26
Intended Learning Outcomes for This Topic
2
➌ Define the principal kinds of measurement uncertainty
By the end of this topic, you will be able to:
➋ Define the essential components of a measurement
➍ Demonstrate how uncertainty in sensor data affects embedded software
➊ Define precision, accuracy, and reliability
➎ Derive / propagate uncertainties through arithmetic operations on sensor data
26
Three Key Components of a Measurement
3
The measurement
instrument or sensor
The phenomenon being
measured: the measurand
The environment
(e.g., ambient vibrations, temperature, etc.)
The measurement is what
comes out of the
measurement instrument
Environment
➊
Measurement
Instrument
➍
➌
➋
26
Precision
4
Repeatability or fineness of control
More preciseLess precise
26
Accuracy
5
Difference from correct value
Example: A sensor value can be measured with great precision (repeatability and
resolution), but the sensed value may differ from the actual value of the signal
More accurate
Less accurate
More precise
Less precise
26
Faults, Masking, Errors, Erasures
6
Hardware or software defect.
A fault that is not masked (and is hence visible)
Example: a signal shorted to ground when it should not be
When a value of a signal is the same as the value induced by
a fault, the fault is said to be masked
A fault whose value is different from any valid signal value
Fault or failure:
Masking:
Error:
Erasure:
26
Sources of Errors and Erasures
7
Microprocessor
LD @(R4), R2
ADD R5, R6
SHRL, R4, #8
Program:
λx.+2x
Temperature
Fluctuations
Electrical Noise
Circuit state disturbance inducement
26
Sources of Errors and Erasures: Soft Errors
8
Radioactive Decay of
238
U and
232
Th from
device packaging mold resin,
210
Po from
PbSn solder (and Al wire)
12
C
α-particles
γ- rays
Lithium
Cosmic rays Thermal neutrons
High energy neutron
(can penetrate up to 5
ft of concrete)
Neutron capture within Si
and B in integrated circuits
Unstable isotope
Magnesium
or
Possible interaction paths
Circuit state disturbance inducement
Microprocessor
–
+
–
+
Temperature
Fluctuations
}
LD @(R4), R2
ADD R5, R6
SHRL, R4, #8
Program:
λx.+2x
?
Electrical Noise
High-Energy Particles
26
Sources of Errors and Erasures: Noise
9
Thermal / Johnson-Nyquist
Noise
Possible interaction paths
Circuit state disturbance inducement
Microprocessor
Temperature
Fluctuations
LD @(R4), R2
ADD R5, R6
SHRL, R4, #8
Program:
λx.+2x
?
Shot Noise
“Flicker” / 1/f Noise
Random Telegraph Noise
26
Some Common Classifications of Errors
10
Random Errors
Systematic Errors
Epistemic Uncertainty
Aleatoric Uncertainty
Type A Uncertainty
Type B Uncertainty
Errors that vary over time (e.g., due to noise)
Errors that are fixed over time (e.g., an offset)
Uncertainty in a measurements due to insufficient (or no) information
Uncertainty in a measurement due to random errors
Uncertainty quantified by (statistical) analysis of measurand
Uncertainty specified as properties of sensor, independent of measurand
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