Ch2-Error in Measurement

8/13/2019 Ch2-Error in Measurement

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INSTRUMENTATION &

MEASUREMENT

Chapter 2:

Error InMeasurement


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CHAPTER OBJECTIVES

In this chapter, student should be able to:

a) Define termsrelated to the error in

measurements.

b) Use basic concept of measurement in error

analysis.

c) Perform basic statistic analysis calculations.


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ERROR IN MEASUREMENT

a) Absolute Error = Expected ValueMeasured Value

a) Percent Error =

nn XYe


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Relative accuracy and percent

accuracy

c) Relative Accuracy, A=

d) Percent of accuracy

Accuracy can be expressed as percent of

accuracy, a, is:

n

nn

Y

XY 1


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Question 1

1. The expected value of the voltage across a

resistor is 50V; however, measurement yields

a value of 49 V. Calculate:

a) The absolute error

b) The percent of error

c) The relative accuracyd) The percent of accuracy


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ACCURACY

Accuracyrefers to how close a measurement

is to the correct/accepted value.

Precisionrefers to the degree of agreement

with a group of measurement or instruments.

n

nn

X

XX

precision

1


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ACCURATE VS PRECISE

Accurate-> after taking a lot of

measurements, you find they agree with the

true value

Precise-> after taking a lot of measurements,

you notice that they are all very close to each

other.


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Precision

Calculate the precision of the fourth

measurement Measurement Output Voltage,V

2 12.11

2 11.99

3 13.004 11.88

5 11.99


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TYPES OF ERROR

Types of Error

Gross Error

SystematicError

InstrumentalError

ObservationalError

EnvironmentalError

Random Error


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Gross Errors

Caused by the fault of the person using the

instrument, incorrect recording of

experimental data, incorrect adjustment and

improper application of instruments and

computational mistakes.

How to avoid gross errors???


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Avoiding Gross Error

The following actions may be necessary to

reduce the effects of gross errors:

Great care should be taken in reading and

recording the data.

Different experiments should take two or more

readings of the same measured quantity.


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Systematic Errors

a) Instrument errors: Caused by the construction, calibration or operation

of mechanical structure in the instruments.

Misuse of the instruments. For example, these may

be caused by failure to adjust zero of the

instruments.

Loading effect of the instruments


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Systematic Errors

b) Observational errors.

Observational errors are those errors introduce by

the observer. The two most common

observational errors arise due to two mainreasons:

Type of instrument display, whether it is analog or

digital

Parallax (eye should be directly in-pine with the

measurement point).


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Systematic Errors

c) Environmental errors.

Due to condition external to the measuring

device such as the area surrounding the

instrument.

These conditions may be caused by the changes

in pressure, humidity, dust, vibration or external

magnetic or electrostatic fields.


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Avoiding Systematic Errors

These errors can be eliminated or at least

reduced by using the following methods:

The procedure of measurement must be

carefully planned

Correction factors should be applied after

detection of these errors

Re-calibration the instrument carefully

Use the instrument intelligently


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Random Errors

Due to unknown causes.

In some experiments, the results show

variation from one reading to another; even

after all systematical and gross errors have

been accounted for.

The best way to offset the errors is by

increasing the number of readings and use

statistical means to obtain the approximation

of the true values of the quantity under

measurement.


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STATISTICAL ANALYSIS IN

MEASUREMENT

The evaluation based on a statistical analysis a

Allows us to obtain such information as the

mean value, average deviationand standard

deviationof our data.

Such information allows us to make

quantitative judgments on the variations or

error in our data.


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MEASUREMENT

Mean value / Arithmetic mean

n

xxxxx n

....321

Deviation


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MEASUREMENT

Average Deviation

n

dddD n

....21

Standard Deviation

n

ddd n22

2

2

1 ...


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Example

a) The arithmetic mean

b) Deviation of each value

c) Sum of the deviations

d) Average Deviation

e) Standard Deviation

,

,

,

1.501 x 7.49

2 x 6.49

3 x 2.50

4 x


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Question 2

Table 1 showsthe output voltage of an amplifier

was measured by the student. Calculate the:

a) Arithmetic mean.

b) Algebraic sum of deviation.c) Average deviation.

d) Standard deviation.

Measureme

nt

Output

Voltage, V

1 12.11

2 11.99

3 13.00

4 11.885 11.99


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LIMITING ERROR

Most manufactures of measuring instruments

state that an instrument is accurate within a

certain percentage of a full-scale reading.

The limits of these deviations from the

specified values are known as limiting errors

or guarantee errors.


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LIMITING ERROR

For example, the manufacture of a certain

voltmeter may specify the instrument to be

accurate within with full-scale deflection.

This specification is called limiting error and

means that a full-scale reading is guaranteed

to be within the limits of 2%of a perfectly

accurate reading


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LIMITING ERROR

Another example, if the resistance of a resistor

is given as 5000 10%, the manufacturer

guarantees that the resistance is between

4500 and 5500 (limiting error is 10% of 5000i.e. 500).


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Question 1

1. A 300V voltmeter is specified to be accurate

within 2% at full scale. Calculate the limiting

error when the instrument is used to

measure a 120V source.


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Question 2

1)The resistor has three different ratings:

R1 = 15 5%

R2 = 33

2%R3 = 75 5%

Determine the limiting errors for all the three

resistors.


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Assignment 1

Given the resistors with following rating:

R1=505%

R2=60

5% Determine:

i. Magnitude of error in each resistor

ii. If the resistors are connected in series, calculate the

resistance and limiting error in ohms and in percentage.

iii. If the resistors are connected in parallel, calculate the

resistance and limiting error in ohms and in percentage.


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EXERCISE 2

The current in a certain circuit was measured and the

results are tabulated as shown in following data.

Ch2-Error in Measurement

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