ISO 15572:1998

INTERNATIONAL IS0
STANDARD 15572
First edition
1998-12-15
Guide for estimating uncertainties in
dosimetry for radiation processing
Guide pour /‘estimation des incertitudes en dosimktrie pour le traitement par
irradiation
Reference number
IS0 15572: 1998(E)
IS0 15572: 1998(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide federation of national standards bodies
(IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.
lnternationai Standard IS0 15572 was prepared by the American Society for Testing and Materials (ASTM)
Subcommittee E1O.O1 (as E 1707-95) and was adopted, under a special “fast-track procedure ”, by Technical
Committee ISOKC 85, Nuclear energy, in parallel with its approval by the IS0 member bodies.
A new ISOrK 85 Working Group WG 3, High-level dosimetry for radiation processing, was formed to review the
voting comments from the IS0 “Fast-track procedure” and to maintain these standards. The USA holds the
convenership of this working group.
International Standard IS0 15572 is one of 20 standards developed and published by ASTM. The 20 fast-tracked
standards and their associated ASTM designations are listed below:
IS0 Designation ASTM Designation Title
15554 E 1204-93 Practice for dosimetry in gamma irradiation facilities for food
processing
15555 E 1205-93 Practice for use of a ceric-cerous sulfate dosimetry system
E1261-94 Guide for selection and calibration of dosimetry systems for
radiation processing
15557 E 1275-93 Practice for use of a radiochromic film dosimetry system
15558 E 1276-96 Practice for use of a polymethylmethacrylate dosimetry system
15559 E 1310-94 Practice for use of a radiochromic optical waveguide dosimetry
system
15560 E 1400-95a Practice for characterization and performance of a high-dose
radiation dosimetry calibration labora tory
15561 E 1401-96 Practice for use of a dichromate dosimetry system
0 IS0 1998
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 l CH-1211 Geneve 20 l Switzerland
Internet iso@ iso.ch
Printed in Switzerland
ii
@ IS0 IS0 15572:1998(E)
E1431-91 Practice for dosimetry in electron and bremsstrahlung irradiation
facilities for food processing
15563 E 1538-93 Practice for use of the ethanol-chlorobenzene dosimetry system
15564 E 1539-93 Guide for use of radiation-sensitive indicators
15565 E 1540-93 Practice for use of a radiochromic liquid dosimetry system
E 1607-94 Practice for use of the alanine-EPR dosimetry system
15567 E 1608-94 Practice for dosimetry in an X-ray (bremsstrahlung) facility for
radiation processing
of calorimetric dosimetry systems electron
15568 E 1631-96 Practice for use
beam dose meas Nurements and dosimeter calibrations
Practice for dosimetry in an electron-beam facility for radiation
E 1649-94
processing at energies between 300 keV and 25 MeV
E 1650-94 Practice for use of cellulose acetate dosimetry system
Practice for dosimetry in a gamma irradiation facility for radiation
15571 E 1702-95
processing
Guide for estimating uncertainties in dosimetry for radiation
15572 E 1707-95
processing
Practice for dosimetry in an electron-beam facility for radiation
15573 E 1818-96
processing at energies between 80 keV and 300 keV
. . .
III
IS0 15572: 1998(E)
@ IS0
AMERICAN SOCIEN FOR TESTING AND MATERIALS
1916 Race St. Philadelphia, Pa 19103
Designation: E 1707 - 95
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
If not listed in the current combined index, will appear in the next edition.
Standard Guide for
Estimating Uncertainties in Dosimetry for Radiation
Processing’
number immediately following the designation indicates the year of
This standard is issued under the fixed designation E i 707; till-
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (c) indicates an editorial change since the last revision or reapproval.
E 1026 Practice for Using the Fricke Reference Standard
1. Scope
Dosimetry System3
1.1 This guide defines possible sources of error in
E 1204 Practice for Dosimetry in Gamma Irradiation
dosimetry performed in gamma, x-ray (bremsstrahlung) and
Facilities for Food Processing3
electron irradiation facilities and offers procedures for esti-
E 1205 Practice for Use of a Ceric-Cerous Sulfate
mating the resulting magnitude of the uncertainties in the
Dosimetry System3
measurement results. Basic concepts of measurement, esti-
E 1249 Practice for Minimizing Dosimetry Errors in
mate of the measured vaiue of a quantity, “true” value, error
Radiation Hardness Testing of Silicon Electronic De-
and uncertainty are defined and discussed. Components of
vices Using Co-60 Sources3
uncertainty are discussed and methods are given for evalu-
E 126 1 Guide for Selection and Calibration of Dosimetry
ating and estimating their values. How these contribute to
I Systems for Radiation Processing3
the standard uncertainty in the reported values of absorbed
1275 Practice for Use of a Radiochromic Film
E
dose are considered and methods are given for calculating
Dosimetry System3
the combined standard uncertainty and an estimate of
E 1276 Practice for Use of a Polymethylmethacrylate
overall (expanded) uncertainty. The methodology for evalu-
Dosimetry System3
ating components of uncertainty follows IS0 procedures (see
E 13 10 Practice for the Use of a Radiochromic Optical
2.3). The traditional concepts of precision and bias are not
Waveguide Dosimetry System3
used. Examples are given in five appendixes.
E 1401 Practice for Use of a Dichromate Dosimetry
1.2 This guide assumes a working knowledge of statistics.
System3
Several statistical texts are included in the references (1, 2, 3,
,
E 143 1 Practice for Dosimetry in Electron and
4)
Bremsstrahlung Irradiation Facilities for Food
‘1.3 This standard does not purport to address all of the
Processing3
sq&y concerns, if any, associated with its use. It is the
E 1607 Practice for Use of the Alanine-EPR Dosimetry
responsibility of the user o/this standard to establish appro-
System3
pritie safety and health practices and determine the applica-
2.2 ICRU Reports!
bility of regulatory limitations prior to use.
ICRU Report 14 Radiation Dosimetry: X-Rays and
Gamma Rays with Maximum Photon Energies Between
0.6 and 50 MeV
2. Referenced Documents
ICRU Report 17 Radiation Dosimetry: X-Rays Generated
at Potentials of 5 to 150 kV
2.1 ASTM Standards:
ICRU Report 33 Radiation Quantities and Units
E 170 Terminology Relating to Radiation Measurements
ICRU Report 34 The Dosimetry of Pulsed Radiation
and Dosimetry3
ICRU Report 35 Radiation Dosimetry: Electron Beams
E 177 Practice for Use of the Terms Precision and
with Energies Between 1 and 50 MeV
Accuracy as Applied to Measurement of a Property of a
ICRU Report 37 Stopping Powers for Electrons and
Material3
Positrons
E 178 Practice for Dealing With Outlying Observations3
b
.
E 456 Terminology Relating to Quality and Statistics4
E 666 Practice for Calculating Absorbed Dose from
3. Terminology
Gamma or X Radiation3
3.1 Definitions:
E 876 Practice for Use of Statistics In the Evaluation of
3.1.1 absorbed dose, D-quantity of radiation energy
Spectrometric Data5
imparted per unit mass of a specified material. The unit of
absorbed dose is the gray (Gy) where 1 gray is equivalent to
the absorption of 1 joule per kilogram (= 100 rad). The
i This guide is under the jurisdiction of ASTM Committee E-10 on Nuclear
mathematical relationship is the quotient of&by dm, where
Technology and Applications and is the direct responsibility of Subcommittee
E 10.0 I on Dosimetry for Radiation Processing. & is the mean energy imparted by ionizing radiation to
Current edition approved May 15, 1995. Published July 1995.
matter of mass dm (see ICRU 33).
2 The boldface numbers in parentheses refer to a list of references at the end of
this guide.
3 Annual Book of ASTM Slandards, Vol 12.02.
6 Available from International Commission on Radiation Units and Measure-
4 Annual Book ofASTM Standards, Vol 14.02.
ments, 79 IO Woodmont Ave., Suite 800 Bethesda, MD 208 14.
5 Annual Book of ASTM Standards, Vol 03.06.
IS0 15572:1998(E) 0 IS0
D = &/dm 3.1.15 expected value- sum of possible values of a vari-
able weighted by the probability of the value occurring. It is
3.1.2 accuracy of measurement-closeness of the agree-
found from the expression:
ment between the result of a m ‘easurement and the true value
E(v) = Zi PiVi
of the measurand.
3.1.3 calibration curve-graphical representation of the
where:
relationship between dosimeter response and absorbed dose
Y. = zth value and
for a given dosimetry system. For a mathematical represen-
Pi’ = probabilky of zth value.
tation, see response function.
3.1.16 influence quantity-quantity that is not included in
3.1.4 coeficient of variation-sample standard deviation
the specification of the measurand but that nonetheless
expressed as a percentage of sample mean value (see 3.37 and
affects the result of the measurement.
3.38).
DIscussroN-This quantity is understood to include values associated
(Cv) = s,-,/x x 100 %
with measurement reference standards, reference materials, and refer-
3.1.5 combined standard uncertainty-standard uncer- ence data upon which the result of the measurement may depend, as
well as phenomena such as short-term instrument fluctuations and
tainty of the result of a measurement when that result is
parameters such as temperature, time, and humidity.
obtained from the values of a number of other quantities,
equal to the positive square root of a sum of terms, the terms 3.1.17 (measurable) quantity-attribute of a phenom-
enon, body or substance that may be distinguished qualita-
being the variances or covariances of these other quantities
weighted according to how the measurement result varies tively and determined quantitatively; for example, the spe-
with changes in these quantities. cific quantity of interest in this guide is absorbed dose.
3.1.6 confidence interval-an interval estimate that con- 3.1.18 measurand-specific quantity subject to measure-
tains the mean value of a parameter with a given probability. ment.
3.1.7 confidence level--the probability that a confidence
DISCU~SON-A specification of a measurand may include statements
interval estimate contains the value of a parameter.
about other quantities such as time, humidity, or temperature. For
3.1.8 corrected result-result of a measurement after cor- example, equilibrium absorbed dose in water at 25°C.
rection for the best estimate of systematic error.
3.1.19 measurement-set of operations having the object
3.1.9 correction- value that, added algebraically to the
of determining a value of a quantity.
uncorrected result of a measurement, compensates for sys-
3.1.20 measurement procedure-set of operations, in spe-
tematic error.
cific terms, used in the performance of particular measure-
DIscussroN-The correction is equal to the negative of the systematic ments according to a given method.
error. Some systematic errors may be estimated and compensated by
3.12 1 measurement system-system used for evaluating
applying appropriate corrections. However, since the systematic error
the measurand.
cannot be known perfectly, the compensation cannot be complete.
3.1.22 measurement traceability-The ability to demon-
3.1.10 correction jktor- numerical factor by which the
strate and document on a continuing basis that the measure-
uncorrected result of a measurement is multiplied to com-
ment results from a particular measurement system are in
pensate for a systematic error.
agreement with comparable measurement results obtained
with a national standard (or some identifiable and accepted
DIscussroN-Since the systematic error cannot be known perfectly,
the compensation cannot be complete. standard) to a specified uncertainty.
3.1.23 method ofmeasurement-logical sequence of oper-
3.1.11 coverage factor- numerical factor used as a multi-
ations used in the performance of measurements according
plier of the combined standard uncertainty in order to obtain
to a given principle.
an overall uncertainty.
DIscu~roN-Methods of measurement may be qualified in various
DISCUSSION-A coverage factor, k, is typically in the range of 2 to 3
ways such as: substitution method, differential method, and null
(see 8.3).
method.
3.1.12 dosimeter batch-quantity of dosimeters made
3.1.24 outlier-a measurement result that deviates mark-
from a specific mass of material with uniform composition,
edly from others within a set of measurement results.
fabricated in a single production run under controlled,
3.1.25 overall uncertainty-quantity defining the interval
consistent conditions and having a unique identification
about the result of a measurement within which the values
code.
that could reasonably be attributed to the measurand may be
3.1.13 dosimetry system- a system used for determining
expected to lie with a high level of confidence.
absorbed dose, consisting of dosimeters, measurement in-
]DISCusSION-Overall uncertainty is referred to as “expanded uncer-
struments and their associated reference standards, and
tainty” (see Guide to the Expression of Uncertainty in Measurement)
procedures for the system ’s use,
(5).’ To associate a specific level of confidence with the interval defined
3.1.14 error (of measurement)-result of a measurement
by the overall uncertainty requires explicit or implicit assumptions
minus a true value of the measurand.
regarding the probability distribution characterized by the measurement
result and its combined standard uncertainty. The level of confidence
DrscusWN+-Since a true value cannot be determined, in practice a
that may be attributed to this interval can be known only to the extent to
conventional true value is used. The quantity is sometimes called
which such assumptions may be justified.
“absolute error of measurement” when it is necessary to distinguish it
from relative error. If the result of a measurement depends on the values
of quantities other than the measurand, the errors of the measured
values of these quantities contribute to the error of the result of the
7 Available from International Organization for Standardization, Case Postal
measurement. 56, CH- 12 1 1 Geneva 20 Switzerland.
IS0 15572: 1998(E)
d# El707
-mathematical representation of
3.1.26 primary standard dosimeter-a dosimeter of the 3.1.35 response function
the relationship between dosimeter response and absorbed
highest metrological quality, established and maintained as
dose for a given dosimetry system. -
an absorbed dose standard by a national or international
standards organization. 3.1.36 result of a measurement-value attributed to a
3.1.27 principle of measurement-scientific basis of a measurand, obtained by measurement.
method of measurement.
DrscussroN-when the term “result of a measurement” is used, it
-a method of estimating overall uncer-
3.1.28 quadrature
should be made clear whether it refers to: the indication, the uncorrected
tainty from independent sources by taking the square root of
result, the corrected result, and whether severa! VZIWS are averaged. A
the sum of the squares of individual components of uncer-
complete statement of the result of the measurement includes informa-
tion about the uncertainty of the measurement.
tainty (for example, coefficient of variation).
3.1.29 random error-result of a measurement minus the
3.1.37 routine dosimeter-dosimeter calibrated against a
mean result of a large number of measurements of the same
primary-, reference-, or transfer-standard dosimeter and used
measurand that are made under repeatable or reproducible
for routine dosimetry measurement.
conditions (see 3.32 and 3.33).
3.1.38 sample mean -a measure of the average value of a
data set which is representative of the population. It is
DIscussroN-In these definitions (and that for systematic error), the
term “mean result of a large number of measurements of the same determined by summing all the values in the data set and
measurand” is understood to mean “the expected value or mean of all
dividing by the number of items (n) in the data set. It is
possible measured values of the measurand obtained under conditions of
found from the expression:
repeatability or reproducibility ”. This ensures that the definition cannot
be misinterpreted to imply that for a series of observations, the random
js=-
= 1,2,3.n
n 2 Xi9 i
error of an individual observation is known and can be eliminated by
applying a correction. The view of this guide is that error is an idealized
i
concept and that errors cannot be known exactly.
3.1.39 sample standard deviation, S,-,-measure of dis-
persion of values expressed as the positive square root of the
3.1.30 reference standard dosimeter-a dosimeter of high
sample variance.
metrological quality, used as a standard to provide measure-
3.1.40 sample variance-the sum of the squared devia-
ments traceable to and consistent with measurements made
tions from the sample mean divided by (n-l), given by the
using primary standard dosimeters.
expression:
3.1.3 1 reference value (ofa quantity)-value attributed to
a specific quantity and accepted, sometimes by convention,
- X)2
p-, = = cxi
as having an uncertainty appropriate for a given purpose; for
(n- 1)
example, the value assigned to the quantity realized by a
where:
reference standard.
= individual value of parameter with i = 1, 2. . .n, and
xi
DIscussroN-This is sometimes called “assigned value ”, or “assigned
x = mean of n values of parameter (see 3.37).
reference value ”.
3.1.4 1 standard uncertainty-uncertainty of the results of
a measurement expressed as a standard deviation.
3.1.32 relative error (of measurement)-error of measure-
3.1.42 systematic error -mean result of a large number of
ment divided by a true value of the measurand.
repeated measurements of the same measurand minus a true
DrSCuSSIOr+-Since a true value cannot be determined, in practice a
value of the measurand.
reference value is used.
DIscussroN-The repeated measurements are carried out under the
3.1.33 repeatability (of results of measurements)-close- conditions of the term “repeatability ”. Like true value, systematic error
and its causes cannot be completely known. The error of the result of a
ness of the agreement between the results of successive
measurement may often be considered as arising from a number of
measurements of the same measurand carried out subject to
random and systematic effects that contribute individual components of
all of the following conditions: the same measurement
error to the error of the result (see E 170, E 177, and E 456).
procedure, the same observer, the same measuring instru-
ment, used under the same conditions, the same location, 3.1.43 traceability-see measurement traceability.
and repetition over a short period of time. 3.1.44 transfer standard dosimeter-a dosimeter, often a
reference standard dosimeter, suitable for transport between
DIscussroN-These conditions are called “repeatability conditions.”
different locations for use as an intermediary to compare
Repeatability may be expressed quantitatively in terms of the dispersion
absorbed dose measurements.
characteristics of the results.
3.1.45 true value-value of measurand that would be
3.1.34 reproducibility (of results of measurements)-close-
obtained by a perfect measurement.
ness of agreement between the results of measurements of
DIscussroN-True values are by nature indeterminate and only an
the same measurand, where the measurements are carried
idealized concept. In this guide the terms “true value of a measurand”
out under changed conditions such as differing: principle or
and “value of a measurand” are viewed as equivalent (see 5.1.1).
method of measurement, observer, measuring instrument,
3.1.46 Type A evaluation (of standard uncertainty)-
location, conditions of use, and time.
method of evaluation of a standard uncertainty by the
DISCUSSION-A valid statement of reproducibility requires specifica-
statistical analysis of a series of observations.
tion of the conditions changed. Reproducibility may be expressed
3.1.47 Type B evaluation (of standard uncertainty)-
quantitatively in terms of the dispersion characteristics of the results. In
method of evaluation of a standard uncertainty by means
this context, results of measurement are understood to be corrected
results. other than the statistical analysis of a series of observations.
@ IS0
IS0 15572: 1998(E)
3.1.48 uncertainty (of measurement)-a parameter, asso- for the result of a measurement therefore ultimately depends
on the understanding, critical analysis, and integrity of those
ciated with a measurand or derived quantity, that character-
who contribute to the assignment of its val ’ue.
izes the distribution of the values that could reasonably be
attributed to the measurand or derived quantity.
DIScuss!oN-For example, uncertainty may be a standard deviation 5. Basic Concepts- Components of Uncertainty
(or a given multiple of it), or the width of a confidence interval.
5. I Measurement.
Uncertainty of measurement comprises, in general, many components.
5.1.1 The objective of a measurement is to determine the
Some of these components may be evaluated from the statistical
value of the measurand, that is, the value of the specific
distribution of the results of series of measurements and can be
characterized by experimental standard deviations. The other compo- quantity to be measured. A measurement therefore begins
nents, which can also be characterized by standard deviations, are
with an appropriate specification of the measurand, the
evaluated from assumed probability distributions based on experience or
method of measurement, and the measurement procedure.
other information. It is understood that all components of uncertainty
5.1.2 In general, the result of a measurement is only an
contribute to the distribution.
approximation or estimate of the value of the measurand
3.1.49 uncorrected result-result of a measurement before
and thus is complete only when accompanied by a statement
correction for the assumed systematic error.
of the uncertainty of that estimate.
3.1.50 value (of a quantity)-magnitude of a specific
5.1.3 In practice, the specification or definition of the
quantity generally expressed as a number with a unit of
measurand depends on the required accuracy of the mea-
measurement, for example, 25 kGy.
surement. The measurand should be defined with sufficient
exactness relative to the required accuracy so that for all
4. Significance and Use
practical purposes the measurand value is unique.
4.1 Gamma, electron and x-ray (bremsstrahlung) facilities
NOTE 2-Incomplete definition of the measurand can give rise to a
routinely irradiate a variety of products such as food,
component of uncertainty sufficiently large that it must be included in
medical devices, aseptic packaging and commodities (see
the evaluation of the uncertainty of the measurement result.
Practices E 1204 and E 143 1). Process parameters for the
products must be carefully controlled to ensure that these 5.1.3.1 Although a measurand should be defined in sufTi-
cient detail that any uncertainty arising from its incomplete
products are processed within specifications (see ANSI/
definition is negligible in comparison with the required
AAMI ST3 l-1 990, ANSI/AAMI ST32- 199 1 and IS0 11137
accuracy of the measurement, it must be recognized that this
(6, 7, 8)? Accurate dosimetry is essential in process control
may not always be practicable. The definition may, for
(see Guide E 126 1). For absorbed dose measurements to be
meaningful, the overall uncertainty associated with these example, be incomplete because it does not specify parame-
measurements must be estimated and its magnitude quanti- ters that may have been assumed, unjustifiably, to have
negligible effect; or it may imply conditions that can never
fied .
fully be met and whose imperfect realization is difficult to
NOTE I-For a comprehensive discussion of various dosimetry
take into account.
methods applicable to the radiation types and energies discussed in this
5.1.4 In many cases, the result of a measurement is
guide, see ICRU Reports 14, 17, 34, 35 and Reference (9).
determined on the basis of repeated observations. Variations
4.2 This standard guide uses the methodology adopted by
in repeated observations are assumed to arise from not being
the International Organization for Standardization for esti-
able to hold completely constant each influence quantity that
mating uncertainties in dosimetry for radiation processing
can affect the measurement result.
(see 2.3). The ASTM traditionally expresses uncertainty in
5.1.5 The mathematical model of the measurement pro-
terms of precision and bias where precision is a measure of
cedure that transforms the set of repeated observations into
the extent to which replicate measurements made under
the measurement result is of critical importance since, in
specified conditions are in agreement and bias is a systematic
addition to the observations, it generally includes various
error (see Practice E 170, E 177 and E 456). As seen from
influence quantities that are inexactly known. This lack of
this standard, sources of uncertainty are evaluated as either
knowledge contributes to the uncertainty of the measure-
Type A or Type B rather than in terms of precision and bias.
ment result along with the variations of the repeated obser-
Both random and systematic error clearly are differentiated
vations and any uncertainty associated with the mathemat-
from components of uncertainty. The methodology for
ical model itself.
treatment of uncertainties is in conformance with current
5.2 Errors, Efects, and Corrections:
internationally accepted practice. (See Guide to the Expres-
5.2.1 In general, a measurement procedure has imperfec-
sion of Uncertainty in Measurement (5).)
tions that give rise to an error in the measurement result.
4.3 Although this guide provides a framework for as-
Traditionally, an error is viewed as having two components,
sessing uncertainty, it cannot substitute for critical thinking,
namely, a random component and a systematic component.
intellectual honesty, and professional skill. The evaluation of
5.2.2 Random error presumably arises from unpredict-
uncertainty is neither a routine task nor a purely mathemat-
able or stochastic temporal and spatial variations of influ-
ical one; it depends on detailed knowledge of the nature of
ence quantities. The effects of such variations, hereafter
the measurand and of the measurement method and proce-
referred to as random effects, give rise to variations in
dure used, The quality and utility of the uncertainty quoted
repeated observations of the measurand. The random error
of a measurement result cannot be compensated by correc-
tion but it can usually be reduced by increasing the number
8 Available from Association for the Advancement of Medical Instrumentation,
3330 Washington Boulevard, Suite 400, Arlington, VA 22201-4598. of observations; its expectation or expected value is zero.
0 IS0
IS0 15572: 1998(E)
NOTE 3-The experimental standard deviation of the arithmetic
532.10 variations in repeated observations of the
mean or average of a series of observations is not the random error of the
measurand under apparently identical conditions.
mean, although it is so referred to in some publications on uncertainty.
It is instead a measure of the uncertainty of the mean due to random
NOTE 7-These sources are not necessarily independent and some
effects. The exact value of the error in the mean arising from these
may contribute to 5.3.2.10. Of course, an unrecognized systematic effect
effects cannot be known. In this guide great care is taken to distinguish
cannot be taken into account in the evaluation of the uncertainty of the
between the terms “error” and “uncertainty ”; they are not synonyms
result of a measurement but contributes to its error.
but represent completely different concepts; they should not be confused
with one another or misused.
5.3.3 Uncertainty components are classified into two
categories based on their method of evaluation, “Type A”
5.2.3 Systematic error, like random error, cannot be
and “Type B” (see Section 3). These categories apply to
eliminated but it too can often be reduced. If a systematic
uncertainty and are not substitutes for the words “random”
error arises from a recognized effect of an influence quantity
and “systematic ”.
The uncertainty of a correction for a
on a measurement result, hereafter referred to as a systematic
known systematic effect may be obtained by either a Type A
effect, the effect can be quantified and, if significant in size
or Type B evaluation, as may be the uncertainty character-
relative to the required accuracy of the measurement, an
izing a random effect.
estimated correction or correction factor can be applied. It is
5.3.4 The purpose of the Type A and Type B classification
assumed that after correction, the expectation or expected
is to indicate the two different ways of evaluating uncertainty
value of the error arising from a systematic effect is zero.
components. Both types of evaluation are based on proba-
NOTE 4-The uncertainty of an estimated correction applied to a
bility distributions and the uncertainty components resulting
measurement result to compensate for a systematic effect is not the
from each type are quantified by a standard deviation or a
systematic error. It is instead a measure of the uncertainty of the result
variance.
due to incomplete knowledge of the value of the correction. In general,
the error arising from imperfect compensation of a systematic effect 5.3.5 The population variance u* characterizing an uncer-
cannot be exactly known.
tainty component obtained from a Type A evaluation is
estimated from a series of repeated observations. The best
5.2.4 It is assumed that the result of a measurement has
estimate of u2 is the sample variance 3 (see 3.39). The
been corrected for all recognized significant systematic
population standard deviation u, the positive square root of
effects.
u*, is thus estimated by s and for convenience is sometimes
NOTE 5-Often, measuring instruments and systems are adjusted or
referred to as a Type A standard uncertainty. For an
calibrated using measurement reference standards to eliminate system-
uncertainty component obtained from a Type B evaluation,
atic effects; however, the uncertainties associated with these standards
must still be taken into account. the population variance u* is evaluated using available
knowledge and the estimated standard deviation u is some-
5.3 Uncertainty:
times referred to as a Type B standard uncertainty.
5.3.1 The uncertainty of the result of a measurement
5.3.5.1 Thus a Type A standard uncertainty is obtained
reflects the lack of exact knowledge of the value of the
from a probability density function derived from an ob-
measurand. The result of a measurement after correction for
served frequency distribution, while a Type B standard
recognized systematic effects is still only an estimate of the
uncertainty is obtained from an assumed probability density
value of the measurand because of the uncertainty arising
function based on the degree of belief that an event will
from random effects and from imperfect correction of the
occur. The two approaches are both valid interpretations of
result for systematic effects.
probability.
NOTE 6-The result of a measurement (after correction) can un-
knowingly be very close to the value of the measurand (and hence have
NOTE 8-A Type B evaluation of an uncertainty component is often
a negligible error) even though it may have a large uncertainty. Thus the
based on a pool of comparatively reliable information.
uncertainty of the result of a measurement should not be interpreted as
representing the remaining unknown error,
5.3.6 The total uncertainty of the result of a measure-
ment, termed combined standard uncertainty and denoted
5.3.2 In practice there are many possible sources of
by u,, is an estimated standard deviation equal to the positive
uncertainty in a measurement, including:
square root of the total variance obtained by summing all
5.3.2.1 incomplete definition of the measurand;
variance and covariance components, however evaluated,
5.3.2.2 imperfect realization of the definition of the
using the law of propagation of uncertainty (see Appendix
measurand;
X9
5.3.2.3 sampling-the sample measured may not repre-
5.i.7 To meet the needs of some industrial and commer-
sent the defined measurand;
cial applications, as well as requirements in the areas of
5.3.2.4 inadequate knowledge of the effects of environ-
health and safety, an overall uncertainty U, whose purpose is
mental conditions on the measurement procedure or imper-
to provide an interval about the result of a measurement
fect measurement of environmental conditions;
within which the values that could reasonably be attributed
5.3.2.5 personal bias in reading analog instruments;
to the measurand may be expected to lie with a high level of
5.3.2.6 instrument resolution or discrimination threshold;
confidence, is obtained by multiplying the combined stan-
5.3.2.7 values assigned to measurement standards;
dard uncertainty u, by a coverage factor k (see 8.3).
5.3.2.8 values of constants and other parameters obtained
from external sources and used in the data reduction
NOTE g-The coverage factor k is always to be stated so that the
algorithm;
standard uncertainty of the measured quantity can be recovered for use
5.3.2.9 approximations and assumptions incorporated in
in calculating the overall standard uncertainty of other measurement
the measurement method and procedure; and results that may depend on that quantity.
0 IS0
IS0 15572:1998(E)
ctm El707
available information; and then calculate the measurement
5.4 Practical Considerations:
result from the estimated values of the input quantities and
5.4.1 By varying all parameters on which the result of a
the combined standard uncertainty of that result from the
measurement depends, its uncertainty could be evaluated by
statistical means. However, because this is rarely possible in standard uncertainties of those estimated values. Only if
there is a sound basis for believing that all of this has been
practice due to limited time and resources, the uncertainty is
done properly, with no significant systematic effects having
usually evaluated using a mathematical model of the mea-
been overlooked, can one assume that the measurement
surement procedure and the law of propagation of uncer-
result is a reliable estimate of the value of the measurand and
tainty. Thus implicit in this guide is the assumption that a
that its combined standard uncertainty is a reliable measure
measurement procedure can be modeled mathematically to
of its possible error.g
the degree imposed by the required accuracy of the measure-
ment.
5.4.2 Because the mathematical model may be incom-
6. Evaluation of Standard Uncertainty
plete, all parameters should be varied to the fullest practi-
6.1 Measurement Procedure:
cable extent so that the evaluation of uncertainty is based as
6.1.1 The measurand Y (absorbed dose) is generally not
much as possible on observed data. Whenever feasible, the
measurable directly, but depends on N other measurable
use of empirical models of the measurement procedure
quantities X,, X2, . . ., Xly through a functional relationshipj
founded on long-term quantitative data, and the use of check
standards and control charts that can indicate if a measure-
y =fK, x2, l l l 3 Xfv) (1)
ment procedure is under statistical control, should be part of
6.1.1.1 The input quantities X,, X2, . . ., Xcl and their
the effort to obtain reliable evaluations of uncertainty. A
associated uncertainties may be determined directly in the
well-designed experiment can greatly facilitate such efforts
current measurement process by means of repeated observa-
and is an important part of the art of measurement.
tions and may involve corrections for influence quantities
5.4.3 In order to decide if a measurement system is
such as temperature or humidity. They may also involve
functioning properly, the experimentally observed variability
uncertainties such as calibration of routine dosimeter re-
of its output values is often compared with the variability
sponse under conditions that differ from actual irradiator
predicted by combining the appropriate uncertainty compo-
facility conditions (different dose rates, temperature cycle,
nents that characterize its constituent parts. When calcu-
etc.). Other quantities that may be involved are those due to
lating the predicted standard deviation of the distribution of
use of reference or transfer standard dosimeters and their
experimentally observed output values, only those compo-
associated uncertainties.
nents (whether obtained from Type A or Type B evaluations)
6.1.2 The Type A component of uncertainty that is due to
that could contribute to the observed variability of these
non-repeatability or non-reproducibility of irradiation condi-
values should be considered.
tions during calibration and non-reproducibility or non-
repeatability of dose measurements at the production irradi-
NOTE IO-Such an analysis may be facilitated by gathering those
components that contribute to the variability and those that do not into
ator facility will cause a random error in the measurements.
two separate and appropriately labeled groups. The evaluation of overall
Sources of these Type A standard uncertainty components
uncertainty must take both groups into consideration.
are discussed in Section 7. Estimates of the magnitude of
these components can be made by performing replicate
5.4.4 An apparent outlier (see 3.23) in a set of measure-
repeated measurements under the same conditions.
ment results may be merely an extreme manifestation of the
6.1.3 The Type B component of uncertainty that has not
random variability inherent in the data. If this is true, then
been obtained by repeated observations can be evaluated by
the value should be retained and processed in the same
using all relevant information on the possible variability of
manner as the other measurements in the set, On the other
the input quantities Xi* This pool of information may
hand, the outlying measurement may be the result of gross
include previous measurement data, documented perfor-
deviation from prescribed experimental procedure or an
mance characteristics of the dosimetry system, and uncer-
error in calculating or recording the numerical value. In
tainties assigned to reference or transfer standard dosimeters.
subsequent data analysis the outlier will be recognized as
Sources of these Type B standard uncertainty components
unlikely to be from the same population as that of the others
are discussed in Section 7.
in the measurement set. An investigation shall be undertaken
6.2 Type A Evaluation of Standard Uncertainty.
to determine the reason for the aberrant value and whether it
6.2.1 The best estimate of the expected value of a quantity
should be rejected (see Practice E 178 for methods of testing
is obtained by n independent measurements made under the
for outliers).
same conditions of measurement (see 3.37) and is given by
5.5 Graphical Representation ofConcepts:
the arithmetic mean, x, or average of those measurements.
5.5.1 Figure 1 depicts some of the ideas discussed in this
The sample standard deviation, s,+ of these observations
Section. It illustrates why the focus of this guide is uncer-
characterizes the variability of the observed values or their
tainty and not error. The exact error of a result of a
dispersion about their mean. For example, at a production
measurement is, in general, unknown and unknowable. All
irradiator facility, repeated measurements of dose at the
one can do is estimate the values of input quantities,
including corrections for recognized systematic effects, to-
gether with their standard uncertainties (estimated standard
g Figures 1 and 2 have been reproduced with the permission of the International
deviations), either from unknown probability distributions
Organization for Standardization (ISO). The complete guide can be obtained from
that are sampled by means of repeated observations, or from
any IS0 member or from the IS0 Central Secretariat, Postal 56, 12 I 1 Geneva 20
subjective or a priori distributions based on the pool of Switzerland. Copyright remains with ISO.
IS0 15572: 1998(E)
Concepts based on observable quantities
ncorrectcd mean
of ob*ervattons
The corrected m can is the
I,\ es Lima ted value of the
ta/
measurand and the result of
the measuremenl.
Standard uncertainty of the y
r
Combinrd standard uncertainty
uncorrected mean due to the
J of the corrected mean.
dirpersion of the observations f-
Estimated correction for all I It comprises the uncertainty
(for illustration purposes. shown
knowh systematic effects I of the uncorrected mean due to
here as -an interval) f
I I the dispersion of the
obterva-tions and uncertain
tY
I
of the applied correction.
Ideal Concepts based on unknowable quantities
: ’ :{ Unknown error in tbe corrected
Unknown populatlon mean
: 1 * mean due to the unknown “random”
(expectation) with unknown
: I I : error in the uncorrected mean and
standard deviation (indicated
: I
by darker rhadlng)
Unknown value of correction
for all known systematic effects
I
I
Unknown “random” error #
Remaining unknown error
I
I
In the uncorrected mean : I
tn the corrected mean due to
I
ot the observations : I 1
an unrecognized systematic
I
I
: 1
effect
I
: 1
I
’ I
I
Unknown value
of Measureand
FIG. 1 Graphical Illustration 01 Value, Error, and Uncertainty
same location within product of the same density, radiation under a state of statistical control, a combined or pooled
absorption properties, and geometry, for the same nominal variance sp2 or pooled sample standard deviation sp may be
dose and environmental conditions would provide an esti- available (see Practice E 876). In such cases the variance of
mate of the random error in the dosimetry system. The the mean of n independent repeated measurements is sp2/n
sample standard deviation, s,-,, can be referred to as a Type
and the Type A standard uncertainty is uA = sJ&.
A standard uncertainty, u,. 6.2.3 For Type A components of uncertainty, increasing
6.2.1.1 The random component of uncertainty may also the degrees of freedom of uA, equal to n - 1 for the case
be estimated from the separate sources that contribute to the
where s,,- 1 is calculated from n independent measurements,
...