Relative Limiting Error in the context of Measurement and Instrumentation refers to the maximum permissible error allowed in a measurement, expressed as a fraction or percentage of the full-scale measurement value. It helps to define the accuracy of an instrument and provides a range within which the measured value can deviate from the true value while still being considered acceptable.
The relative limiting error takes into account both systematic errors (which include calibration errors, zero errors, etc.) and random errors (which are typically associated with noise and variability in the measurement process). It gives users an idea of the instrument's performance and how much confidence they can have in the reported measurements.
Mathematically, the relative limiting error (ε) is calculated using the following formula:
=
Maximum Permissible Error
−
×
100
%
ε=
textFull−ScaleReading
Maximum Permissible Error
×100%
Where:
Maximum Permissible Error: The maximum allowable difference between the measured value and the true value.
Full-Scale Reading: The maximum value that can be measured by the instrument.
For example, let's say you have a digital thermometer that measures temperatures in the range of -50°C to 150°C with a maximum permissible error of ±0.5°C. The full-scale reading would be 150°C, and the relative limiting error would be:
=
0.5
°
150
°
×
100
%
≈
0.33
%
ε=
150°C
0.5°C
×100%≈0.33%
This means that the instrument's measurements can deviate by up to 0.33% of the full-scale reading (or ±0.5°C in this case) and still be considered accurate within its specified limits.
In summary, the relative limiting error provides a standardized way to communicate the acceptable level of error in measurements made by an instrument. It helps users understand the precision and reliability of the instrument's readings and aids in making informed decisions based on the measurements taken.