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```Measurement Uncertainty
Overview
• Factors which decide System
Performance
• Types of Error in Measurement
• Mean, Variance and Standard Deviation
• Error = Xm - Xtrue
Xm-> Measured Value
Xtrue->Actual Value
•What is the “true” value?
•Is it possible to take measurement data without any
error?
•What is the source of error?
•How can we minimize the impact of these errors ?
System Performance Depends on
the following factors :
->System accuracy is the magnitude of the
maximum expected error. Usually specified as
percentage of full scale.
->System precision is an estimate of repeatability
.The more precise a system, the less random error
affects the result.
->System resolution is the smallest possible
discernible increment .Higher the resolution, smaller
the smallest increment !
Types of Error
• Systematic errors (or “bias” errors):
Occur in a repeatable fashion (i.e., every time a
measurement is made under similar conditions).
• Offset error: is a constant error which occurs
every time a measurement is taken.
Offset Error: Xm = Xtrue ± Constant
Xm=Measured value
Xtrue=Actual value
Types of Error contd.
• Scale error:
Xm = Xtrue x Constant
implies Xtrue = Xm / Constant
• Nonlinear errors:
Can result from poor design or from
inappropriate system use Ex: y= x2, y =
cos xt, or y = log x
Types of Error contd.
• Drift Errors:
• Ambient temperature, humidity and aging
can change the characteristics of an
electronic component.
• Random errors: Absolutely random in
nature !
Definitions
Sample median - The middle value when
the measurements are arranged from
smallest to largest.
Sample mean: (Sum / No. of Samples)
Definitions contd.
• Sample Mean:
Xmean=sum(Xi)/n
• Sample deviation: Difference between
the measured value and the sample mean
Deviation = X – Xmean
• Sample variance = sum(Xi-Xmean)²/(n-1)
Definitions contd.
• Sample Standard Deviation:
s=sqrt(sum(Xi-Xmean)²/(n-1))
Sample standard deviation gives us an
estimate of the variability of the sample in
the same units as the data .
• Components manufactured with a small
standard deviation, cost more than
components that are manufactured to a
looser standard.
clear all
R1=5.1
V=24
R2=13.8:0.1:15.2
V1=(R1/(R1+R2))* V
I1=V / (R1+R2)
figure(1)
subplot(2,1,1)
plot(R2,V1)
subplot(2,1,2)
plot(R2,I1)
```
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