Errors in measurement

 Sources of Errors

In the process of measurement, errors are bound to occur. If the sources of errors are known, then efforts can be made to reduce them and partly eliminate them. The various possible sources of errors are,

1. Faulty design of the instrument which directly leads to the serious measurement
   errors.
2. Due to insufficient knowledge of the quantity to be measured and the design
   conditions can cause errors.
3. For the instruments frequent maintenance is necessary. If such maintenance is not done then errors may occur.
   
4. If there are irregularities in quantity to be measured or sudden changes in the
   parameter to be measured then errors may exist.
5. The unskilled operator of the instrument can cause serious errors.
6. The certain limitations while designing the instrument can cause errors.
7. Loading effect i.e. improper way of using the instrument can cause errors.
8. The effects of environmental conditions, temperature changes, and stray capacitances also can cause the errors. Proper care taken considering the sources of errors can help to reduce the percentage of errors and to improve the accuracy of measurement.

Types of Errors:

The static error is defined earlier as the difference between the true value of the variable and the value indicated by the instrument. The static error may arise due to a number of reasons. The static errors are classified as

1) Gross errors 2) Systematic errors 3) Random errors

1. Gross Errors

Gross errors mainly occur due to carelessness or lack of experience in a human
being. These cover human mistakes in readings, recordings and calculating results. These errors also occur due to incorrect adjustments of instruments. These errors cannot be treated mathematically. These errors are also called personal errors. Some gross errors are easily detected while others are very difficult to detect.

The complete elimination of gross errors is not possible but one can minimise them
by the following ways

1. Taking great care while taking the reading, recording the reading and calculating
   the result
   
2. Without depending on only one reading. At least three or even more readings be taken and preferably by different persons. The readings must be taken must preferably under the conditions in which the instruments are switched on and off.

Systematic Errors:

Systematic errors mainly result due to the shortcomings of the instrument and the characteristics of the material used in the instrument, such as defective or worn parts, ageing effects, environmental effects, etc.

A constant uniform deviation of the operation of an instrument is known as a systematic error.

There are three types of systematic errors ns
1) Instrumental errors 2) Environmental errors 3) Observational errors.

1) Instrumental errors 

These errors can be mainly due to the following three reasons.

a) Shortcomings of Instruments:

These are because of the mechanical structure of the instruments. For example, friction in the bearings of various moving parts, irregular spring tensions, reduction in tension due to improper handling,

hysteresis, gear backlash, stretching of spring, variation in air gap, etc. These errors can be avoided by the following methods

1) Selecting a proper instrument and planning the proper procedure for the measurement.

2) Recognizing the effect of such errors and applying the proper correction factors.

3) Calibrating the instrument carefully against a standard.

b) Misuse of Instruments: A good instrument if used in an abnormal way gives misleading results. Poor initial adjustments, improper zero setting, using leads of high resistance etc. are examples of misusing a good instrument. Such things do not cause permanent damage to the instruments but definitely cause serious errors.

c) Loading Effects: Loading effects due to improper way of using the instrument cause serious errors. The best example of such loading effect error is connecting a well-calibrated voltmeter across the two points of high resistance circuit. The same voltmeter connected in a low resistance circuit gives accurate readings. Thus, the errors due to the loading effect can be avoided by using an instrument intelligently and correctly.

2) Environmental errors

These errors are due to the conditions external to the measuring instrument The various factors resulting in these environmental errors are temperature changes, pressure changes, thermal e.m.f., stray capacitance, cross capacitance, the effect of external fields, ageing of equipment and frequency sensitivity of an instrument. 

The various methods which can be used to reduce these errors are
1. Using the proper correction factors and using the information supplied by the manufacturer of the instrument.
2. Using the arrangements which will keep the surrounding conditions constant. This includes the use of air conditioning, temperature control enclosures etc

3. Reducing the effect of dust, and humidity on the components by hermetically sealing the components in the instruments.

4. The effect of external fields can be minimized by using the magnetic or electrostatic fields or screens.

5.Using the equipment which is immune to such environmental effect.

3) Observational errors

These are the errors introduced by the observer. There are many sources of observational errors such as parallax error while reading a meter, wrong scale selection, the habits of individual observers etc. To eliminate such observational errors, one should use instruments with mirrors, knife-edged pointers, etc. Nowadays, instruments with digital displays are available which can largely eliminate such observational errors.

Systematic errors can be subdivided into static and dynamic errors. The static error is caused by the limitations of the measuring device while the dynamic errors are caused by the instrument not responding fast enough to follow the changes in the variable to be measured.

Random Errors

Some errors still result, though the systematic and instrumental errors are reduced or at least accounted for. The causes of such errors are unknown and hence, the errors are called random errors. These errors cannot be determined in the ordinary process of taking the measurements.

These errors are generally due to the accumulation of a large number of small effects. These errors are generally small. Hence, these errors are of real concern only when a high degree of accuracy is required.

The random errors follow the laws of probability and hence, these errors can be analyzed statistically and treated mathematically. These errors cannot be corrected by any method of calibration or other known methods of control as the causes of such errors are unknown. The only way to reduce these errors is by increasing the number of observations and using statistical methods to obtain the best approximation of the reading.