ASTM ISO/ASTM51707-22

Standard Guide for Estimation of Measurement Uncertainty in Dosimetry for Radiation Processing

SIGNIFICANCE AND USE
4.1 Standards such as ISO 11137-1 (radiation sterilization of health care products) and ISO 14470 (irradiation of food) contain requirements that dosimetry used in the development, validation, and routine control of the process shall have measurement traceability to national or international standards and shall have a known level of uncertainty. The magnitude of the measurement uncertainty is important for assessing the results of the measurement system.  
4.1.1 This guide provides information on how to meet the fundamental requirement to determine a known level of uncertainty associated with a dose measurement, how to calculate the overall uncertainty, and how the uncertainty may differ depending on the application (e.g., OQ and PQ dose measurements, routine dose measurement, determination of minimum absorbed dose (Dmin) or maximum absorbed dose (Dmax) from the monitoring location dose (Dmon)). Information is provided on how to identify and calculate different components of uncertainty used to establish an uncertainty budget.  
4.2 Information on the range of achievable uncertainty values for specific dosimetry systems is given in the ISO/ASTM standards for the specific dosimetry systems. While the uncertainty values given in specific dosimetry standards are achievable, it should be noted that both smaller and larger uncertainty values might be obtained depending on measurement conditions and instrumentation. For more information, see also ISO/ASTM 52628.  
4.3 This guide uses the methodology adopted by the GUM for estimating uncertainties in measurements (see 2.4). Therefore, components of uncertainty are evaluated as either Type A uncertainty or Type B uncertainty.  
4.3.1 Quantifying individual components of uncertainty may assist the user in identifying actions to reduce the combined measurement uncertainty.  
4.4 Although this guide provides a framework for assessing uncertainty, it cannot substitute for critical thinking, intellectual honesty, and experi...
SCOPE
1.1 This standard provides guidance on the use of concepts described in the JCGM (Joint Committee for Guides in Metrology) Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement (GUM) to estimate the uncertainties in the measurement of absorbed dose in radiation processing.  
1.2 Methods are given for identifying, evaluating, and estimating the components of measurement uncertainty associated with the use of dosimetry systems, and for calculating combined standard measurement uncertainty and expanded uncertainty of dose measurements based on the GUM methodology.  
1.3 Examples are given on how to develop a measurement uncertainty budget and a statement of uncertainty.  
1.3.1 Key components of uncertainty are derived as part of the derivation of the uncertainty budget. This standard identifies which components of uncertainty are carried forward as part of other analyses (e.g., assessment of process capability and process targets, and process variability), and which components from other standards are brought forward into this standard (e.g., precision of the dose measurement, calibration curve fit, and indirect measurement of dose).  
1.4 This document is one of a set of standards that provides recommendations for properly implementing dosimetry in radiation processing, and provides guidance for achieving compliance with the requirements of ISO 11137-1 (radiation sterilization of health care products), ISO 14470 (treatment of food), and ISO/ASTM 52628 related to the evaluation and documentation of the uncertainties associated with measurements made with a dosimetry system. It is intended to be read in conjunction with ISO/ASTM 52628 (Standard Practice for Dosimetry in Radiation Processing), and ISO/ASTM 51261 (Practice for Calibration of Routine Dosimetry Systems for Radiation Processing).  
1.5 To achieve compliance with the requirements of ISO 11137-1 (radiation sterilization of hea...

General Information

• Status: Published
• Publication Date: 30-Nov-2022
• ICS: 17.240 - Radiation measurements
• Technical Committee: E61 - Radiation Processing
• Drafting Committee: E61.01 - Dosimetry

Relations

• Replaces: ASTM ISO/ASTM51707-15 - Standard Guide for Estimation of Measurement Uncertainty in Dosimetry for Radiation Processing
• Effective Date: 01-Dec-2022

Overview

ASTM ISO/ASTM51707-22: Standard Guide for Estimation of Measurement Uncertainty in Dosimetry for Radiation Processing provides comprehensive guidance on evaluating and documenting measurement uncertainty in the use of dosimetry systems. Developed by ASTM International, this standard aligns with globally recognized quality and metrology practices, including those from the Joint Committee for Guides in Metrology (JCGM) and the Guide to the Expression of Uncertainty in Measurement (GUM).

Measurement uncertainty is a critical factor in radiation processing, impacting both product quality and regulatory compliance. This guide addresses requirements found in key sector standards such as ISO 11137-1 (for health care product sterilization) and ISO 14470 (for food irradiation), which mandate traceable dosimetry and clearly defined uncertainty levels.

Key Topics

• Measurement Uncertainty Estimation: Provides methods for identifying, evaluating, and estimating components of measurement uncertainty in dosimetry systems, including both Type A (statistical) and Type B (expert judgment or prior knowledge) evaluations.
• Uncertainty Budget Development: Offers step-by-step guidance and examples on assembling an uncertainty budget, encapsulating all major uncertainty components, probability distributions, estimation methods, and calculation approaches.
• Traceability and Calibration: Stresses the importance of traceability to national or international standards, achieved through calibration by an approved laboratory (accredited to ISO/IEC 17025 or recognized as a national metrology institute).
• Application-Specific Considerations: Details how uncertainty may vary depending on the intended use, such as operational qualification (OQ), performance qualification (PQ), routine process control, and determination of minimum or maximum absorbed dose.
• Documentation Practices: Recommends clear documentation and periodic reassessment of the uncertainty budget to ensure sustained process reliability and regulatory compliance.
• Integration with Other Standards: Clarifies overlap and integration with key dosimetry and calibration standards, including ISO/ASTM 52628 and ISO/ASTM 51261.

Applications

This standard is invaluable in any context where radiation dosimetry is used for process control, product validation, or regulatory certification, including:

• Medical Device Sterilization: Assures that measurement uncertainty in radiation dose is well characterized and documented, as required by ISO 11137-1.
• Food Irradiation: Supports compliance with ISO 14470 by enabling consistent determination and documentation of dose uncertainty.
• Industrial Radiation Processing: Used for routine control, process development, and validation activities in polymer modification, material processing, and sterilization of various products.
• Quality Management Systems: Allows facilities to support ISO/IEC 17025 accreditation and demonstrate robust uncertainty evaluation during audits and reviews.
• Research and Development: Enables accurate reporting and assessment of dosimetry results for experimental and pilot-scale radiation processing.

Related Standards

For comprehensive implementation and to ensure full compliance, users should reference the following related standards:

• ISO/ASTM 52628 - Practice for Dosimetry in Radiation Processing
• ISO/ASTM 51261 - Practice for Calibration of Routine Dosimetry Systems for Radiation Processing
• ISO 11137-1 - Sterilization of Health Care Products - Radiation - Requirements for Development, Validation and Routine Control
• ISO 14470 - Food Irradiation - Requirements for Process Development, Validation and Control
• ISO/IEC 17025 - General Requirements for the Competence of Testing and Calibration Laboratories
• JCGM 100 (GUM) - Guide to the Expression of Uncertainty in Measurement

Practical Value

By following ASTM ISO/ASTM51707-22, organizations involved in radiation processing dosimetry can:

• Achieve robust, repeatable, and traceable measurement systems
• Quantify and minimize sources of error in dose measurement
• Support regulatory submissions with evidence-based uncertainty documentation
• Enhance quality assurance measures leading to improved product safety and compliance
• Facilitate global trade by demonstrating adherence to international metrology and standardization principles

Implementation of this guide ensures your dosimetry practices are state-of-the-art and fully aligned with international best practices and regulatory expectations for measurement uncertainty in radiation processing.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: 51707 − 22
Standard Guide for
Estimation of Measurement Uncertainty in Dosimetry for
Radiation Processing
This standard is issued under the fixed designation 51707; the number immediately following the designation indicates the year of
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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope (Practice for Calibration of Routine Dosimetry Systems for
Radiation Processing).
1.1 This standard provides guidance on the use of concepts
1.5 To achieve compliance with the requirements of ISO
described in the JCGM (Joint Committee for Guides in
11137-1 (radiation sterilization of health care products), ISO
Metrology) Evaluation of Measurement Data – Guide to the
14470 (treatment of food), and other applications, a measure-
Expression of Uncertainty in Measurement (GUM) to estimate
ment is accompanied by a statement of the uncertainty.
the uncertainties in the measurement of absorbed dose in
radiation processing.
1.6 This guide does not address the establishment of process
specifications or conformity assessment.
1.2 Methods are given for identifying, evaluating, and
estimating the components of measurement uncertainty asso-
1.7 This standard does not purport to address all of the
ciated with the use of dosimetry systems, and for calculating
safety concerns, if any, associated with its use. It is the
combined standard measurement uncertainty and expanded
responsibility of the user of this standard to establish appro-
uncertainty of dose measurements based on the GUM meth-
priate safety, health, and environmental practices and deter-
odology.
mine the applicability of regulatory limitations prior to use.
1.8 This international standard was developed in accor-
1.3 Examples are given on how to develop a measurement
dance with internationally recognized principles on standard-
uncertainty budget and a statement of uncertainty.
ization established in the Decision on Principles for the
1.3.1 Key components of uncertainty are derived as part of
Development of International Standards, Guides and Recom-
the derivation of the uncertainty budget. This standard identi-
mendations issued by the World Trade Organization Technical
fies which components of uncertainty are carried forward as
Barriers to Trade (TBT) Committee.
part of other analyses (e.g., assessment of process capability
and process targets, and process variability), and which com-
2. Referenced documents
ponents from other standards are brought forward into this
2.1 ASTM Standards:
standard (e.g., precision of the dose measurement, calibration
E178 Practice for Dealing With Outlying Observations
curve fit, and indirect measurement of dose).
E456 Terminology Relating to Quality and Statistics
1.4 This document is one of a set of standards that provides
E2232 Guide for Selection and Use of Mathematical Meth-
recommendations for properly implementing dosimetry in
ods for Calculating Absorbed Dose in Radiation Process-
radiation processing, and provides guidance for achieving
ing Applications
compliance with the requirements of ISO 11137-1 (radiation
E3083 Terminology Relating to Radiation Processing: Do-
sterilization of health care products), ISO 14470 (treatment of
simetry and Applications
food), and ISO/ASTM 52628 related to the evaluation and
2.2 ISO/ASTM Standards:
documentation of the uncertainties associated with measure-
51261 Practice for Calibration of Routine Dosimetry Sys-
ments made with a dosimetry system. It is intended to be read
tems for Radiation Processing
in conjunction with ISO/ASTM 52628 (Standard Practice for
51608 Practice for dosimetry in an X-ray (bremsstrahlung)
Dosimetry in Radiation Processing), and ISO/ASTM 51261
facility for radiation processing at energies between 50
keV and 7.5 MeV
51649 Practice for Dosimetry in an Electron Beam Facility
This guide is under the jurisdiction of ASTM Committee E61 on Radiation
Processing and is the direct responsibility of Subcommittee E61.01 on Dosimetry.
Originally developed as a joint ASTM/ISO standard in conjunction with ISO/TC
85/WG 3. For referenced ASTM and ISO/ASTM standards, visit the ASTM website,
Current edition approved Dec. 1, 2022. Published May 2024. Originally www.astm.org, or contact ASTM Customer Service at [e-mail]. For
approved in 1995. Last previous edition approved in 2015 as ISO/ASTM Annual Book of ASTM Standards volume information, refer to the standard’s
51707:2015(E). DOI: 10.1520/51707-22. Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
51707 − 22
for Radiation Processing at Energies Between 300 keV 3.2.1 approved calibration laboratory—calibration labora-
and 25 MeV tory that is a recognized national metrology institute; or has
51702 Practice for Dosimetry in a Gamma Facility for been formally accredited by ISO/IEC 17025.
Radiation Processing 3.2.1.1 Discussion—A recognized national metrology insti-
52628 Practice for Dosimetry in Radiation Processing tute or other calibration laboratory accredited by ISO/IEC
17025 should be used for irradiation of dosimeters or dose
2.3 ISO Documents:
measurements for calibration in order to ensure traceability to
ISO 11137-1 Sterilization of Health Care Products — Ra-
a national or international standard.
diation — Part 1: Requirements for development, valida-
tion and routine control of a sterilization process for
3.2.2 arithmetic mean, average [GUM, C.2.19]—sum of
medical devices
values divided by the number of values:
ISO 11137-3 Sterilization of Health Care Products — Ra-
diation — Part 3: Guidance on Dosimetric Aspects of
x¯ 5 x , i 5 1, 2, 3 … n (1)
( i
n
i
Development, Validation and Routine Control
ISO 11137-4 Sterilization of health care products — Radia- where:
tion — Part 4: Guidance on process control. General
x = individual values of parameters with i = 1, 2, 3 . n.
i
information
3.2.2.1 Discussion—The term ‘mean’ is used generally
ISO 12749-4 Nuclear energy, nuclear technologies, and
when referring to a population parameter and the term ‘aver-
radiological protection — Vocabulary — Part 4: Dosim-
age’ when referring to the result of a calculation on the data
etry for radiation processing
obtained in a sample.
ISO 14470 Food irradiation — Requirements for the
3.2.3 calibration curve [VIM, 4.31]—expression of the
development, validation and routine control of the process
of irradiation using ionizing radiation for the treatment of relation between indication and corresponding measured quan-
tity value.
food
ISO/IEC 17025 General Requirements for the Competence 3.2.3.1 Discussion—In radiation processing standards, the
term “dosimeter response” is generally used for “indication.”
of Testing and Calibration Laboratories
2.4 Joint Committee for Guides in Metrology (JCGM)
3.2.4 coeffıcient of variation (CV)—sample standard devia-
Reports:
tion expressed as a percentage of sample average value:
JCGM 100:2008, GUM 1995, with minor correc-
S
tions, Evaluation of measurement data — Guide to the CV 5 × 100 % (2)
x¯
Expression of Uncertainty in Measurement
3.2.5 combined standard measurement uncertainty [VIM,
JCGM 200:2008, VIM, International vocabulary of metrol-
6 2.31]—standard measurement uncertainty that is obtained us-
ogy — Basis and general concepts and associated terms
ing the individual standard measurement uncertainties associ-
2.5 ICRU Reports:
ated with the input quantities in a measurement model.
ICRU Report 80 Dosimetry Systems for Use in Radiation
3.2.5.1 Discussion—
Processing
(1) It is also referred to as ‘combined standard uncertainty.’
ICRU Report 85a Fundamental Quantities and Units for
(2) In case of correlations of input quantities in a measure-
Ionizing Radiation
ment model, covariances must also be taken into account when
calculating the combined standard measurement uncertainty. A
3. Terminology
description of covariances may be found in the GUM
3.1 VIM Definitions:
reference, Annex C.
3.1.1 For definitions quoted here from the VIM, only
3.2.6 coverage factor (k) [VIM, 2.38]—number larger than
selected NOTES and EXAMPLES are included in 3.2. See
one by which a combined standard measurement uncertainty is
VIM for further information.
multiplied to obtain an expanded measurement uncertainty.
3.2 Definitions:
3.2.7 expanded uncertainty [GUM, 2.3.5]—quantity defin-
ing the interval about the result of a measurement that may be
expected to encompass a large fraction of the distribution of
Available from Association for the Advancement of Medical Instrumentation
values that could reasonably be attributed to the measurand.
(AAMI), 4301 N. Fairfax Dr., Suite 301, Arlington, VA 22203-1633, http://
www.aami.org.
3.2.7.1 Discussion—Expanded uncertainty is obtained by
Available from International Organization for Standardization (ISO), ISO
multiplying the combined standard uncertainty by a coverage
Central Secretariat, Chemin de Blandonnet 8, CP 401, 1214 Vernier, Geneva,
factor, the value of which determines the magnitude of the
Switzerland, https://www.iso.org.
Document produced by Working Group 1 of the Joint Committee for Guides in ‘fraction.’ Expanded uncertainty is also referred to as ‘overall
Metrology (JCGM/WG 1). Available free of charge at the BIPM website (http://
uncertainty.’
www.bipm.org).
3.2.8 influence quantity [VIM, 2.52]—quantity that, in a
Document produced by Working Group 2 of the Joint Committee for Guides in
Metrology (JCGM/WG 2). Available free of charge at the BIPM website (http://
direct measurement, does not affect the quantity that is actually
www.bipm.org).
measured, but affects the relation between the indication and
Available from International Commission on Radiation Units and Measure-
the measurement result.
ments (ICRU), 7910 Woodmont Ave., Suite 400, Bethesda, MD 20841-3095,
http://www.icru.org. 3.2.8.1 Discussion—In radiation processing dosimetry, this
51707 − 22
term includes temperature, relative humidity, time intervals, (3) The abbreviated term “traceability” is sometimes used
light, radiation energy, absorbed dose rate, and other factors to mean ‘metrological traceability’ as well as other concepts,
such as ‘sample traceability,’ ‘document traceability,’ ‘instru-
that might affect dosimeter response, as well as quantities
associated with the measurement instrument. ment traceability,’ or ‘material traceability,’ where the history
(“trace”) of an item is meant. Therefore, the full term of
3.2.9 level of confidence—probability that the value of a
“metrological traceability” is preferred if there is any risk of
parameter will fall within the given range.
confusion.
3.2.10 measurand [VIM, 2.3]—quantity intended to be mea-
3.2.14 quadrature—method used in estimating combined
sured.
standard uncertainty from independent sources by taking the
3.2.10.1 Discussion—In radiation processing dosimetry, the
positive square root of the sum of the squares of individual
measurand is the absorbed dose (Gy) or simply ‘dose.’
components of uncertainty, for example, coefficient of varia-
3.2.11 measurement [VIM, 2.1]—process of experimentally
tion.
obtaining one or more quantity values that can reasonably be
3.2.15 quantity [VIM, 1.1]—property of a phenomenon,
attributed to a quantity.
body, or substance, where the property has a magnitude that
3.2.12 measurement uncertainty [VIM, 2.26]—non-negative
can be expressed as a number and a reference.
parameter characterizing the dispersion of the quantity values
3.2.16 quantity value [VIM, 1.19]—number and reference
being attributed to a measurand, based on the information used.
together expressing magnitude of a quantity.
3.2.12.1 Discussion—
3.2.16.1 Discussion—For example, absorbed dose of
(1) Measurement uncertainty includes components arising
from systematic effects, such as components associated with 25 kGy.
3.2.17 repeatability (of results of measurements) [GUM,
corrections and the assigned quantity values of measurement
B.2.15]—closeness of the agreement between the results of
standards. Sometimes estimated systematic effects are not
successive measurements of the same measurand carried out
corrected for but, instead, associated measurement uncertainty
under the same conditions of measurement.
components are incorporated.
(2) The parameter may be, for example, a standard devia- 3.2.17.1 Discussion—
tion called standard measurement uncertainty (or a specified
(1) These conditions are called ‘repeatability conditions.’
multiple of it), or the half-width of an interval, having a stated
(2) Repeatability conditions include: the same measure-
coverage probability. ment procedure, the same observer, the same measuring
(3) Measurement uncertainty is comprised of many com-
instrument used under the same conditions, the same location,
ponents. Some of these may be evaluated by Type A evaluation repetition over a short period of time.
of measurement uncertainty from the statistical distribution of (3) Repeatability may be expressed quantitatively in terms
the quantity values from a series of measurements and can be of the dispersion characteristics of the results.
characterized by standard deviations. The other components,
3.2.18 reproducibility (of results of measurements) [GUM,
which may be evaluated by Type B evaluation of measurement
B.2.16]—closeness of the agreement between the results of
uncertainty, can also be characterized by standard deviations,
measurements of the same measurand carried out under
evaluated from probability density functions based on experi-
changed conditions of measurement.
ence or other information.
3.2.18.1 Discussion—
(4) In general, for a given set of information, it is under-
(1) A valid statement of reproducibility requires specifica-
stood that the measurement uncertainty is associated with a
tion of the conditions changed.
stated quantity value attributed to the measurand. A modifica-
(2) The changed conditions may include principle of
tion of this value results in a modification of the associated
measurements, method of measurement, observer, measuring
uncertainty.
instrument, reference standard, location, conditions of use, and
(5) In radiation processing applications, the quantity of
time.
interest is usually absorbed dose to water. The uncertainty
(3) Reproducibility may be expressed quantitatively in
estimate therefore should also pertain to absorbed dose to
terms of the dispersion characteristics of the results.
water. Any differences between absorbed dose to water and
3.2.19 sample standard deviation (S)—measure of disper-
absorbed dose to product are outside the scope of this guide.
sion of values of the same measurand expressed as the positive
3.2.13 metrological traceability [VIM, 2.41]—property of a
square root of the sample variance.
measurement result whereby the result can be related to a
3.2.19.1 Discussion—This definition has been adapted from
reference through a documented unbroken chain of
GUM.
calibrations, each contributing to the measurement uncertainty.
3.2.20 sample variance [GUM, C.2.20]—measure of
3.2.13.1 Discussion—
dispersion, which is the sum of the squared deviations of
(1) The unbroken chain of calibrations is referred to as
observations from their average divided by (n – 1), given by
“traceability chain.”
the expression:
(2) Metrological traceability of a measurement result does
not ensure that the measurement uncertainty is adequate for a x 2 x¯
~ !
( i
S 5 (3)
given purpose or that there is an absence of mistakes. n 2 1
~ !
51707 − 22
where: is provided on how to identify and calculate different compo-
nents of uncertainty used to establish an uncertainty budget.
x = individual value of parameter with i = 1, 2 . n, and
i
x¯ = mean of n values of parameter (see 3.2.2).
4.2 Information on the range of achievable uncertainty
3.2.21 standard measurement uncertainty [VIM, 2.30]—
values for specific dosimetry systems is given in the ISO/
measurement uncertainty expressed as a standard deviation. ASTM standards for the specific dosimetry systems. While the
3.2.21.1 Discussion—Also referred to as ‘standard uncer-
uncertainty values given in specific dosimetry standards are
tainty of measurement’ or ‘standard uncertainty.’ achievable, it should be noted that both smaller and larger
uncertainty values might be obtained depending on measure-
3.2.22 true value [VIM, 2.11]—quantity value consistent
ment conditions and instrumentation. For more information,
with the definition of a quantity.
see also ISO/ASTM 52628.
3.2.22.1 Discussion—True value is by its nature indetermi-
nate and only an idealized concept. In this guide, the terms
4.3 This guide uses the methodology adopted by the GUM
“true value of a measurand” and “value of a measurand” are
for estimating uncertainties in measurements (see 2.4).
viewed as equivalent (see 5.1.1).
Therefore, components of uncertainty are evaluated as either
3.2.23 Type A evaluation of measurement uncertainty [VIM, Type A uncertainty or Type B uncertainty.
2.28]—evaluation of a component of measurement uncertainty
4.3.1 Quantifying individual components of uncertainty
by a statistical analysis of measured quantity values obtained
may assist the user in identifying actions to reduce the
under defined measurement conditions.
combined measurement uncertainty.
3.2.24 Type B evaluation of measurement uncertainty [VIM,
4.4 Although this guide provides a framework for assessing
2.29]—evaluation of a component of measurement uncertainty
uncertainty, it cannot substitute for critical thinking, intellec-
determined by means other than a Type A evaluation of
tual honesty, and experience. The evaluation of uncertainty
measurement uncertainty.
depends on detailed knowledge of the nature of the measurand
3.2.25 uncertainty budget [VIM, 2.33]—statement of a mea- and of the measurement method and procedure used. The
surement uncertainty, of the components of that measurement utility of the uncertainty quoted for the result of a measurement
uncertainty, and of their calculation and combination. therefore ultimately depends on the understanding, critical
3.2.25.1 Discussion—An uncertainty budget should include analysis, and integrity of those who contribute to the assign-
the measurement method, estimates, and measurement uncer- ment of its value (GUM 3.4.8 JCGM 100:2008).
tainties associated with the quantities in the measurement
method, covariances, type of applied probability density 5. Determination of the uncertainty budget
functions, degrees of freedom, type of evaluation of measure-
5.1 Measurement:
ment uncertainty, and any coverage factor.
5.1.1 The objective of a measurement is to determine the
3.3 Definitions of other terms used in this standard that
value of the measurand, that is, the value of the specific
pertain to radiation measurement and dosimetry may be found
quantity to be measured (absorbed dose). A measurement
in ISO/ASTM Practice 52628. Other terms that pertain to
therefore begins with an appropriate specification of the
radiation measurement and dosimetry may be found in ASTM
measurand, the method of measurement, the measurement
Terminology E3083 and ISO Terminology ISO 12749-4.
system, and the measurement procedure.
Where appropriate, definitions used in these standards have
5.1.2 With the completion of the dosimetry system’s cali-
been derived from and are consistent with definitions in ICRU
bration and establishment of metrological traceability, the
Report 85a, and general metrological definitions given in the
result of each dose measurement represents the best estimate of
VIM.
dose. The associated uncertainty should always be included
when reporting a dose measurement, but the reported measure-
4. Significance and use
ment result should not be corrected for the uncertainty.
4.1 Standards such as ISO 11137-1 (radiation sterilization of
5.2 Uncertainty:
health care products) and ISO 14470 (irradiation of food)
5.2.1 A measurement is always accompanied by a statement
contain requirements that dosimetry used in the development,
of the uncertainty. The uncertainty of the measurement result
validation, and routine control of the process shall have
reflects the inability to know the true value of the measurand.
measurement traceability to national or international standards
A lower value of overall uncertainty reflects a higher degree of
and shall have a known level of uncertainty. The magnitude of
confidence in the estimate of the value of the measurand.
the measurement uncertainty is important for assessing the
5.2.2 This guide will allow the user to evaluate known and
results of the measurement system.
potentially significant components of uncertainty that should
4.1.1 This guide provides information on how to meet the
be included in the uncertainty estimate, including those arising
fundamental requirement to determine a known level of
from calibration, dosimeter response, instrument stability, and
uncertainty associated with a dose measurement, how to
the effect of influence quantities.
calculate the overall uncertainty, and how the uncertainty may
differ depending on the application (e.g., OQ and PQ dose 5.2.3 A quantitative analysis of components of uncertainty
measurements, routine dose measurement, determination of is referred to as an uncertainty budget and is often presented in
minimum absorbed dose (D ) or maximum absorbed dose the form of a table (see Table 1 and Annex A1). Typically, the
min
(D ) from the monitoring location dose (D )). Information uncertainty budget will identify all significant components of
max mon
51707 − 22
TABLE 1 Example of an uncertainty budget (dosimetry system calibration)
Relative Standard Deviation (k=1)
Component of Uncertainty Reference Probability Distribution
Type A Type B
Approved calibration laboratory Sections 5.3, 5.4 Gaussian 1.30 %
Certified Dose (u ) Annex A1
lab
Calibration Curve Fit Section 5.5 Gaussian 0.95 %
(u ) Annex A1.5
fit
Environmental Effects Section 5.6 Rectangular 0.70 %
(Irradiation Temperature, Dose Rate, Annex A1.6
Energy Spectrum)
(u )
environment
Dosimeter Thickness Uncertainty (or Section 5.6 Gaussian 1.35 %
mass) Annex A1.7
(u )
thickness
Uncertainty in Dosimeter Response Section 5.7 Gaussian 1.55 %
(Precision of the measurement) Eq A1.1,
(u ) Annex A1.4
precision
Combined Uncertainty (k=1) Eq 4 2.7 %
Combined Expanded Uncertainty (k=2) Eq 5 5.4 %
NOTE 1—In specific cases, either a Type A or a Type B route may be
uncertainty together with their methods of estimation, statisti-
used in the assessment of the component of uncertainty, for example
cal distributions (for example, rectangular, triangular,
uncertainty due to dosimeter placement might be estimated using a
Gaussian), magnitudes, and methods of combination. The
rectangular distribution or a mathematical model.
Gaussian and rectangular probability distributions are dis-
5.2.4.3 In many cases, an estimate of the expected value of
cussed in more detail in Annex A2. Step-by-step guidance is in
a quantity is obtained by multiple independent measurements
the GUM (JCGM 100:2008, GUM 1995, Section 4.3).
made under conditions of repeatability and is given by the
5.2.4 The uncertainty associated with a measurement can
arithmetic mean, x¯, or average of those measurement results.
arise from several different components. In the assessment of
The sample standard deviation, s, of these observations char-
measurement uncertainty, it is necessary to consider all steps
acterizes the variability of the observed values or their disper-
associated with making a measurement and assign to each step
sion about the mean. The standard uncertainty of the mean
an uncertainty value, in the form of a standard deviation or
value is given by s/√n. Therefore, for Type A components of
standard uncertainty. These individual components can be
uncertainty, increasing the number of measurements will re-
collected to produce a combined uncertainty for the
duce the standard uncertainty of the mean.
measurement, generally by summing in quadrature the indi-
vidual component standard uncertainties (i.e. calculating the
5.2.4.4 In cases where only a single or very few measure-
square root of the sum of the squares of the individual
ments are made, the estimate of the sample standard deviation
components). Refer to Eq 4. Components of uncertainty are
has to be taken from prior measurements made using the same
generally classified as Type A or Type B, depending on their
dosimetry system. The sample standard deviation could be
evaluation method.
determined from a single set of prior measurements or derived
5.2.4.1 The purpose of the Type A and Type B classification
as a pooled standard deviation from several sets of prior
is to indicate two different ways of evaluating uncertainty
measurements.
components. Both types of evaluation are based on probability
5.2.4.5 The Type A standard uncertainties are determined by
distributions and the uncertainty components resulting from
the experimental design that is used to collect the observations
each type are quantified by a standard deviation or a variance.
for the uncertainty estimate. If the estimated Type A uncer-
5.2.4.2 A Type A standard uncertainty is obtained from a
tainty is unacceptably large, the individual components of
probability density function (PDF) inferred from a series of
uncertainty may be estimated by a more refined experimental
repeated observations, while a Type B standard uncertainty is
design. Knowledge of the components contributing to the
obtained from an assumed probability density function based
estimated uncertainty might allow identification of components
on the degree of belief that an event will occur. Both ap-
that can be controlled to reduce uncertainty.
proaches are considered statistical methods and are valid
interpretations of probability. For example, the random scatter NOTE 2—For example, if optical absorbance of a film dosimeter is
measured during calibration without controlling film thickness, relative
between replicate dosimeters is a Type A component of
humidity, or temperature, the dose uncertainty from this calibration may
uncertainty, whereas estimations of the effect of irradiation
be unacceptably large. An experimental design that controls these factors
temperature are generally evaluated as Type B components,
may indicate the film thickness and relative humidity have significant
based on the known ranges of temperature during the irradia-
effects on measured absorbance. Controlling these influence quantities
tion. during calibration and routine dosimetry will reduce the uncertainty.
51707 − 22
5.2.5 The Type B component of uncertainty is evaluated by on the risk assessment for the product and process assumed by
using all relevant information on the possible variability of the the user and customer. See Annex A1 for a description of the
input quantities X . For the input value X that has not been normal distribution.
i i
obtained from repeated measurements, the estimated variance,
NOTE 4—The coverage factor k is always stated when reporting
u , or standard uncertainty, u , is evaluated by judgment using
B B
expanded uncertainty in order that the combined standard uncertainty of
all relevant information on the possible variability of X . This
the measured quantity can be recovered.
i
pool of information may include previous measurement data or
5.2.8 An understanding of the individual uncertainty com-
documented performance characteristics of the dosimetry sys-
ponents is essential when assessing the significance of routine
tem.
measurements. For example, in relative dose mapping the only
5.2.5.1 Several methods may be used to develop estimates
significant component of uncertainty may be dosimeter
of the magnitude of Type B standard uncertainty. One method
reproducibility, whereas it will be necessary to consider all
estimates the maximum magnitude likely to be observed for
components of uncertainty for traceable dose measurements.
each input quantity. For example, if the dosimeter response is
5.2.9 The uncertainty budget should be periodically re-
known to vary with irradiation temperature, then the tempera-
assessed by the user to confirm the estimate is still valid.
ture range routinely seen in operation should be used to
5.2.9.1 There should be a documented rationale for the time
estimate this component of uncertainty. If there is no specific
interval between re-assessments that should include, for
knowledge about the possible values of X within its estimated
i
example, the potential effects on the dosimetry system calibra-
bounds of a to a , it is assumed that it is equally probable for
– + tion of seasonal changes in temperature and humidity and
X to take on any value within those bounds (that is a
i
changes in dose rate.
rectangular distribution, see Fig. A2.2). As stated in JCGM
5.2.10 The user should define limits for acceptable changes
100:2008 (GUM), the sample standard deviation is a/√3 for
of the uncertainty budget, and the user should perform assess-
such a distribution. In some cases, it is more realistic to expect
ment of effects of changes.
that values near the bounds are less likely than those near the
5.2.11 As per ISO/ASTM 51261, the calibration of a routine
midpoint. It may then be reasonable to replace the rectangular
dosimetry system consists of:
distribution with a symmetric triangular distribution with a
5.2.11.1 The selection of the calibration dosimeters;
base width of a – a = 2a, see Fig. A2.2. Assuming such a
+ – 5.2.11.2 The determination of the target dose levels and the
triangular distribution for X , the expectation value of X is (a
i i –
irradiation of the calibration dosimeters;
+ a )/2 and its variance is a /6. Thus, the Type B standard
+
5.2.11.3 The calibration and performance verification of
uncertainty, u = a/√6 (see JCGM 100:2008 (GUM)).
B
measurement instrumentation;
5.2.5.2 It is important not to “double count” uncertainty
5.2.11.4 The measurement of the calibration dosimeter re-
components. For example, if a component of uncertainty
sponse;
arising from a particular effect is obtained from a Type B
5.2.11.5 The analysis of the calibration dosimeter response
evaluation, it should be included as an independent component
data;
of uncertainty in the calculation of the combined standard
5.2.11.6 The calibration curve determination;
uncertainty of the measurement result only to the extent that
5.2.11.7 The verification of the calibration curve for actual
the effect does not contribute to the observed variability of the
conditions of use, if required; and
observations. This is because the uncertainty due to that
5.2.11.8 The determination of the uncertainty budget.
portion of the effect that contributes to the observed variability
Note that 5.2.11.1, 5.2.11.2, and 5.2.11.3 do not have an
is already included in the component of uncertainty obtained
associated component of uncertainty, but they will have an
from the statistical analysis of the observations (GUM).
impact on the components of uncertainty associated with the
calibration curve and dosimeter response data.
NOTE 3—An example is time-dependent (or seasonal) drift in dosimeter
response. This drift would not be seen in a Type A experiment, but could
5.3 Uncertainties in Calibration Doses from the Approved
be captured as a Type B component.
Calibration Laboratory:
5.2.6 The combined standard uncertainty, denoted by u , of
5.3.1 The approved calibration laboratory’s certificate con-
c
the result of a measurement is obtained by combining the tains the uncertainty of the absorbed-dose value (i.e. calibration
components of uncertainty of both types. This is done by
irradiations performed by the approved calibration laboratory),
taking the square root of the sum of the squares of each or the absorbed-dose measurement (i.e. reference dosimeter),
component of uncertainty.
typically at 95 % confidence level, but the value of the
uncertainty and its confidence level should be stated.
5.2.7 The coverage factor k is generally taken as k=2,
approximating equivalent a 95 % level of confidence for a 5.3.2 The component of uncertainty in the dose reported by
the approved calibration laboratory may include:
two-sided Gaussian distribution, or a 97.5 % level of confi-
dence for a one-sided Gaussian distribution. Two-sided distri- 5.3.2.1 Response of the reference dosimeters;
5.3.2.2 Irradiation time of the calibration dosimeters;
butions are used for calculating combined standard measure-
ment uncertainty and expanded uncertainty of dose 5.3.2.3 Gamma source decay corrections;
measurements based on the GUM methodology. Therefore, a 5.3.2.4 Non-uniformities in the irradiation field; and
dose measurement established with k=2 means that there is 5 % 5.3.2.5 Corrections for attenuation and irradiation geometry
chance (risk) that the dose might lie outside the defined (between the reference dosimeter and the calibration dosim-
confidence interval. Different values of k are applicable based eter).
51707 − 22
5.3.3 The approved calibration laboratory may provide the 5.4.6.8 If the calculated differences are within predefined
details of their uncertainty budget, or simply provide a single limits, a component of uncertainty should be included. This
value for the combined overall uncertainty. In either case, the component is estimated using a/√3 and carried forward as a
combined uncertainty reported by the approved lab is, by Type B uncertainty.
convention, carried forward by the user as a Type B component 5.4.6.9 If the calculated differences are outside predefined
of uncertainty. limits but have a consistent bias over the full range, a
correction factor can be applied to the calibration curve.
5.4 Uncertainty Components Related to Specific Methods of
5.4.6.10 The component of uncertainty associated with the
Dosimetry System Calibration:
correction factor is performed according to 5.4.6.6 or 5.4.6.7
5.4.1 For the “in-situ” calibration method (and the in-situ
and carried forward as a Type B uncertainty.
verification process for a calibration-laboratory calibration), it
5.5 Uncertainty Due to the Fit of Calibration Function:
is important for the user to consider potentially significant
sources of uncertainty such as: 5.5.1 The uncertainty arising from fitting the measurement
results to a calibration curve can be obtained from the
5.4.1.1 The effect irradiation temperature on the reference
dose measurement; and residuals, i.e. the difference between doses calculated using the
calibration curve and the calibration doses. This component of
5.4.1.2 The potential variation in dose within the phantom
uncertainty may be evaluated as a Type A uncertainty. This
containing the reference and routine dosimeters and might
component of uncertainty estimate may include:
contain a temperature indicator.
5.5.1.1 Variation in response of dosimeters; and
5.4.2 These sources of uncertainty are often treated as Type
5.5.1.2 Analytical function used in fit.
B estimates (i.e. prior knowledge of the temperature variation
5.5.2 The absorbed dose is the independent variable (X),
in the irradiator can be estimated).
and the dosimeter response (Y) is the dependent variable which
5.4.3 Dosimeter phantoms should be designed to minimize
is expressed as Y=f(X).
the dose variation within the dosimeter volume. However, in
5.5.3 The calibration function has an associated uncertainty
practice, differences will exist and can be estimated or calcu-
since the mathematical form does not truly represent the data
lated using mathematical methods.
set; in addition, the function has been derived from a finite
5.4.4 The effective standard deviation for a rectangular
number of data points. Accurate determination of the uncer-
distribution is a/√3.
tainty due to curve fitting may be complex, but commercial
5.4.5 If the calculated differences are within predefined
software packages and approved calibration laboratories are
limits, a component of uncertainty should be included. This
available to assist with the evaluation.
component is estimated using a/√3 and carried forward as a
5.5.3.1 The calibration curve can be broken into separate
Type B uncertainty.
dose ranges; each range will have a different uncertainty
5.4.5.1 If the calculated differences are outside predefined
assessment.
limits but have a consistent bias over the full range, a
5.5.3.2 One example of the calculation of the curve fit
correction factor can be applied to the calibration curve.
uncertainty is provided in Annex A1. In general terms, the
5.4.5.2 The component of uncertainty associated with the
statistics of the fitting process mean the fractional uncertainty
correction factor is carried forward as a Type B uncertainty.
will be smallest near the centre of the calibration curve dose
5.4.6 For the “calibration laboratory” calibration method, it
range and increase towards the extremes.
is important for the user to consider potentially significant
5.5.3.3 Depending on the characteristics of the dosimetry
sources of uncertainty:
system, the uncertainty might increase at the lower extreme of
5.4.6.1 The approximate correction for the effects seen in
the curve, where the “signal-to-noise” ratio deteriorates (i.e.
the calibration verification and can be estimated from the
the signal becomes markedly smaller), and at high doses when
difference between the measurements of the reference dosim-
the calibration function begins to saturate (i.e. the dosimeter
eters and from the calibration dosimeters.
response per unit dose becomes increasingly smaller). In
5.4.6.2 Corrections for differences between the laboratory’s
addition, within a dataset, there is more information near the
reference-standard dosimeter and the routine dosimeter within
middle portion of the curve than near the dose extremes. This
the dosimeter stand.
is especially true in an unweighted linear least-squares regres-
5.4.6.3 The effect irradiation temperature on the reference
sion fit where all data points are equally treated.
dose measurement.
5.5.3.4 For a given mathematical function, the use of the
5.4.6.4 The dosimeter measurements are those obtained
curve fit uncertainty near the centre of the calibrated range is a
when replicates have been averaged and correction made for
common approach. For some applications, it may be necessary
potential systematic offsets.
to use a separate curve fit uncertainty in the low dose part of the
5.4.6.5 There are two approaches for estimating the value
curve. In many applications, a single value for the curve fit
for this standard uncertainty:
percentage uncertainty is carried forward in the uncertainty
5.4.6.6 Calculate the root-mean-square value of the indi-
budget.
vidual differences observed between the two types of dosim-
eter; or 5.6 Uncertainty Due to Influence Quantities:
5.4.6.7 Use the formula a/√3 where “a” is the maximum 5.6.1 Contributions to the combined uncertainty in mea-
calculated difference between the reference dosimeters and the sured dose from influence quantities which are different during
calibration dosimeters. routine use and calibration may include the following:
51707 − 22
5.6.1.1 The temperature and humidity at which unirradiated 5.6.2.2 If seasonal variations in temperature and humidity
and post-irradiated dosimeters are stored will usually be lead to significant effects, recalibration or a redetermination of
the uncertainty may be necessary. For example, calibration
defined as a range by the dosimeter manufacturer, the user’s
procedures, and published data. verification exercises conducted during extremes of seasonal
variation, or immediately following a source reload in a
(1) Dispersion of dosimeter response values caused by
gamma facility, can be used to detect these effects.
variation in temperature and humidity before irradiation may
give rise to uncertainty of the dosimeter’s unirradiated signal.
5.7 Uncertainty in Dosimeter Response (Precision of the
This component of uncertainty may be evaluated as Type B
dose measurement):
uncertainty.
5.7.1 The uncertainty of the response of the dosimeters is
(2) Dispersion of dosimeter response values caused by
obtained from the measurement of dosimeters irradiated during
variation in storage temperature and humidity after irradiation
calibration to the same doses. This component of uncertainty is
may give rise to uncertainty of dosimeter response. This
evaluated as a Type A uncertainty from the statistical analysis
component of uncertainty may be evaluated as Type B uncer-
of repeated dosimeter response measurements. The uncertainty
tainty.
in dosimeter response determined during calibration is the first
estimate; the uncertainty during routine measurements is ex-
5.6.1.2 The temperature and humidity at which dosimeters
pected to increase relative to the first estimate but has to be
are irradiated should be known within a given range. Uncer-
quantified by the user. This component of uncertainty estimate
tainties in response caused by variation in temperature and
associated with dosimeter response may include:
humidity within this range may give rise to uncertainty of
5.7.1.1 Intrinsic variation in the dosimeter response;
dosimeter response. This component of uncertainty may be
5.7.1.2 Intrinsic variations in the dosimeter thickness/mass;
evaluated as Type B uncertainty.
5.7.1.3 Measurement of thickness/mass of individual do-
5.6.1.3 The thickness or mass component of uncertainty can
simeters; and
be determined by measurement and carried forward as a Type
5.7.1.4 Intrinsic variation in the measurement equipment
A uncertainty. Dosimeter thickness or mass might also be
performance (which may include variation in dosimeter posi-
within a range, in which case this component of uncertainty
tioning within the instrument).
may be evaluated as Type B uncertainty. One method for
5.7.2 A well-controlled radiation process requires an accu-
determining this component of uncertainty is given in Annex
rate estimate of the repeatability of the routine dose measure-
A1.
ment. Repeatability of the dose measurement is estimated
5.6.1.4 Time of Measurement after Irradiation—The re-
using the inverse of the fit regression curve (X=f(Y)) and the
sponse of some dosimeters might not be stable with time after
calibration dosimeter’s measured response.
irradiation. The time of measurement is usually specified to be
5.7.3 An estimate of measurement repeatability may be
within a given range. Variation in time within this range may
calculated as a pooled relative variance given by Eq A1.1.
give rise to uncertainty of dosimeter response. This component
Refer to Annex A1 for an example. The dosimeter’s response
of uncertainty may be evaluated as Type B uncertainty.
is used to calculate the dose for each calibration sample
5.6.1.5 Instrument Stability—Variations in the instrument
replicate.
performance may have a direct effect on dosimetry uncertainty.
6. Examples of uncertainty budget components
Information about stability of measurement instruments can be
obtained from characterization measurement using standard 6.1 An example of an uncertainty budget listing some of the
reference materials, such as optical filters in case of spectro- components of uncertainty is given in Table 1. It is based on a
photometers. This component of uncertainty may be evaluated calibration carried out by the in-situ calibration method and
as either a Type A or Type B uncertainty. Periodic instrument should be taken only as guide.
recalibration in combination with regular instrument perfor- 6.1.1 As per JCGM 100:2008, GUM 1995, each component
mance checks enable the instrument stability to be determined, of uncertainty in Table 1 includes the type of applied probabil-
and its effect on dose measurements expressed. ity density functions (PDF). Knowledge of the type of PDF and
the k value help to ensure the correct divisor is applied in the
5.6.2 Changes in the environmental conditions in the plant
determination of the relative standard deviation (RSD). Refer
relative to calibration or verification conditions (e.g.,
to Table 1.
temperature, dose rate, or humidity) can influence the routine
dosimeter’s response. This addi
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: ISO/ASTM 51707 − 2015(E) 51707 − 22
Standard Guide for
Estimation of Measurement Uncertainty in Dosimetry for
Radiation Processing
This standard is issued under the fixed designation ISO/ASTM 51707; the number immediately following the designation indicates the
year of 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This standard provides guidance on the use of concepts described in the JCGM (Joint Committee for Guides in Metrology)
Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement (GUM) to estimate the uncertainties
in the measurement of absorbed dose in radiation processing.
1.2 Methods are given for identifying, evaluating, and estimating the components of measurement uncertainty associated with the
use of dosimetry systems, and for calculating combined standard measurement uncertainty and expanded (overall) uncertainty of
dose measurements based on the GUM methodology.
1.3 Examples are given on how to develop a measurement uncertainty budget and a statement of uncertainty.
1.3.1 Key components of uncertainty are derived as part of the derivation of the uncertainty budget. This standard identifies which
components of uncertainty are carried forward as part of other analyses (e.g., assessment of process capability and process targets,
and process variability), and which components from other standards are brought forward into this standard (e.g., precision of the
dose measurement, calibration curve fit, and indirect measurement of dose).
1.4 This document is one of a set of standards that provides recommendations for properly implementing dosimetry in radiation
processing, and provides guidance for achieving compliance with the requirements of ISO 11137-1 (radiation sterilization of health
care products), ISO 14470 (treatment of food), and ISO/ASTM 52628 related to the evaluation and documentation of the
uncertainties associated with measurements made with a dosimetry system. It is intended to be read in conjunction with ISO/ASTM
52628, (Standard Practice for Dosimetry in Radiation Processing), and ISO/ASTM 51261 and ISO/ASTM(Practice for
52701.Calibration of Routine Dosimetry Systems for Radiation Processing).
1.5 To achieve compliance with the requirements of ISO 11137-1 (radiation sterilization of health care products), ISO 14470
(treatment of food), and other applications, a measurement is accompanied by a statement of the uncertainty.
1.6 This guide does not address the establishment of process specifications or conformity assessment.
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and healthsafety, health, and environmental practices and determine
the applicability of regulatory limitations prior to use.
This guide is under the jurisdiction of ASTM Committee E61 on Radiation Processing and is the direct responsibility of Subcommittee E61.01 on Dosimetry, and is also
under the jurisdiction of . Originally developed as a joint ASTM/ISO standard in conjunction with ISO/TC 85/WG 3.
Current edition approved Dec. 1, 2022Sept. 8, 2014. . Published May 2024February 2015. Originally published as ASTM E 1707–95. Last previous ASTM edition
ε1 ε1
E 1707–95. Originally approved in 1995. Last previous edition approved . ASTM E 1707–95 was adopted by ISO in 1998 with the intermediate designation ISO
15572:1998(E). The present International Standard ISO/ASTM 51707:2015(E) is a major revision of the last previous edition ISO/ASTM 51707:2005(E), which replaced
ISO/ASTM 51707:2002(E).in 2015 as ISO/ASTM 51707:2015(E). DOI: 10.1520/51707-22.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
51707 − 22
1.8 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced documents
2.1 ASTM Standards:
E178 Practice for Dealing With Outlying Observations
E170E456 Terminology Relating to Radiation Measurements and DosimetryQuality and Statistics
E2232 Guide for Selection and Use of Mathematical Methods for Calculating Absorbed Dose in Radiation Processing
Applications
E456E3083 Terminology Relating to Quality and StatisticsRadiation Processing: Dosimetry and Applications
2.2 ISO/ASTM Standards:
51261 Practice for Calibration of Routine Dosimetry Systems for Radiation Processing
51608 Practice for Dosimetry in an X-Ray (Bremsstrahlung) Facility for Radiation Processingdosimetry in an X-ray
(bremsstrahlung) facility for radiation processing at energies between 50 keV and 7.5 MeV
51649 Practice for Dosimetry in an Electron Beam Facility for Radiation Processing at Energies Between 300 keV and 25 MeV
51702 Practice for Dosimetry in a Gamma Facility for Radiation Processing
52628 Practice for Dosimetry in Radiation Processing
52701 Guide for Performance Characterization of Dosimeters and Dosimetry systems for Use in Radiation Processing
2.3 ISO Documents:
ISO 11137-1 Sterilization of Health Care Products – Radiation – Requirements for Development, Validation and Routine Control
of a Sterilization Process— Radiation — Part 1: Requirements for development, validation and routine control of a
sterilization process for medical devices
ISO 11137-3 Sterilization of Health Care Products — Radiation — Part 3: Guidance on Dosimetric Aspects of Development,
Validation and Routine Control
ISO 11137-4 Sterilization of health care products — Radiation — Part 4: Guidance on process control. General information
ISO 12749-4 Nuclear energy, nuclear technologies, and radiological protection — Vocabulary — Part 4: Dosimetry for radiation
processing
ISO 14470 Food irradiation — Requirements for the development, validation and routine control of the process of irradiation
using ionizing radiation for the treatment of food
ISO/IEC 17025 General Requirements for the Competence of Testing and Calibration Laboratories
2.4 Joint Committee for Guides in Metrology (JCGM) Reports:
JCGM 100:2008, GUM 1995, with minor corrections, Evaluation of measurement data –— Guide to the Expression of
Uncertainty in Measurement
JCGM 200:2008, VIM, International vocabulary of metrology –— Basis and general concepts and associated terms
2.5 ICRU Reports:
ICRU Report 80 Dosimetry Systems for Use in Radiation Processing
ICRU Report 85a Fundamental Quantities and Units for Ionizing Radiation
3. Terminology
3.1 VIM Definitions:
NOTE 1—For definitions quoted here from VIM, only the text of the definition is kept here. Any NOTES or EXAMPLES are not included. They can be
reviewed by referring to VIM (JCGM 200:2008).
For referenced ASTM and ISO/ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book
of ASTM Standards volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from Association for the Advancement of Medical Instrumentation, 1110 North Glebe Road, Suite 220, Arlington, VA 22201-4795, U.S.A.Instrumentation
(AAMI), 4301 N. Fairfax Dr., Suite 301, Arlington, VA 22203-1633, http://www.aami.org.
Available from International Organization for Standardization (ISO), 1, ch. de la Voie-Creuse, CP 56, CH-1211 Geneva 20, Switzerland, http://www.iso.org.ISO Central
Secretariat, Chemin de Blandonnet 8, CP 401, 1214 Vernier, Geneva, Switzerland, https://www.iso.org.
Document produced by Working Group 1 of the Joint Committee for Guides in Metrology (JCGM/WG 1). Available free of charge at the BIPM website
(http://www.bipm.org).
Document produced by Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2). Available free of charge at the BIPM website
(http://www.bipm.org).
Available from International Commission on Radiation Units and Measurements, Measurements (ICRU), 7910 Woodmont Ave., Suite 800400, Bethesda, MD 20814,
U.S.A.20841-3095, http://www.icru.org.
51707 − 22
3.1.1 For definitions quoted here from the VIM, only selected NOTES and EXAMPLES are included in 3.2. See VIM for further
information.
3.2 Definitions:
3.2.1 approved calibration laboratory—calibration laboratory that is a recognized national metrology institute; or has been
formally accredited to ISO/IEC 17025; or has a quality system consistent with the requirements of ISO/IEC by ISO/IEC 17025.
3.2.1.1 Discussion—
A recognized national metrology institute or other calibration laboratory accredited toby ISO/IEC 17025 should be used for
irradiation of dosimeters or dose measurements for calibration in order to ensure traceability to a national or international standard.
A calibration certificate provided by a laboratory not having formal recognition or accreditation will not necessarily be proof of
traceability to a national or international standard.
3.2.2 arithmetic mean, average [GUM, C.2.19]—sum of values divided by the number of values:
x¯ 5 x , i 5 1, 2, 3 … n (1)
( i
n
i
where:
x = individual values of parameters with i = 1, 2, 3 . n.
i
3.2.2.1 Discussion—
The term ‘mean’ is used generally when referring to a population parameter and the term ‘average’ when referring to the result
of a calculation on the data obtained in a sample.
3.2.3 calibration curve [VIM, 4.31]—expression of the relation between indication and corresponding measured quantity value.
3.2.3.1 Discussion—
In radiation processing standards, the term “dosimeter response” is generally used for “indication”.“indication.”
3.2.4 coeffıcient of variation (CV)—sample standard deviation expressed as a percentage of sample average value (see value:3.2.2
and 3.2.19):
S
CV 5 ×100% (2)
x¯
3.2.5 combined standard measurement uncertainty [VIM, 2.31]—standard measurement uncertainty that is obtained using the
individual standard measurement uncertainties associated with the input quantities in a measurement model.
3.2.5.1 Discussion—
(1) It is also referred to as ‘combined standard uncertainty’.uncertainty.’
(2) In case of correlations of input quantities in a measurement model, covariances must also be taken into account when
calculating the combined standard measurement uncertainty. A description of covariances may be found in the GUM reference,
Annex C.
3.2.6 coverage factor (k) [VIM, 2.38]—number larger than one by which a combined standard measurement uncertainty is
multiplied to obtain an expanded measurement uncertainty.
3.2.6.1 Discussion—
A coverage factor, k, is typically in the range of 2 to 3 (see 5.2.4).
3.2.7 expanded uncertainty [GUM, 2.3.5]—quantity defining the interval about the result of a measurement that may be expected
to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand.
3.2.7.1 Discussion—
Expanded uncertainty is obtained by multiplying the combined standard uncertainty by a coverage factor, the value of which
determines the magnitude of the ‘fraction’.‘fraction.’ Expanded uncertainty is also referred to as ‘overall uncertainty’.uncertainty.’
3.2.8 influence quantity [VIM, 2.52]—quantity that, in a direct measurement, does not affect the quantity that is actually measured,
but affects the relation between the indication and the measurement result.
3.2.8.1 Discussion—
51707 − 22
In radiation processing dosimetry, this term includes temperature, relative humidity, time intervals, light, radiation energy, absorbed
dose rate, and other factors that might affect dosimeter response, as well as quantities associated with the measurement instrument.
3.2.9 level of confidence—probability that the value of a parameter will fall within the given range.
3.2.10 measurand [VIM, 2.3]—quantity intended to be measured.
3.2.10.1 Discussion—
In radiation processing dosimetry, the measurand is the absorbed dose (Gy) or simply ‘dose’.‘dose.’
3.2.11 measurement [VIM, 2.1]—process of experimentally obtaining one or more quantity values that can reasonably be
attributed to a quantity.
3.2.12 measurement uncertainty [VIM, 2.26]—non-negative parameter characterizing the dispersion of the quantity values being
attributed to a measurand, based on the information used.
3.2.12.1 Discussion—
(1) Measurement uncertainty includes components arising from systematic effects, such as components associated with
corrections and the assigned quantity values of measurement standards, as well as the definitional uncertainty. standards.
Sometimes estimated systematic effects are not corrected for but, instead, associated measurement uncertainty components are
incorporated.
(2) The parameter may be, for example, a standard deviation called standard measurement uncertainty (or a specified multiple
of it), or the half-width of an interval, having a stated coverage probability.
(3) Measurement uncertainty comprises, in general,is comprised of many components. Some of these may be evaluated by
Type A evaluation of measurement uncertainty from the statistical distribution of the quantity values from a series of measurements
and can be characterized by standard deviations. The other components, which may be evaluated by Type B evaluation of
measurement uncertainty, can also be characterized by standard deviations, evaluated from probability density functions based on
experience or other information.
(4) In general, for a given set of information, it is understood that the measurement uncertainty is associated with a stated
quantity value attributed to the measurand. A modification of this value results in a modification of the associated uncertainty.
(5) In radiation processing applications, the quantity of interest is usually absorbed dose to water. The uncertainty estimate
therefore should also pertain to absorbed dose to water. Any differences between absorbed dose to water and absorbed dose to
product are outside the scope of this guide.
3.2.13 metrological traceability [VIM, 2.41]—property of a measurement result whereby the result can be related to a reference
through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty.
3.2.13.1 Discussion—
(1) The unbroken chain of calibrations is referred to as “traceability chain”.chain.”
(2) Metrological traceability of a measurement result does not ensure that the measurement uncertainty is adequate for a given
purpose or that there is an absence of mistakes.
(3) The abbreviated term “traceability” is sometimes used to mean ‘metrological traceability’ as well as other concepts, such
as ‘sample traceability’, ‘document traceability’, ‘instrument traceability’ or ‘material traceability’,traceability,’ ‘document
traceability,’ ‘instrument traceability,’ or ‘material traceability,’ where the history (“trace”) of an item is meant. Therefore, the full
term of “metrological traceability” is preferred if there is any risk of confusion.
3.2.14 quadrature—method used in estimating combined standard uncertainty from independent sources by taking the positive
square root of the sum of the squares of individual components of uncertainty, for example, coefficient of variation.
3.2.15 quantity [VIM, 1.1]—property of a phenomenon, body, or substance, where the property has a magnitude that can be
expressed as a number and a reference.
3.2.16 quantity value [VIM, 1.19]—number and reference together expressing magnitude of a quantity.
3.2.16.1 Discussion—
For example, absorbed dose of 25 kGy.25 kGy.
3.2.17 repeatability (of results of measurements) [GUM, B.2.15]—closeness of the agreement between the results of successive
measurements of the same measurand carried out under the same conditions of measurement.
3.2.17.1 Discussion—
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(1) These conditions are called ‘repeatability conditions’.conditions.’
(2) Repeatability conditions include: the same measurement procedure, the same observer, the same measuring instrument used
under the same conditions, the same location, repetition over a short period of time.
(3) Repeatability may be expressed quantitatively in terms of the dispersion characteristics of the results.
3.2.18 reproducibility (of results of measurements) [GUM, B.2.16]—closeness of the agreement between the results of
measurements of the same measurand carried out under changed conditions of measurement.
3.2.18.1 Discussion—
(1) A valid statement of reproducibility requires specification of the conditions changed.
(2) The changed conditions may include:include principle of measurements, method of measurement, observer, measuring
instrument, reference standard, location, conditions of use, and time.
(3) Reproducibility may be expressed quantitatively in terms of the dispersion characteristics of the results.
3.2.19 sample standard deviation (S) (S)—[adapted from GUM, C.2.21]—measure of dispersion of values of the same measurand
expressed as the positive square root of the sample variance.
3.2.19.1 Discussion—
This definition has been adapted from GUM.
3.2.20 sample variance [GUM, C.2.20]—measure of dispersion, which is the sum of the squared deviations of observations from
their average divided by (n –1), – 1), given by the expression:
x 2 x¯
~ !
i
(
S 5 (3)
~n 2 1!
where:
x = individual value of parameter with i = 1, 2 . n, and
i
x¯ = mean of n values of parameter (see 3.2.2).
3.2.21 standard measurement uncertainty [VIM, 2.30]—measurement uncertainty expressed as a standard deviation.
3.2.21.1 Discussion—
Also referred to as ‘standard uncertainty of measurement’ or ‘standard uncertainty’.uncertainty.’
3.2.22 true value [VIM, 2.11]—quantity value consistent with the definition of a quantity.
3.2.22.1 Discussion—
True value is by its nature indeterminate and only an idealized concept. In this guide, the terms “true value of a measurand” and
“value of a measurand” are viewed as equivalent (see 5.1.1).
3.2.23 Type A evaluation of measurement uncertainty [VIM, 2.28]—evaluation of a component of measurement uncertainty by a
statistical analysis of measured quantity values obtained under defined measurement conditions.
3.2.24 Type B evaluation of measurement uncertainty [VIM, 2.29]—evaluation of a component of measurement uncertainty
determined by means other than a Type A evaluation of measurement uncertainty.
3.2.25 uncertainty budget [VIM, 2.33]—statement of a measurement uncertainty, of the components of that measurement
uncertainty, and of their calculation and combination.
3.2.25.1 Discussion—
An uncertainty budget should include the measurement model,method, estimates, and measurement uncertainties associated with
the quantities in the measurement model,method, covariances, type of applied probability density functions, degrees of freedom,
type of evaluation of measurement uncertainty, and any coverage factor.
3.3 Definitions of other terms used in this standard that pertain to quality and statisticsradiation measurement and dosimetry may
be found in ASTM TerminologyISO/ASTM Practice E45652628. Definitions of other terms used in this standard Other terms that
pertain to radiation measurement and dosimetry may be found in ASTM Terminology E170E3083. Definitions in ASTM
Terminology and ISO Terminology ISO 12749-4. Where appropriate, definitions used in these standards E170 are compatible with
ICRU 85a; that document, therefore, may be used as an alternative reference.have been derived from and are consistent with
definitions in ICRU Report 85a, and general metrological definitions given in the VIM.
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4. Significance and use
4.1 All measurements, including dose measurements, have an associated Standards such as ISO 11137-1 (radiation sterilization
of health care products) and ISO 14470 (irradiation of food) contain requirements that dosimetry used in the development,
validation, and routine control of the process shall have measurement traceability to national or international standards and shall
have a known level of uncertainty. The magnitude of the measurement uncertainty is important for assessing the quality of the
results of the measurement system.
4.1.1 This guide provides information on how to meet the fundamental requirement to determine a known level of uncertainty
associated with a dose measurement, how to calculate the overall uncertainty, and how the uncertainty may differ depending on
the application (e.g., OQ and PQ dose measurements, routine dose measurement, determination of minimum absorbed dose (D )
min
or maximum absorbed dose (D ) from the monitoring location dose (D )). Information is provided on how to identify and
max mon
calculate different components of uncertainty used to establish an uncertainty budget.
4.2 Information on the range of achievable uncertainty values for specific dosimetry systems is given in the ISO/ASTM standards
for the specific dosimetry systems. While the uncertainty values given in specific dosimetry standards are achievable, it should be
noted that both smaller and larger uncertainty values might be obtained depending on measurement conditions and instrumentation.
For more information, see also ISO/ASTM 52628.
4.3 This guide uses the methodology adopted by the GUM for estimating uncertainties in measurements (see 2.4). Therefore,
components of uncertainty are evaluated as either Type A uncertainty or Type B uncertainty.
4.3.1 Quantifying individual components of uncertainty may assist the user in identifying actions to reduce the combined
measurement uncertainty.
4.4 Quantifying individual components of uncertainty may assist the user in identifying actions to reduce the measurement
uncertainty.
4.5 Periodically, the uncertainty should be reassessed to confirm the existing estimate. Should changes occur that could influence
the existing component estimates or result in the addition of new components of uncertainty, a new estimate of uncertainty should
be established.
4.4 Although this guide provides a framework for assessing uncertainty, it cannot substitute for critical thinking, intellectual
honesty, and professional skill. experience. The evaluation of uncertainty is neither a routine task nor a purely mathematical one;
it depends on detailed knowledge of the nature of the measurand and of the measurement method and procedure used. The quality
and utility of the uncertainty quoted for the result of a measurement therefore ultimately depends on the understanding, critical
analysis, and integrity of those who contribute to the assignment of its value (JCGM 100:2008). (GUM 3.4.8 JCGM 100:2008).
5. Basic concepts—components of uncertainty
5.1 Measurement:
5.1.1 The objective of a measurement is to determine the value of the measurand (for example, dose), that is, the value of the
specific quantity to be measured (dose). A measurement therefore begins with an appropriate specification of the measurand, the
method of measurement, the measurement system and the measurement procedure.
5.1.2 In general, the result of a measurement is the approximation or best estimate of the true value of the measurand (dose) and
thus is complete only when accompanied by a statement of the uncertainty of that estimate.
5.2 Uncertainty:
5.2.1 The uncertainty of the measurement result reflects the inability to know the true value of the measurand. A lower value of
overall uncertainty reflects a higher degree of confidence in the estimate of the value of the measurand.
NOTE 2—The result of any individual measurement can unknowingly be very close to the value of the measurand even though it may have a large
uncertainty. Thus the uncertainty of a measurement result should not be confused as the unknown error.
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5.2.2 The uncertainty associated with a measurement can arise from a number of different components, examples of some of which
are listed in Section 7. In assessing measurement uncertainty, it is necessary to consider all steps associated with making a
measurement and assign to each step a value for the uncertainty introduced. These individual components can then be collected
together to produce a combined uncertainty for the measurement. The results of this type of analysis are often presented in the form
of a table, referred to as an uncertainty budget (see Annex A2). Components of uncertainty are generally classified as Type A or
Type B, depending on the method used to evaluate them.
5.2.2.1 The purpose of the Type A and Type B classification is to indicate the two different ways of evaluating uncertainty
components. Both types of evaluation are based on probability distributions and the uncertainty components resulting from each
type are quantified by a standard deviation or a variance.
5.2.2.2 Thus, a Type A standard uncertainty is obtained from a probability density function derived from a series of repeated
observations (see 8.1), while a Type B standard uncertainty is obtained from an assumed probability density function based on the
degree of belief that an event will occur (see 8.2). Both approaches are valid interpretations of probability.
5.2.3 The combined standard uncertainty, denoted by u , of the result of a measurement is obtained by combining all the
c
components of uncertainty of both categories (see 9.1.1).
5.2.4 Typically, an expanded uncertainty U is calculated to provide an interval about the result of a measurement within which
the true value is expected to lie. The value of U is obtained by multiplying the combined standard uncertainty u by a coverage
c
factor k (see 9.2).
NOTE 3—The coverage factor k is always to be stated when reporting expanded uncertainty, so that the combined standard uncertainty of the measured
quantity can be recovered.
5. Evaluation of Type A and Type B standard uncertainty Determination of the uncertainty budget
5.1 Measurement Procedure: Measurement:
5.1.1 The measurandobjective Yof (absorbed dose) is generally not measurable directly, but depends ona measurement is to
determine the value of the measurand, Nthat other quantitiesis, the Xvalue , Xof , ., the Xspecific through a functional
1 2 N
relationship:quantity to be measured Y5f~X , X , …, X !. (absorbed dose). A measurement therefore begins with an appropriate
1 2 N
specification of the measurand, the method of measurement, the measurement system, and the measurement procedure.
6.1.1.1 The input quantities X , X , . X and their associated uncertainties may be determined directly in the current measurement
1 2 N
process by means of repeated observations (such as Type A); these input quantities may include influence quantities such as
temperature or humidity. They may also involve input quantities related to activities such as calibration of routine dosimetry
systems under conditions that differ from those during use (different dose rates, temperature cycle, etc.). Other quantities that may
be involved are those due to use of reference or transfer standard dosimeters.
6.1.1.2 The input quantities X , X , X . X and associated uncertainties may be treated either individually, for example, X or
1 2 3 N 1
X or as aggregates, for example, (X . X ) where p < N.
2 1 p
6.1.1.3 Grouping of input quantities is determined by the characteristics of the selected dosimetry system, method of calibration,
measurement application environment, and the ability within these sets of conditions to generate experimental measurements either
for individual or aggregate input quantities.
6.1.1.4 Both individual and aggregate input quantities may be used to estimate the combined standard uncertainty.
5.1.2 With the completion of the dosimetry system’s calibration and establishment of metrological traceability, the result of each
dose measurement represents the best estimate of dose. The associated uncertainty should always be included when reporting a
dose measurement, but the reported measurement result should not be corrected for the uncertainty.
6.2 Type A Evaluation of Standard Uncertainty:
6.2.1 Type A evaluations of uncertainty are made by statistical analysis of a series of measurement results of a quantity value.
51707 − 22
6.2.2 In most cases, the best estimate of the expected value of a quantity is obtained by n independent measurements made under
repeatability conditions and is given by the arithmetic mean, x¯, or average of those measurement results. The sample standard
deviation, s, of these observations characterizes the variability of the observed values or their dispersion about their mean. The
standard uncertainty of the mean value is given by s/√n. Therefore, for Type A components of uncertainty, increasing the number
of measurements will reduce the standard uncertainty of the mean.
6.2.3 In cases where only a single, or very few, measurements are made, the estimate of the sample standard deviation has to be
taken from prior measurements made using the same dosimetry system. The sample standard deviation could be determined from
a single set of prior measurements, or derived as a pooled standard deviation from several sets of prior measurements.
NOTE 4—See GUM H.3.6 for further information on pooled variance and pooled standard deviation.
NOTE 5—Repeatability of dosimeter response is an example of a Type A component of uncertainty that is usually determined from a set, or sets, of prior
measurements.
6.2.4 The Type A standard uncertainties are determined by the experimental design that is used to collect the observations for the
uncertainty estimate. If the estimated Type A uncertainty is unacceptably large, the individual components of uncertainty may be
estimated by a more refined experimental design. Knowledge of the components contributing to the estimated uncertainty might
allow identification of components that can be controlled so as to reduce uncertainty.
NOTE 6—For example, if optical absorbance of a film dosimeter is measured during calibration without controlling film thickness, relative humidity, or
temperature, the uncertainty of dose estimates from this calibration may be unacceptably large. An experimental design that controls these factors may
indicate the film thickness and relative humidity have significant effects on measured absorbance. Controlling these influence quantities during calibration
and routine dosimetry will reduce the uncertainty in dose estimates.
5.2 Type B Evaluation of Standard Uncertainty:
5.2.1 A measurement is always accompanied by a statement of the uncertainty. The uncertainty of the measurement result reflects
the inability to know the true value of the measurand. A lower value of overall uncertainty reflects a higher degree of confidence
in the estimate of the value of the measurand.
5.2.2 This guide will allow the user to evaluate known and potentially significant components of uncertainty that should be
included in the uncertainty estimate, including those arising from calibration, dosimeter response, instrument stability, and the
effect of influence quantities.
5.2.3 A quantitative analysis of components of uncertainty is referred to as an uncertainty budget and is often presented in the form
of a table (see Table 1 and Annex A1). Typically, the uncertainty budget will identify all significant components of uncertainty
together with their methods of estimation, statistical distributions (for example, rectangular, triangular, Gaussian), magnitudes, and
methods of combination. The Gaussian and rectangular probability distributions are discussed in more detail in Annex A2.
Step-by-step guidance is in the GUM (JCGM 100:2008, GUM 1995, Section 4.3).
5.2.4 The Type B component of uncertainty is evaluated by using all relevant information on the possible variability of the input
quantitiesuncertainty associated with a measurement can arise from several different components. In the assessment of
measurement uncertainty, it Xis . For the input valuenecessary to consider all Xsteps that has not been obtained from repeated
i i
measurements, the estimated variance,associated with making a measurement and assign to each step an uuncertainty , or
B
standard uncertainty, value, in the form of a standard deviation or standard uncertainty. uThese , is evaluated by judgment using
B
all relevant information on the possible variability ofindividual components can be collected to produce a combined uncertainty
for the measurement, generally by Xsumming . This pool of information may include previous measurement data or documented
i
performance characteristics of the dosimetry system. The uncertaintyin quadrature the individual component standard uncertainties
(i.e. calculating the square root of the sum of the squares of the individual components). Refer to Eq 4estimated in this way is
referred to as a Type B standard uncertainty,. Components of uncertainty are generally classified as Type A or Type uB, . depending
B
on their evaluation method.
5.2.4.1 The purpose of the Type A and Type B classification is to indicate two different ways of evaluating uncertainty components.
Both types of evaluation are based on probability distributions and the uncertainty components resulting from each type are
quantified by a standard deviation or a variance.
51707 − 22
TABLE A2.1
Relative standard uncertainty
Probability
Component of uncertainty Value
distribution
Type A Type B
Calibration doses from 1.3 Normal 1.3 %
laboratory certificate %
Fit of 0.8 Normal 0.8 %
calibration curve %
Dosimeter response variability due to 1.0 % Rectangular 0.6 %
irradiation temperature
Difference in dose to reference and 1.0 Rectangular 0.6 %
calibration dosimeters %
Dosimeter-to-dosimeter scatter 1.4 % Normal 1.4 %
(repeatability)
Combined uncertainty
2.2 %
Expanded uncertainty (k=2) 4.4 %
TABLE 1 Example of an uncertainty budget (dosimetry system calibration)
Relative Standard Deviation (k=1)
Probability
Component of Uncertainty Reference
Distribution
Type A Type B
Approved calibration laboratory Sections 5.3, 5.4 Gaussian 1.30 %
Certified Dose (u ) Annex A1
lab
Calibration Curve Fit Section 5.5 Gaussian 0.95 %
(u ) Annex A1.5
fit
Environmental Effects Section 5.6 Rectangular 0.70 %
(Irradiation Temperature, Dose Rate, Annex A1.6
Energy Spectrum)
(u )
environment
Dosimeter Thickness Uncertainty (or Section 5.6 Gaussian 1.35 %
mass) Annex A1.7
(u )
thickness
Uncertainty in Dosimeter Response Section 5.7 Gaussian 1.55 %
(Precision of the measurement) Eq A1.1,
(u ) Annex A1.4
precision
Combined Uncertainty (k=1) Eq 4 2.7 %
Combined Expanded Uncertainty (k=2) Eq 5
5.4 %
5.2.4.2 A Type A standard uncertainty is obtained from a probability density function (PDF) inferred from a series of repeated
observations, while a Type B standard uncertainty is obtained from an assumed probability density function based on the degree
of belief that an event will occur. Both approaches are considered statistical methods and are valid interpretations of probability.
For example, the random scatter between replicate dosimeters is a Type A component of uncertainty, whereas estimations of the
effect of irradiation temperature are generally evaluated as Type B components, based on the known ranges of temperature during
the irradiation.
NOTE 1—In specific cases, either a Type A or a Type B route may be used in the assessment of the component of uncertainty, for example uncertainty
due to dosimeter placement might be estimated using a rectangular distribution or a mathematical model.
5.2.4.3 In many cases, an estimate of the expected value of a quantity is obtained by multiple independent measurements made
under conditions of repeatability and is given by the arithmetic mean, x¯, or average of those measurement results. The sample
standard deviation, s, of these observations characterizes the variability of the observed values or their dispersion about the mean.
The standard uncertainty of the mean value is given by s/√n. Therefore, for Type A components of uncertainty, increasing the
number of measurements will reduce the standard uncertainty of the mean.
5.2.4.4 In cases where only a single or very few measurements are made, the estimate of the sample standard deviation has to be
taken from prior measurements made using the same dosimetry system. The sample standard deviation could be determined from
a single set of prior measurements or derived as a pooled standard deviation from several sets of prior measurements.
5.2.4.5 The Type A standard uncertainties are determined by the experimental design that is used to collect the observations for
51707 − 22
the uncertainty estimate. If the estimated Type A uncertainty is unacceptably large, the individual components of uncertainty may
be estimated by a more refined experimental design. Knowledge of the components contributing to the estimated uncertainty might
allow identification of components that can be controlled to reduce uncertainty.
NOTE 2—For example, if optical absorbance of a film dosimeter is measured during calibration without controlling film thickness, relative humidity, or
temperature, the dose uncertainty from this calibration may be unacceptably large. An experimental design that controls these factors may indicate the
film thickness and relative humidity have significant effects on measured absorbance. Controlling these influence quantities during calibration and routine
dosimetry will reduce the uncertainty.
5.2.5 Several methods may be used to develop estimates of the magnitude of Type B standard uncertainty. One method estimates
the maximum magnitude likely to be observed for each input quantity. For example, if the dosimeter response is known to vary
with irradiation temperature, then the temperature range routinely seen in operation should be used to estimate this component of
uncertainty. If there is no specific knowledge about the possible values of The Type B component of uncertainty is evaluated by
using all relevant information on the possible variability of the input quantities X . within its estimated bounds of For a to a , it
i – +
is assumed that it is equally probable for X to take on any value within those bounds (that is a rectangular distribution, see Fig.
i
2). As stated in JCGM 100:2008 (GUM), the sample standard deviation is the input a/√3 for such a distribution. In some cases it
is more realistic to expect that values near the bounds are less likely than those near the midpoint. It may then be reasonable to
replace the rectangular distribution with a symmetric triangular distribution with a base width of a – a = 2a, see Fig. 2. Assuming
+ –
such a triangular distribution for X , the expectation value of X is (that hasa +not abeen )/2 and its variance is obtained from
i i – +
2 2
repeated measurements, athe /6. Thus, the estimated variance, Typeu B, or standard uncertainty, u , = is evaluated by judgment
B B
using all relevant information on the possible variability of aX ./√6 (see JCGM 100:2008 (GUM)). This pool of information may
i
include previous measurement data or documented performance characteristics of the dosimetry system.
5.2.5.1 Several methods may be used to develop estimates of the magnitude of Type B standard uncertainty. One method estimates
the maximum magnitude likely to be observed for each input quantity. For example, if the dosimeter response is known to vary
with irradiation temperature, then the temperature range routinely seen in operation should be used to estimate this component of
uncertainty. If there is no specific knowledge about the possible values of X within its estimated bounds of a to a , it is assumed
i – +
that it is equally probable for X to take on any value within those bounds (that is a rectangular distribution, see Fig. A2.2). As stated
i
in JCGM 100:2008 (GUM), the sample standard deviation is a/√3 for such a distribution. In some cases, it is more realistic to
expect that values near the bounds are less likely than those near the midpoint. It may then be reasonable to replace the rectangular
distribution with a symmetric triangular distribution with a base width of a – a = 2a, see Fig. A2.2. Assuming such a triangular
+ –
distribution for X , the expectation value of X is (a + a )/2 and its variance is a /6. Thus, the Type B standard uncertainty, u =
i i – + B
a/√6 (see JCGM 100:2008 (GUM)).
5.2.5.2 It is important not to “double count” uncertainty components. For example, if a component of uncertainty arising from a
particular effect is obtained from a Type B evaluation, it should be included as an independent component of uncertainty in the
calculation of the combined standard uncertainty of the measurement result only to the extent that the effect does not contribute
to the observed variability of the observations. This is because the uncertainty due to that portion of the effect that contributes to
the observed variability is already included in the component of uncertainty obtained from the statistical analysis of the
observations (GUM).
NOTE 3—An example is time-dependent (or seasonal) drift in dosimeter response. This drift would not be seen in a Type A experiment, but could be
captured as a Type B component.
5.2.6 It is important not to “double-count” uncertainty components. For example, if a component of uncertainty arising from a
particular effect is obtained from a Type B evaluation, it should be included as an independent component of uncertainty in the
calculation of the combined standard uncertainty The combined standard uncertainty, denoted by u , of the measurement result only
c
to the extent that the effect does not contribute to the observed variability of the observations. This is because the uncertainty due
to that portion of the effect that contributes to the observed variability is already included in the component of uncertainty obtained
from the statistical analysis of the observations (GUM 4.3.10).result of a measurement is obtained by combining the components
of uncertainty of both types. This is done by taking the square root of the sum of the squares of each component of uncertainty.
5.2.7 The coverage factor k is generally taken as k=2, approximating equivalent a 95 % level of confidence for a two-sided
Gaussian distribution, or a 97.5 % level of confidence for a one-sided Gaussian distribution. Two-sided distributions are used for
calculating combined standard measurement uncertainty and expanded uncertainty of dose measurements based on the GUM
methodology. Therefore, a dose measurement established with k=2 means that there is 5 % chance (risk) that the dose might lie
outside the defined confidence interval. Different values of k are applicable based on the risk assessment for the product and process
assumed by the user and customer. See Annex A1 for a description of the normal distribution.
51707 − 22
NOTE 4—The coverage factor k is always stated when reporting expanded uncertainty in order that the combined standard uncertainty of the measured
quantity can be recovered.
5.2.8 An understanding of the individual uncertainty components is essential when assessing the significance of routine
measurements. For example, in relative dose mapping the only significant component of uncertainty may be dosimeter
reproducibility, whereas it will be necessary to consider all components of uncertainty for traceable dose measurements.
5.2.9 The uncertainty budget should be periodically re-assessed by the user to confirm the estimate is still valid.
5.2.9.1 There should be a documented rationale for the time interval between re-assessments that should include, for example, the
potential effects on the dosimetry system calibration of seasonal changes in temperature and humidity and changes in dose rate.
5.2.10 The user should define limits for acceptable changes of the uncertainty budget, and the user should perform assessment of
effects of changes.
5.2.11 As p
...