Errors In Measurement Systems

Chapter 7 Errors in Measurement Systems

Errors in the measurement of a physical quantity are defined as its deviation from actual value. Understanding the factors that contributes to measurement errors is very important. This helps to determine and design the appropriate measures to improve accuracy of the instruments up to the larger extent possible.. Measurement errors are classified into following main categories Measurement Error

Any measurement made with measuring devices or instruments is approximate to certain extent. If the measurand of certain quantities are repeatedly measured a number of times, measured value may not be the exactly same. The difference in the measured value in repeated measurement of same quantity is called the

For instance some cup anemometers with high mass or inertia cannot detect small wind speeds.

II Calibration \

The processes used to maintain instrument accuracy is called instrument calibration and it is used to configure an instrument to provide a result for a sample within an acceptable range.

It ensures the accuracy of test equipment and minimizes any measurement uncertainty. In addition, it also quantifies and controls errors or uncertainties within measurement processes to an acceptable level.

Calibration errors are another type of instrument errors. Calibration of all instruments are essential and it should be performed against a standard instrument that is very accurate Instruments are calibrated according to mathmatical theory, standards and sub standard instruments.

III Ageing Effects of Instruments

All instruments are assigned a finite lifespan of their use even when they are frequently calibrated. Electronic instruments drift with ageing and introduce drift errors while instruments having moving parts normally experience hysteresis

- - - (7.6)

The above is a quotient. For these numbers, the relative uncertainty limits are 0.74% for Force (F), and 0.080% for acceleration (a).

According to Rule 2 uncertainty of both force and acceleration are added to get the relative uncertainty limit of the quotient m, which is 0.82%. The value of m determined in this way is then (17.53 N)/(2.504 m/s2) = 7.0008 kg,

And the absolute uncertainty limit in kilograms is 0.82% of 7.0008 kg, or 0.057 kg: m = 7.001 ± 0.057 kg

Note that the value of m is rounded off here to three decimal places. That’s because the uncertainty of m (0.057 kg) was in the second and third decimal places, so there can be no meaning to the numeral “8” in the fourth decimal place of m.

Solved Example 7.9 The resistance of a circuit is found by measuring current flowing and the power fed into the circuit. Find the relative limiting error in the measurement of resistance when the limiting errors in the measurement of power and current are respectively ±2.5% and ±1%.

Solution

P = I2 R - - - (7.7)

R = P / I2 - - - (7.8)

The percentage errors can be expressed as,

(ΔR / R) 100 = (ΔP / P ) 100 + 2 (ΔI / I ) = 2.5 + 2 x 1= 4.5 % - - - (7.9)

Error in the measurement of R is ± 4.5