error calculations & types of errors

7/30/2019 Error Calculations & Types of Errors

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ANIRUDDHA MISHRA (111408)ANKIT PATHAK (111409)B.Tech. IInd YEAR

CHEMICAL ENGINEERING

ELECTRICAL &ELECTRONICS ENGINEERING

PRESENTATION


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ERROR

CALCULATIONS


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Every measurement of any value

always has some error. Therefore, every time a result ofan experiment should be

presented in the following way:X X [units];

For example (20 2)V.


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Mean value

Standard deviation

Error propagation Graphical data presentation

The least squares method

Regression errors


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where X is the mean value, n is the numberof experiments(repetitions), xi are the

results of individual experiments, and thesum extends from 1 to n.


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Accuracy of MEAN VALUE

We need to find how accurate the mean valueis.

Lets say the maximum difference of meanvalue is 1.0 A, and therefore it is called the

maximum error. This number is thereforetaken as the experimental error.

If the error exceeds 100 %, something is VERYwrong


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2.

When we have performed more than at least 5repetitions of an experiment, we can use thestandard deviation to estimate the errors.


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Standard deviation a statistical measure of the error, andcan only be applied to a large series of data (many

repetitions).


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3.

We often have values that depend on other

values. For example, voltage measured across a

resistor depends on current across it.


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4.

In some cases, we need to present our resultsgraphically, and most often there is a mathematicalfunction that theoretically describes the graph.


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5.


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We need to measure how much the experimentalvalue differs from the actual value.

For which there is introduced a coefficient of

regression


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Types of Errors

&How to reduce them


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Errors

1. Gross error

2. Systematic error3. Random error


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I. Gross error

Some gross error can be detected & some

others cannot.

Complete elimination is not possible.


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Due to humansa) may be due to misreading of

instruments.

b) Incorrect adjustments

c) Improper application of instruments

d) Computational mistakes etc.common in beginners


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Take care in reading and recording measureddata

Take at least three separate readings

(preferably under conditions in which instrumentsare switched off-on) needs good practice


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Due to improper applications faultyinsulations is predominant if device used

beyond limit Or if used in excess temp. , vibration,

pressure Or poor impedance matching


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Use devices according to the specificationsrecommended by manufactures


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If the instrument is not set to zero beforetaking measurement.

Due to variation in ambient conditions

Due to ageing


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II. Systematic error Relatively constant error frequency evident

in direct observation


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Instrumental error

eg. Irregularity of spring in galvanometerscalibration error


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Selecting a suitable instruments for theparticular measurements according toapplications

Applying correction factors after determiningthe amount of error.

Calibrating the instruments against a knownstandard


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Due to surroundings

Eg. Noise from electrical machine. Magnetic

field, temperature.


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By providing proper shielding.


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Errors due to unknown Causes.

Magnitude and direction not known

Expressed as average deviation of probaleerrors or standard deviation


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Increase the no. of readings andusing statically method


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Random errors have different magnitude

during subsequent measurements of thesame quantity.

For well behaved systems, random errors

in a measurement cause a cluster ofobserved values. We will assume that random errors arenormally distributed.

This is reasonable for large sample sizesand truly random errors


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error calculations & types of errors

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