Systematic and Accidental Errors

• There are 2 classes of measurement errors: systematic and accidental.
• Systematic errors influence all measurements in the same way.
• Accidental errors are random and unpredictable.
• Analyzing errors helps to avoid them, use diagnostic tools to recognize them, and apply necessary corrections.

Systematic Errors

• Systematic errors affect all measurements.
• They produce a constant shift or a slow variation between the true and measured value.
• Possible detection methods include theoretical calculation to verify order of magnitude and using different measurement methods/instruments.
• It's often possible to avoid, reduce, or correct them after the measurement.

Systematic Errors (cont.)

• Error can occur on the value of a reference quantity.
• Common causes when using sensors with electronic circuits are zero drift (offset), an erroneous reference quantity value, and an inaccurate supply voltage.
• Correction involves careful verification of devices.
• Experimental work requires a lot of attention, and calibrating new sensors is suggested.

Systematic Errors (cont.)

• Error can occur on the sensor's characteristics.
• Causes include erroneous calibration coefficients and calibration changes due to aging/mechanical fatigue.
• Correction involves frequent recalibration, especially for sensors used in severe conditions or over long periods.

Accidental Errors

• Accidental errors' randomness relates to the moment of appearance, amplitude, and sign.

Internal Errors

• Reading error Eℓ occurs.

• Analog devices have a reading error of half of the smallest division.

• Digital devices either have no reading error if the value is fixed, or the extreme values should be evaluated and the half used when variable.

• Mobility error Em is the maximum variation of the measurand that doesn't cause a detectable variation in the sensor output and isn't present for all sensors.

• Resolution error Er is the quadratic sum of the mobility and reading errors.

• Threshold error Es is the resolution error calculated at zero.

• Hysteresis error Eh is defined relatively.

• If m increases, s' = f'(m) is obtained.

• If m decreases, s" = f"(m) is obtained.

• The maximum difference between s' and s" found at measure i is calculated as Δ = ½|s'(mi) - s"(mi)|.

• Hysteresis error is expressed as Eh = Δ / EM, relative to the measurement span EM.

Influence on External Sensor Errors

• Two cases can occur, depending on the measurement duration:
• Rapid measurement results in systematic error.
• Slow measurement results in accidental error.
• Temperature or ambient pressure affecting the measurement can cause a zero shift or sensitivity change.

Errors from Exceeding Linearity Range

• L₁ is the supposed response, L₂ is the real response, and x is the error.
• There's a risk of breaking the device.
• This shouldn't be confused with a normal slope change for certain devices.