Titoloin
presentazione
The role of metrology
the future human activities
sottotitolo
Alessandro Ferrero
Milano, XX mese 20XX
Dipartimento di Elettronica, Informazione e Bioingegneria – DEIB
Politecnico di Milano – Milano – Italy
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Future scenarios
Forecasting the future is always a dangerous exercise
◉ According to the present trends, the following fields will significantly
develop
◉
– Big Data
– Artificial Intelligence
– Autonomous devices
•
•
•
•
•
Industrial robots
Collaborative robots
Self-driving cars
Drones
…
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Data: the oil of the future
◉
◉
◉
◉
◉
◉
◉
Data will become more and more important
Decisions will be taken based on the available data
Data are expected to be collected remotely, under somebody’s else
control, and stored in repositories
Decisions’ outcome depend on data correctness
Assessing data reliability is the big challenge we need to win
Sensing devices provide in-field data to autonomous devices
Measurement results will affect human activities more and more
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
From measurements to decisions
Sensors
Measurement uncertainty
Data
processing
Decision
Alessandro Ferrero, DEIB.
Risk of
wrong
decision
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The role of metrology
◉
Improve sensor design
–
–
–
–
Improved sensing resolution
Better accuracy, improved reliability
Immunity to disturbances
…
Evaluate measurement uncertainty
◉ Analyze its propagation through data processing
◉ Evaluate the risk of wrong decision
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
What do we do when we measure?
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
How do we achieve this?
There is phenomenon in the
empirical world
◉ q is a manifestation of this
phenomenon
◉ When we measure it, we
assign a symbol x to q
◉
– A number and a measurement
unit and an uncertainty value
◉
When we measure, we map the empirical world of phenomena q
onto the abstract world of symbols x
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
A helpful model
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Identification
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Identification
◉
The first step is to identify:
– the measurand
– the measurement system
– the influence quantities
◉
Problem: if they’re not correctly identified or the effect of some
influence quantity is neglected, the measurement result may be
incorrect
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Modeling
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Modeling
◉
The model describes the measurement context and the interactions
between measurand, measurement system and environment
– The model provides the symbolical description of the measurement process
Models provide always incomplete knowledge of the measurement
context
◉ The measurement process provides only a limited amount of
information about the measurand
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Definitional uncertainty
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Definitional uncertainty
These two processes generate a contribution to uncertainty called
definitional uncertainty.
◉ Component of measurement uncertainty resulting from the finite
amount of detail in the definition of a measurand (VIM 2.27)
◉ This contribution represents the lower bound of measurement
uncertainty
◉
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The experimental process
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Instrumental uncertainty
Specific processes and measuring devices shall be considered for
each measurement application
◉ The imperfect description of the instruments, measurement
procedures and the mutual interactions with the environment originate
the so-called instrumental uncertainty.
◉ Component of measurement uncertainty arising from a measuring
instrument or measuring system in use (VIM 4.24)
◉ It can be partly originated outside the instruments
◉
– Uncertainty of the references used in the calibration process
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Uncertainty
◉
It is now widely recognized that, when all of the known or suspected
components of error have been evaluated and the appropriate
corrections have been applied, there still remains an uncertainty about
the correctness of the stated result, that is, a doubt about how well
the result of the measurement represents the value of the quantity
being measured (GUM 0.2).
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Uncertainty
In many industrial and commercial applications, as well as in the areas
of health and safety, it is often necessary to provide an interval about
the measurement result that may be expected to encompass a large
fraction of the distribution of values that could reasonably be
attributed to the quantity subject to measurement.
◉ Thus the ideal method for evaluating and expressing uncertainty in
measurement should be capable of readily providing such an interval,
in particular, one with a coverage probability or level of confidence
that corresponds in a realistic way with that required (GUM 0.4).
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
A measurement result
p
xm - U
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xm
xm + U
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The impact on decision
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
A risk exist that the
decision is wrong!
What kind of decison?
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In general, a measurement result is compared with a given threshold.
– Comparison with a tolerance
– Comparison with a maximum admissible limit
–…
◉
According to the comparison result a decision is taken
– Accept or reject a part or a component
– Decide whether a crime has been committed
–…
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
A popular decision rule
◉
ISO 14253-1 “Geometrical Product Specifications (GPS) – Inspection
by measurement of workpieces and measuring equipment – Part 1:
Decision rules for proving conformance or nonconformance with
specifications”
U(x)
U(x)
x
MAL
sure conformity
zone
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ambiguity zone
sure nonconformity
zone
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What about risk?
◉
Let's suppose that we have to check whether a limit has been
exceeded
– Limit value: 50
– Expanded uncertainty: 5
It is possible to state that the limit has been exceeded if the measured
value xm > 55
◉ If xm = 55 it is not possible to state that the limit has been exceeded
◉ What is the probability that the limit has actually been exceeded?
◉
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The risk of wrong decision
The sure nonconformity value
is 55
◉ The sure
conformity value
is 45
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The risk of wrong decision
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The measured
value is 55
The risk of wrong decision
◉
The probability that the
actual value is above the
limit is:
∞
𝑃 𝑥 ≥ MAL =
= 97.7%
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
𝑝 𝑥 𝑑𝑥
MAL
What if we reduce uncertainty?
◉
Let's suppose that we have to check whether a limit has been
exceeded
– Limit value: 50
– Expanded uncertainty: 1
It is possible to state that the limit has been exceeded if the measured
value xm > 51
◉ If xm = 51 it is not possible to state that the limit has been exceeded
◉ What is the probability that the limit has actually been exceeded?
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The risk of wrong decision
The sure nonconformity value
is 51
◉ The sure
conformity value
is 49
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The risk of wrong decision
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The measured
value is 51
The risk of wrong decision
◉
The probability that the
actual value is above the
limit is:
∞
𝑃 𝑥 ≥ MAL =
= 97.7%
𝑝 𝑥 𝑑𝑥
MAL
again!
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
A better approach
A more modern approach is a risk-based approach
◉ An acceptable risk R of wrong decision is defined, not to be exceeded
◉ Given the measurement uncertainty, a new limit is set, not to be
exceeded by the measured value.
◉ For a normal distribution, this can be computed using the inverse error
function
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
An example
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◉
◉
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Let's suppose that the limit is still 50
Let's suppose that the expanded uncertainty U is still 5
Let's also suppose that we don't want the risk of wrong decision
exceed 5%.
This leads to reduce the limit to 45.9
Measured values below this limit will ensure that the risk of exceeding
the limit is lower than the 5% set value
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Example
◉
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YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The new limit is set
to 45.9
Example
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The measured
value is 45.9
Example
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The risk of
exceeding the limit
value of 50 is the
preset 5 %!
What if we reduce uncertainty?
◉
◉
◉
◉
◉
Let's supposed that the limit is still 50
Let's suppose that the expanded uncertainty U is now 1
Let's also suppose that we don't want the risk of wrong decision
exceed 5%.
This leads to reduce the limit to 49.2
Measured values below this limit will ensure that the risk of exceeding
the limit is lower than the 5% set value
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Example – reduced uncertainty
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The new limit is set
to 49,2
Example – reduced uncertainty
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
The measured
value is 49.2
Example – reduced uncertainty
The risk of
exceeding the limit
value of 50 is the
preset 5 %!
◉ The reduced limit is
much closer to the
real limit
◉
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020
Conclusion
◉
◉
◉
◉
◉
◉
Metrology can play a significant role in
helping decisions
If uncertainty on the input data is correctly
evaluated …
… then the risk of making a wrong decision
can be evaluated as well
Better decisions make a better life
Better measurement results yield better
decisions
Better measurement results improve our
lives!
Alessandro Ferrero, DEIB.
YQ ISIF 2020 – Bejing, September 4 – 6, 2020