge into feasible actions.

    • Emphasis on understanding device specifications and how they affect accuracy and precision in real-world measurements.