2. Concepts and Terms
Calibration:
Determining the deviation of the indication of a measuring instrument
from the conventional true value of the measurand.
Traceability:
A Process whereby the indication of a measuring instrument can be compared
with a national / International Standard for the measurement in question in
one or more stages. Calibration performed with a standard, the metrological
quality determined by calibration with a higher level standard.
← →
→ ←
→
←
Metrological Infrastructure in a country Domain of the
Company
Manufactured
Products
Company’s test
equipment
In – house Calibration
Laboratory
Working Standards or
Factory Standards
Calibration Center
Company’s Reference
Standard
Transfer
Standards
Transfer
Standards
Accreditated
Calibration Laboratory
NMI
SI Units
3. Concepts and Terms
Traceability:
a.Traceability is the property of the result of a
measurement and not an instrument or laboratory
b.National Metrological Institute like NPL need to document
the measurement assurance. These use to demonstrate
traceability to standards representing SI systems of units.
c.Laboratory below the national level need to document
measurement assurance. These use to demonstrate from their
levels to national level.
d.Traceability only exists when scientifically rigorous
evidence is collected on continuing basis Showing that the
measurement process is producing documented results for
which the total measurement uncertainty is quantified
continuously.
4. Concepts and Terms
Why Calibration and Traceability Necessary?
a)For Companies: Traceability of measurement process to
national standards by means of calibration is
necessitated so that manufactured product is
interchangeable. Possible only when suppliers that make
the product and customers which integrate them with
other parts measure with the same measure (Traceable
measure)
b) Legal and Technical reasons: Relevant laws and
Regulations of Product Quality, Contractual Provisions
agreed with the Purchasers, Statutory requirements (e.g.
Safety)
8. Concepts and Terms
Metrology:
The Science of Measurement.
Classification:
Industrial
Scientific and
Legal Metrology
Another View of Classification are Physical and Chemical.
Random Error
Result of a measurement minus the mean that would result from an infinite
number measurements of the same measurand carried out under repeatability
conditions.
RE = Error – SE
Systematic Error
Mean that would result from an infinite no of measurements of the same
measurand carried out under repeatability conditions minus a true value of
the measurands.
SE = Error – RE
Precision
The Closeness of agreement between independent test results obtained under
stipulated conditions.
9. Concepts and Terms
Uncertainty of Measurements:
A Parameter as associated with the result of a measurement (e.g.
Calibration or test) that defines the range of the values that could
reasonably be attributed to the measured quantity. It indicates the level of
confidence that the value actually lies within the range defined by the
uncertainty interval
Measurand:
The Particular Quantity subject to measurement
Measurement:
Is a set of operations to determine the value of given quantity. It is a
process, it has both input namely measuring equipment, item under
measurement, measurement procedures, environment, a reference to a standard
and output namely- measurement results.
Input Quantity:
A quantity on which the measurand depends, including the process of
evaluating the result of measurement.
Output Quantity:
Quantity that represents the measurand in the evaluation of measurement.
10. Organization Structure for tracking test results within a company to National
Standards
Standard
( Test equipment)
Responsible Tasks Basis for the
Calibration or
Measurement
Documentation of the
calibration or
measurement
National Standard NMI To maintain and
Disseminate the
national
standards
Statutory duty to
represent SI units
and ensure
International
comparability
Calibration
Certificate for
Reference Standards
Reference
Standards
Accredited
calibration
Laboratories
To Safeguard
the
metrological
infrastructure
of a country
Calibration
certificate from NMI
or another
accredited
laboratory
Calibration
Certificate for
Working Standard or
factory standard
Working Standard
Factory Standard
In-house
Calibration
laboratories
Supervision of
test equipment
for in-house
purposes
Calibration
certificate from NMI
or an accredited
laboratory
Factory calibration
certificate,
calibration mark or
the like for test
equipment
Test Equipment All Sections
of a Company
Measurements
and tests as
part of quality
assurance
measures
Factory calibration
certificate,
calibration mark or
the like
Test mark or the
like
11. Conclusive Specific Requirements for Traceability
1. All Calibrations and Verifications of measuring and test
equipment, reference standards, and reference materials
conducted by a calibration laboratories accredited by a
mutually recognized accreditation body or by a recognized
national metrology institute.
2. These calibrations or verifications documented in a
calibration certificate or report by recognized
accreditation body logo or otherwise makes reference to
accredited status.
3. Laboratories define their Policy for achieving
measurement traceability in compliance with this policy
document.
4. Where MU are applicable, calculate it in accordance with
the ISO guide to the expression on uncertainty in
measurement. These uncertainties supported by uncertainty
budgets and represented as expanded uncertainties
typically using a coverage factor of k = 2 to approximate
the 95% confidence level.
12. Conclusive Specific Requirements for Traceability
5. If a Calibration Certificate or report contains a
statement of the measurement result and the associated
uncertainty, then the uncertainty statement accompanied
by an explanation of the meaning of the uncertainty
statement. Expanded uncertainties typically using a
Coverage factor of k = 2 to approximate the 95%
confidence level.
6. Total Uncertainties calculated using the expanded
uncertainty of the measurement
7. Implicit uncertainty statement accompanied by words to
the effect that the uncertainty ratio was calculated
using the expanded measurement uncertainty. In addition
the coverage factor and confidence level stated.
8. Calibration Reports and Certificated issued by accredited
calibration laboratories contain a traceability
statement.
13. Conclusive Specific Requirements for Traceability
9. All In-house Calibrations supported by the following
minimal set of elements;
a)The in-house laboratories maintain documented procedures
for the in house calibration and evidenced by the Calibration
report, certificate or sticker or other suitable method and
calibration records retained for an appropriate prescribed
time.
b) The in-house laboratories maintain training records for
the calibration personnel and these records demonstrate the
technical competence of the personnel performing the
calibration.
c) The in-house laboratories able to demonstrate traceability
to national or international standards of measurement by
procuring calibration services from accredited calibration
labs or a national metrology institute.
d) The in-house laboratories apply procedures for evaluating
measurement uncertainty. MU taken into account when
statements of compliance with specifications are made.
e) Reference Standards recalibrated at appropriate intervals
to ensure that the reference value is reliable. Policy and
procedures for establishing and changing calibration
intervals based on the historical behavior of the reference
14. Distributions
Rectangular or Uniform Distribution:
Probability density function p(x) of rectangular
distribution
P(x) = 1/2a , a_<x<a+, its Standard Deviation =
a/√3
Symmetrical Trapezoidal Distribution:
Equal sloping sides (an isosceles trapezoid), a base of width
a + (-a) = 2a and a top of Width 2βa, Where 0 ≤β≤1
E(X) = a+ + (-a) /2, and its Standard Deviation is
SD(X) = a √ 1+β2)/6), Where β = 1 , the STD
is reduced to a rectangular distribution
Triangular Distribution:
When the greatest concentration of the values is at the center
of the distribution, then one must use the triangular
distribution.
E(X) = (a+) + (a-) / 2, and Standard Deviation = a/ √6
Normal Distribution:
Symmetrical, Uniquely determined by the two Parameters
15. Method of Evaluation of Uncertainty in Measurement
MU is evaluated by first identifying all the quantities
that are involved in or influence the measurement i.e.
input quantities and writing a model/relationship formula
between the input estimates and output estimates.
This is followed by evaluating uncertainty in
measurement associated with each of the input estimates
using Type A and Type B method of Evaluation.
Finally these are combined to get the uncertainty
associated with output estimate. Statement of uncertainty
is given by expanding the combined uncertainty be a
coverage factor.
16. Step by Step Evaluation of Uncertainty in Measurement
Express in mathematical terms the dependence of the measurand (output
quantity) Y on the input quantities X1 and X2 e.g. Y = X1 +X2
•Identify & apply all significant corrections
•List all Sources of uncertainty
•Calculate the standard uncertainty for repeatedly measured
quantities by type A evaluation
•For Single values, adopt the standard uncertainty (type B
evaluation)
•Calculate for each input quantity xi the contribution ui (y) to the
uncertainty associated with the output estimate from xi
•Obtain the standard uncertainty u(y) of the measurand by RSS method
•Calculate the expanded uncertainty U = k u(v)
•Report the result of the measurement comprising the estimate of the
measurand y+-U and the coverage factor k (95%) in the calibration
certificate
17. Type A Formula of Uncertainty in
Measurement
Average Formula:
Standard Deviation Formula:
18. Type B Evaluation of Uncertainty in Measurement
Rectangular Distribution: if the limits can be determined
but there is no other knowledge of behavior with in the
limits and the value of measurand is equally likely to lie
anywhere with in the limits,
u(xi) = a/√3
Triangular Distribution: if the values near the center of
distribution rather than extreme limits,
u(xi) = a/√6
Trapezoidal Distribution: if the limits near the mid
points, outcome of the convolution of two rectangular
distributions.
u2(xi) = a2 (1+b2)/6
19. Type B Evaluation of Uncertainty in Measurement
Complete result consisting of the estimate y and
associated expanded uncertainty U is given in the form
y±U
The reported expanded uncertainty in measurement is
stated as the standard uncertainty in measurement
multiplied by the coverage factor k = xx, effective
degree of freedom corresponds to a coverage probability
of approximately 95%
1 lbs = 453.592 gram so, 10 lbs = 4535.92 gram
Z Score = X - µ / Ø
Where, X = Value, µ = Mean , Ø = Standard Deviation
