(signal to noise ratio).pdf
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SIGNAL TO NOISE S/N) RATIO
GROUP-2ANKIT SAXENA (PGMSE 136013)
VIVEK GUPTA (PGMSE136016)
ANAND PRAKASH (PGMSE136021)
VAIBHAV SHARMA (PGMSE136024)
SHEM DEBBARMA (PGMSE136027)
Submitted to :- DR. JAGTAR SINGH
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INTRODUCTION Taguchi has proposed various performance measures known as
Signal-to-Noise (S/N) ratio for evaluating the performance of
engineering systems.
The concept of signal (S) to noise (N) ratios has high visibility in
design of experiment circles due to the work of Taguchi to carry out
complete analysis.
The signal is what you are measuring that is the result of the
presence of your action.
Noise is extraneous information that can interfere with or alter thesignal.
It can not be completely eliminated, but hopefully reduced. Noise is
considered random.
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EnergyTransformation
Noise
Squeal
Wear
Heat
Signal Slow Car
Fig. 1 Block diagram showing concept of S/N ratio
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Since noise can not be eliminated (it is random), we are more
interested in the S/N ratio than the intensity of the noise.
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S/N OBJECTIVE?
Reduce as much of the noise as possible by carefully controlling
conditions
Temperature, power supply variations, etc.
Increase the signal to noise ratio
More signal vs. noise means a lower Standard Deviation.
More precise measurement
Lower St. Deviation means a better LOD
Lower limits of detection
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TYPESOFNOISE..
Chemical Noise:
Undesired chemical reactions.
Reaction/technique/instrument specific.
Instrumental Noise:
Affects all types of instruments.
Can often be controlled physically (e.g. temp) orelectronically (software averaging).
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Thermal (Johnson) Noise:
Thermal agitation of electrons affects their smooth flow.
Due to different velocities and movement of electrons in
electrical components.
Dependent upon both temperature and the range of
frequencies (frequency bandwidths) being utilized.
Can be reduced by reducing temperature of electrical
components.
Eliminated at absolute zero.
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Flicker Noise:
Frequency dependent.
Magnitude is inversely proportional to frequency.
Significant at frequencies less than 100 Hz.
Results in long-term drift in electronic components.
Can be reduced by using resisters that are metallic, wire
wound.
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Environmental noise: Unlimited possible sources.
Can often be eliminated by eliminating the source.Other noise sources can not be eliminated.
Methods of eliminating it
Moving the instrument somewhere else.
Isolating /conditioning the instruments power source.Controlling temperature in the room.
Control expansion/contraction of components ininstrument.
Eliminating interferences
Stray light from open windows, panels oninstrument.
Turning off radios, TVs,other instruments.
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There are many different S/N Ratios. The important
S/N ratios are:
Nominal the Best
Target the Best
Smaller the BetterLarger the Better
Dynamic
Classified Attribute.
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NOMINAL-THE-BEST :
This case arises when a specified value is MOST desired,
meaning that neither a smaller nor a larger value is desirable.
n = 10 log10(square of mean/ variance)
Examples are;
(i) most parts in mechanical fittings have dimensions which
are nominal-the-best type.
(ii) Thickness should be uniform in deposition /growth
/plating /etching.
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Fig. 2 Robust Design without noise
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Fig. 3 Robust Design with noise
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SMALLERTHEBETTER:
This is usually the chosen S/N ratio for all undesirable
characteristics like " defects " etc. for which the ideal value is
zero.
n = -10 Log10[ mean of sum of squares of measured data ]
Also, when an ideal value is finite and its maximum or
minimum value is defined (like maximum purity is 100% or
maximum Tc is 92K or minimum time for making a telephone
connection is 1 sec) then the difference between measured
data and ideal value is expected to be as small as possible. Thegeneric form of S/N ratio then becomes
n = -10 Log10[ mean of sum of squares of {measured -
ideal} ]
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Fig. 4 Automotive emission
The S/N ratio for
smaller the better is
used for the situations
where the target value
is zero, such ascomputer response
time, automotive
emission or corrosion.
S/N= -10 Log10(MSD)
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The negative sign is used to ensure that the largest value
gives the optimum value for the response variable and ,
therefore, Robust design.
Mean standard deviation is given to show the
relationship to the loss function.
Loss function is an ideal measure for quality of products
as it is shipped by the supplier to the customer.
Minimizing loss function leads to quality improvement.
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Larger the Better :-
It is used where the largest value is desired such
as weld strength, gasoline mileage or yield.
Mathematically the largest value is 00 like thelost function. It is the reciprocal of smaller the
better .
n = -10 Log10[mean of sum squares ofreciprocal of measured data]
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S/N RATIOS FOR DYNAMIC PROBLEMS
Types of Dynamic Problems:
Continuous - Continuous type ( C - C )
Continuous - Digital type ( C - D ) Digital - Continuous type ( D - C )
Digital - Digital type ( D - D )
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CONTINUOUS - CONTINUOUS
TYPE PROBLEM
Both signal factor and quality characteristics take
positive or negative values.
When signal m = 0,Quality characteristic = 0,
Ideal function y = m
Scaling factor exists to adjust slope (proportionality
constant) between y and m.
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CONTINUOUS- DIGITALTYPE( C- D)
temperature controller
input temperature setting - continuous
output of heating unit - ' on ' or ' off
divide into two separate problemsone for ' on ' function
other for ' off ' function
each one continuous - continuous type or nominal
- the - best type problem
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DIGITAL - CONTINUOUS TYPE ( D - C )
digital to analog converter
conversion to ' 0 ' and ' 1
divide into two separate problems
one for ' 0 ' functionother for ' 1 ' function
each one continuous - continuous type or nominal
- the - best type problem
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CONCLUSION
Signal-to-Noise ratio is also one more contribution of
Taguchi.
We came across different types of noise which affect the
performance of the system.
Thermal noise can only be eliminated if temperature is
absolute zero.
Environmental noise can be eliminated by certain
methods as explained.
Nominal-the-best is used when a specified value is
MOST desired.
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Smaller-the-better is used for undesirable values such as
defects, automotive emission, corrosion etc.
Larger the better is used where the largest value isdesired such as weld strength, gasoline mileage or yield.
Taguchi strongly recommended this approach for
multiple runs.
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