# Errors in Measurement

Gross errors: Largely human errors, among them misreading of instruments, incorrect adjustment and improper application of instruments.

Errors in Measurement

Gross errors: Largely human errors, among them misreading of instruments, incorrect adjustment and improper application of instruments.

Systematic errors: Short coming of instruments such as defective or worn parts, andeffects of environment on the equipment or the user.

Random errors: Those dueto causes that can’t be directly established because ofrandom variation in the parameter or the system of measurement.

Errors are to be expected; they are intrinsic in the physical processes of measurement making. Categories of measurement errors and some subcategories, as follows.

## Theoretical errors:

The explicit or implicit model on which we base our interpretation of our measurements may be inapplicable or inaccurate.

Range of Validity: A model is applicable only within a limited range of Conditions.Be-yond that, it will give inaccurate predictions.

Approximation: Models have finite precision even within their range of validity

## Static errors:

Due to misreading, or a difficulty in accurately reading, the display of the instrument.

i. Parallax: Analog meters use a needle as a pointer to indicate the measured value. Reading this at an oblique angle causes a misreading, known as a parallax reading error.

ii. Interpolation: The needle often rests between two calibrated marks. Guessing its position by interpolation is subject to an error that depends on the size of the scale, and on the visual acuity and experience of the person reading the meter.

iii. Last-digit bobble: Digital readouts re often observed to oscillate between two neighboring values, for example a digital voltmeter (DVM) may alternately show 3.455 and 3.456 volts. This occurs when the actual value is about midway between the two displayed values. Small variations in the system under test, or in the meter itself, are sufficient to change the reading when it is delicately poised between the two values.

## Environmental errors:

Measurements can be affected by change in ambient factors

I.                Temperature

II.              Pressure

III.          Electromagnetic field: Static electric or magnetic f i e l d s , dynamic (changing) fields, and propagating fields (radiation) can interfere with measurements.

A particularly common example is the mains electricity supply, which is ideally a  sinusoid; in Australia this is specialized to have a frequency of 50 Hz. In reality, mains  power is not a pure sinusoid, so it contributes interference at other frequencies also.

## Characteristic errors:

Static errors intrinsic to the measuring instrument or process. Physical limitation and manufacturing quality control are factors in several characteristic errors.

Incorrect calibration can also contribute Manufacturing tolerance: Design and manufacturing process a r e frequently in- exact. For example, the calibrated marks on a ruler are not1.0000 millimeters apart. Hopefully some will be slightly above and some slightly below, so that over a series of measurements these errors will be random and so balance out, but they might not the errors in the manufacturing process of one or more batches of rulers might be systematically biased.

Zero Offset: a meter (for example) may read zero when the actual value is nonzero. This is a common form of calibration error.

Gain error: amplifiers are widely used in instruments such as CRO probes, and we may trust that “times 10” means precisely what it says only when the amplification has been carefully calibrated.

Processing error: modern instruments contain complex processing devices such as analog computers which can introduce errors into the process leading to thedisplayed value of a measurement. Digital devices have f i nite precision (see quantization errors, below) and are occasionally wrongly programmed: a small programming error often produces large errors in the results.

Repeatability error: instruments change over time, which is why they must be regularly calibrated, just as a car must be serviced. Instruments change, however slightly, even between consecutive measurements. The act of measurement itself may affect the instrument, for example spring scales lose some elasticity with every use.

Nonlinearity: ideally, an instrument designed to be linear has an output which is proportional to its input, but this is only approximately true, and then only within a range of validity. Drive an amplifier to too high a gain and it will operate in its nonlinear regions, producing a severely distorted output signal.

Resolution: devices can only resolve (that is, distinguish) values that are sufficiently separated .For example, optical instruments cannot easily resolve objects less than one wavelength apart.

## Drift:

It is now necessary to consider a major problem of instrument performance called instrument drift . This is caused by variations taking place in the parts of the instrumentation over time. Prime sources occur as chemical structural changes and changing mechanical stresses.

Drift is a complex phenomenon for which the observed effects are that the sensitivity and offset values vary. It also can alter the accuracy of the instrument differently at the various amplitudes of the signal present.

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