Characteristics that change very slowly with time
The static characteristics of instruments are attributes that changes slowly with time. Static characteristics can be divided in to desirable and undesirable.
Desirable characteristics - what we want to achieve - are
Undesirable characteristics - what we want to avoid - are
- Dead zone
- Static error
- the closeness of a measurement to the true value
Relative accuracy can be expressed as
ar = (ymax - x) / x (1)
ar = relative accuracy (unit/unit)
x = input true value (unit)
y = instrument output (unit)
Example - Accuracy
The true length of a steel beam is 6 m. Three repeated readings with a laser meter indicates a length of 6.01 m, 6.0095 and 6.015 m. The accuracy based on maximum difference can be calculated as
an absolute value like
aa = 6.015 m - 6 m
= 0.015 m
or as a relative value
ar = (6.015 m - 6 m) / 6 m
= 0.0025 m/m
or as relative value in percentage
a% = ((6.015 m - 6 m) / 6 m) 100%
= 0.25 %
The accuracy of an instrument can be related to
- maximum measured value possible for the instrument
- maximum range for the instrument
- actual output from the instrument
Two terms commonly used in connection with accuracy are precision, trueness and calibration.
- Precision is the closeness of agreement among a set of results
Example - for the steel beam above all measurements are within ±0.01 m - and we could say that the precision is good.
- Trueness is the closeness of the mean of a set of measurement results to the actual (true) value
Example - for the steel beam above the mean value of the set of measurements is 6.01 m - and we could say that the trueness could have been better.
The precision of the laser meter used in the example above is good and the accuracy of the meter can be improved with calibration as
calibration = 6.01 m - 6 m
= 0.01 m
Sensitivity is the increment of the output signal (or response) to the increment of the input measured signal - and can be expressed as
s = dy / dx (2)
s = sensitivity (output unit / input unit)
dy = change instrument output value (output unit)
dx = change in input true value (input unit)
Example - Temperature measurement with a Pt100 Platinum Resistance Thermometer
When temperature is changed from 0oC to 50oC - the resistance in a Pt100 thermometer changes from 100 ohm to 119.4 ohm. The sensitivity for this range can be calculated as
s = (119.4 ohm - 100 ohm) / (50oC - 0oC)
= 0.388 ohm/oC
Repeatability is the variation in measurements taken on the same item under the same conditions.
Reproducibility is the ability of a measurement to be duplicated, either by the same person or by someone else under changed conditions.
Drift is the change in instrument output over time - when the true value is constant.
Dead zone errors are created by
Threshold is when a minimum input is required to generate change in output.
Hysteris is when unloading applied input don't creates the same output.
An example can be a nut that is screwed a number of turns on a threaded rod. When turned back the same number of turns the nut will not be in the exact the same position as at the start. This is a typical a problem that must be adressed in applications like cnc machines and 3d printers.
Creep is caused by the time an instrument need to adapt to change in aplied input.
Depending on the instrument - but minimum change in input may required for change in output.
Uncertainty in measurements or calculated values is indicated by the number of significant figures.
- Significant figures are the digits of a number known with certain certainty
The last digit in a number is taken as uncertain while the other digits are regarded as certain.
Example - Significant Figures
For the number 31.2 we regard the two first digits 30 as certain and the last digit 6 as uncertain. Unless otherwise stated an uncertainity of ±1 is assumed for the last digit.