Error & Uncertainty
The error of an instrument is the deviation from the true value of measurement. All that any measurement procedure can do is to give a value as the result which we can say may be close to the true value. We can never say that this is the true result. We can only ascertain that we have a result that may fall within a range of uncertainty.
Example: Consider that a Vernier Caliper is used to record the size of a round object that has a diameter 10 mm. And while recording it is observed that the reading on the Vernier Caliper is 10.02 mm.
Then the difference between the observed reading and actual reading is the error which is 0.02mm (in this case). This is also called the deviation.
Error = Observed Reading –Standard Reading
% Error = (Observed Reading – Standard Reading) X 100 / Standard Reading
Types of error
Systematic error – A systematic error is one that is associated with a particular measuring instrument or experimental technique.
Random error – Random error occurs due to lack of observer precision, perhaps in misreading an analogue scale due to parallax.
Reading error – The reading error in a measurement indicates how accurately a scale can be read.
Calibration error – Calibration error in a measurement indicates how well the measuring instrument has been calibrated and is usually quoted by the manufacturer.
Total error – Total occurs when more than one physical quantity has been measured and the results are combined to give a final result,
Uncertainty of Measurement
Most of the measurements that are carried out will have several factors that may affect its deviation from the true value of reading. Though they do affect the reading, it is difficult to calculate the real time value. With uncertainty we are trying to assume some of the factors and trying to measure its dispersion from the true value. Most of the factors depend on the type of instrument and their application.
Some of the factors are:
· Environmental conditions like temperature and humidity
· Human error
· Repeatability and reproducibility of the equipment
· Creep (long term stability)
· Traceability of the master (where the master was calibrated)
· Resolution of the UUC (Unit under calibration).
· Drift of the master (the deviation between consecutive calibrations of the reference equipment).
Uncertainty is calculated using Type A & Type B Errors. Type A comes from the repeatability of the readings and with training of operator it can be reduced to large extent.
Type B is basically inherent errors and cannot be easily reduced which means they constantly affect the results of measurement. Hence they are always present.
Therefore with uncertainty we are trying to produce a confidence level of 95% (approximately), with which a user can safely operate an instrument within the accepted levels of accuracy,
Ucom = Ua2+Ub2−−−−−−−−−√Ua2+Ub2
Uexp = 2 x Ucomb
Where Uexp is the expended uncertainty
Ucom is the combined uncertainty
Ua is the type A error uncertainty
Ub is the type B error uncertainty
Example of Type A error is repeatability
The different types of type B errors are
· Uncertainty of Reference equipment
· Temperature Effect
· Uncorrected Error