ISO/TS 22704:2022

Mechanical vibration - Uncertainty of the measurement and evaluation of human exposure to vibration

This document specifies methods for determining the uncertainty of the measurement and evaluation of human exposure to vibration. It applies to measurements of vibration quantities (measurands), calculated following a relevant measurement model on the basis of directly measured values, to evaluate a) human exposure to hand-transmitted vibration at the workplace, b) vibration emission of hand-held and hand-guided machinery in a laboratory setting, c) human exposure to whole-body vibration at the workplace, and d) whole-body vibration emission of vehicles. Examples of the application of the individual methods in practical situations are provided in the annexes. In this document a measurement error is defined as the difference between a measured and a reference quantity value. In this document “uncertainty” does not include errors that result from bad measurement strategies, faulty use of measurement equipment or other mistakes.

Vibrations mécaniques — Incertitude de mesure et évaluation de l'exposition humaine aux vibrations

General Information

• Status: Published
• Publication Date: 05-Apr-2022
• ICS: 13.160 - Vibration and shock with respect to human beings
• Technical Committee: ISO/TC 108/SC 4 - Human exposure to mechanical vibration and shock
• Drafting Committee: ISO/TC 108/SC 4/WG 19 - General aspects of human exposure to vibration
• Current Stage: 9093 - International Standard confirmed
• Start Date: 13-Jun-2025
• Completion Date: 13-Dec-2025

Overview

ISO/TS 22704:2022 - Mechanical vibration - Uncertainty of the measurement and evaluation of human exposure to vibration - is a technical specification that provides practical methods to determine the measurement uncertainty associated with assessing human exposure to vibration. It covers both hand‑transmitted (hand–arm) vibration and whole‑body vibration, and applies to workplace exposure assessments, laboratory emission tests of hand‑held or hand‑guided machinery, and vehicle vibration emission testing. The specification clarifies that “uncertainty” here excludes errors caused by poor measurement strategy or misuse of equipment.

Key topics and requirements

• Measurement models and input/output quantities: defines input and output quantities used to calculate measurands and how sensitivity coefficients affect uncertainty.
• Types and sources of uncertainty: treatment of Type A (statistical) and Type B (informed) uncertainties; instrumentation and environmental influence sources are identified.
• Evaluation methods:
  • Mathematical modelling of uncertainty (propagation via sensitivity coefficients).
  • Interlaboratory comparisons to estimate reproducibility components.
  • Estimation from field measurements where laboratory data are not available.
• Statistical treatment: definitions of variance, standard deviation, combined and expanded uncertainty, coverage factor and coverage probability.
• Presentation and use: guidance on how to report uncertainties and use them when comparing measured values or compliance decisions.
• Practical examples: informative annexes provide worked examples for hand–arm exposure (task‑based according to ISO 5349‑2), emission measurements of handheld machines, typical error sources, and statistical background.

Applications and practical value

• Provides a consistent framework for quantifying measurement uncertainty in vibration exposure assessments used in occupational health, product testing, and regulatory compliance.
• Helps test laboratories and measuring bodies evaluate repeatability and reproducibility, support accreditation, and justify measurement results.
• Assists occupational hygienists, safety engineers, and manufacturers in:
  • Interpreting exposure measurements with quantified confidence.
  • Comparing measured vibration levels against action or limit values with uncertainty taken into account.
  • Designing measurement campaigns and selecting instrumentation with known uncertainty contributors.

Who should use this standard

• Test laboratories and measuring personnel performing vibration emission or exposure measurements
• Metrologists and quality managers responsible for uncertainty budgets
• Occupational health and safety professionals and regulators assessing worker exposure
• Manufacturers of hand‑held/hand‑guided machinery and vehicle testing facilities

Related standards

• Normative references include ISO/IEC Guide 99 (VIM) and GUM principles (ISO/IEC Guide 98‑3) for uncertainty concepts. Annex A specifically references ISO 5349‑2 for task‑based hand–arm measurements. Use ISO/TS 22704:2022 in conjunction with applicable exposure and emission standards for complete measurement and compliance procedures.

Keywords: ISO/TS 22704:2022, mechanical vibration, measurement uncertainty, human exposure, hand‑arm vibration, whole‑body vibration, uncertainty evaluation, measurement model.

Standards Content (Sample)

TECHNICAL ISO/TS
SPECIFICATION 22704
First edition
2022-04
Mechanical vibration — Uncertainty
of the measurement and evaluation of
human exposure to vibration
Vibrations mécaniques — Incertitude de mesure et évaluation de
l'exposition humaine aux vibrations
Reference number
© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Considerations regarding the uncertainty of vibration measurements .7
4.1 Measurement objectives and fixed parameters . 7
4.2 Types of uncertainties . 8
4.3 Measurement instrumentation uncertainty sources . 8
5 Evaluation of the uncertainty .9
5.1 Evaluation of the uncertainty through mathematical modelling . 9
5.2 Determination of the uncertainty from interlaboratory tests . 10
5.3 Determination (estimation) of uncertainties from field measurements . 10
6 Presentation of results .11
7 Use of uncertainties .13
7.1 General .13
7.2 Use of uncertainties in comparisons . 13
Annex A (informative) Uncertainty in the measurement of hand-arm vibration at the
workplace — Example for determination of the measurement uncertainty of the
vibration exposure during task-based measurements according to ISO 5349-2 .14
Annex B (informative) Example for determination of the measurement uncertainty of
emission measurements on hand-held and hand-guided machines .25
Annex C (informative) Typical errors .28
Annex D (informative) Statistical background.30
Bibliography .31
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and
condition monitoring, Subcommittee SC 4, Human exposure to mechanical vibration and shock.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
Introduction
This document takes the form of a guide and describes how to deal with the uncertainty of vibration
quantities associated with human exposure to vibrations.
The uncertainty arises from various sources. These uncertainties need to be distinguished from errors,
such as when using measuring instruments or selecting the measurement strategy, which may falsify
the measurand. Errors are not considered in this guide.
Calculations of measurement uncertainty are meaningful and valid only if all significant mistakes have
been identified.
This document is intended to be used as a reference document for other standards. Examples of
the application of the individual methods in practical situations are provided in the annexes. These
examples are related to hand-arm vibration but the principles also apply for whole-body vibration.
v
TECHNICAL SPECIFICATION ISO/TS 22704:2022(E)
Mechanical vibration — Uncertainty of the measurement
and evaluation of human exposure to vibration
1 Scope
This document specifies methods for determining the uncertainty of the measurement and evaluation
of human exposure to vibration. It applies to measurements of vibration quantities (measurands),
calculated following a relevant measurement model on the basis of directly measured values, to
evaluate
a) human exposure to hand-transmitted vibration at the workplace,
b) vibration emission of hand-held and hand-guided machinery in a laboratory setting,
c) human exposure to whole-body vibration at the workplace, and
d) whole-body vibration emission of vehicles.
Examples of the application of the individual methods in practical situations are provided in the
annexes.
In this document a measurement error is defined as the difference between a measured and a reference
quantity value.
In this document “uncertainty” does not include errors that result from bad measurement strategies,
faulty use of measurement equipment or other mistakes.
2 Normative references
The following document is referred to in the text in such a way that some or all of it’s content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
input quantity in a measurement model
input quantity
X
quantity that must be measured, or a quantity, the value of which can be otherwise obtained, in order
to calculate a measured quantity value of a measurand
EXAMPLE When evaluating the daily vibration exposure, vibration magnitude and exposure time are input
quantities of a measurement model.
Note 1 to entry: An input quantity in a measurement model is often an output quantity of a measuring system.
Note 2 to entry: Indications, corrections and influence quantities can be input quantities in a measurement
model.
Note 3 to entry: An estimated value for X is x.
[SOURCE: ISO/IEC Guide 99:2007, 2.50, modified — example adapted and Note 3 added]
3.2
output quantity in a measurement model
output quantity
Y
quantity, the measured value of which is calculated using the values of input quantities in a measurement
model
Yf= (,XX ,.) (1)
Note 1 to entry: An estimated value for Y is y.
[SOURCE: ISO/IEC Guide 99:2007, 2.51, modified — Formula and Note 1 added]
3.3
arithmetic mean value
x
best estimated value for the expected value of the individual measured values when N independent
observations xx,, …, x are available for the input quantity (3.1), X :
ii,,12 iN, i
N
x = x (2)
ii∑ ,k
N
k=1
Note 1 to entry: The arithmetic mean value of the output quantity for N independent observations is
N
y= y (3)
∑
k
N
k=1
3.4
variance
s
measure for the scattering of the measured values when N individual measured values are available for
the variable X :
i
N
s = xx− (4)
()
ii∑ ,ki
N −1
k=1
Note 1 to entry: This Formula produces an estimated value for the variance of the measured values.
Note 2 to entry: An estimated value for the variance of the mean value is
s
i
sx()= (5)
i
N
Note 3 to entry: The variance of the mean value is always smaller than the variance of the measured values.
3.5
standard deviation
s
positive square root of the variance (3.4)
Note 1 to entry: The standard deviation of the individual measured values is therefore
N
s = xx− s (6)
()
ii∑ ,ki i
N−1
k=1
The standard deviation of the measured values is a measure for the scattering of the measured values in a sample
(measurement series) around their (arithmetic) mean value. It is also referred to as s in standards to determine
n–1
vibration emission values of machines (see Annex A).
Note 2 to entry: The standard deviation of the mean value is
N
1 2
sx()= xx− (7)
()
ii,ki
∑
NN()−1
k=1
The standard deviation of the mean value is a measure for the accuracy of repeated measurements. Formula (7)
is used when Type A evaluation is applied (see A.2).
3.6
sensitivity coefficient
c
i
partial derivative of the output quantity (3.2) according to X at the location of the estimated values of
i
the input quantities (3.1):
∂f
c = (8)
i
∂X
i
xx,.,
1 N
Note 1 to entry: If the output quantity has a linear relation to the input quantity, c is a constant that can have any
i
greater or lesser value. The X relation can also be selected in the model so that c = 1.
i i
3.7
uncertainty
parameter assigned to the result of a measurement or calculation which identifies the scattering of the
values that can sensibly be assigned to the measured or calculated variable
Note 1 to entry: The uncertainty does not necessarily have to be a standard deviation.
3.8
standard uncertainty
u
uncertainty (3.7) of the result of a measurement or calculation expressed as a standard deviation (3.5)
Note 1 to entry: The standard uncertainty u(x) of a variable x has the same unit as x. The relative standard
uncertainty u(x)/(x) is dimensionless.
3.9
combined standard uncertainty
u
c
standard uncertainty (3.7) of a result y that is obtained from L values of other variables, X
i
Note 1 to entry: The combined standard uncertainty is equal to the positive square root of a sum of terms,
whereby the terms are variances or co-variances of these other variables X , weighted according to the sensitivity
i
coefficients c .
i
For a mathematical model of the measurand Y = f (X ) with uncorrelated input quantities X , the following applies
i i
in the first approximation:
L
uy()= cu ()x (9)
ci∑ i
i=1
The standard uncertainties u(x ) can be determined according to two types of evaluation (Type A and Type B
i
evaluation, see ISO/IEC Guide 98-3).
3.10
coverage factor
k
factor by which the combined standard uncertainty (3.9), u , is multiplied to obtain the expanded
c
uncertainty U
3.11
coverage interval
interval containing the set of true quantity values of a measurand with a stated probability, based on
the information available
Note 1 to entry: A coverage interval does not need to be centred on the chosen measured quantity value (see
ISO/IEC Guide 98-3:2008/Suppl.1).
Note 2 to entry: A coverage interval should not be termed “confidence interval” to avoid confusion with the
statistical concept (see ISO/IEC Guide 98-3:2008, 6.2.2).
Note 3 to entry: A coverage interval can be derived from an expanded measurement uncertainty (see
ISO/IEC Guide 98-3:2008, 2.3.5).
[SOURCE: ISO/IEC Guide 99:2007, 2.36]
3.12
coverage probability
probability that the set of true quantity values of a measurand is contained within a specified coverage
interval
Note 1 to entry: This definition pertains to the uncertainty approach as presented in the GUM.
Note 2 to entry: The coverage probability is also termed “level of confidence” in the GUM.
[SOURCE: ISO/IEC Guide 99:2007, 2.37]
3.13
expanded uncertainty
U
product of the coverage factor (3.10), k and the combined standard uncertainty (3.9), u , which describes
c
the range y ± U around the result y, which can be expected to comprise a majority of the distribution of
those values that can be reasonably attributed to the result:
Uk= u (10)
c
Note 1 to entry: In EN 12096, the expanded uncertainty is indicated by the letter K. It is used in the determination
of the measured vibration value a and also indicates the dispersion in the production of batches of machines. The
value K, however, does not include all uncertainty components.
3.14
test subject
person exposed to the vibration that is determined by a measuring body
Note 1 to entry: The test subject is also referred to as the operator, operating personnel or exposed person.
3.15
measuring personnel
persons responsible for performing the measurements, in particular managing the measuring
instruments
3.16
measuring body
organizational unit that is responsible for conducting the measurements, in particular managing the
measuring instruments and personnel
3.17
reproducibility conditions
conditions where test results are obtained with the same method on identical test items in different
measuring bodies by different measuring personnel (3.15) using different equipment
Note 1 to entry: The method can define operating conditions, type and number of test subjects, or measurement
environments, for example.
Note 2 to entry: The measurement time or the measurement object can vary depending on the problem or aim of
the measurement; for example, if the measurement object is a workpiece that changes during measurement or if
the influence of aging of a machine is to be determined.
[SOURCE: ISO 5725-1:1994, 3.18, modified — “Laboratory” replaced by “measuring body”, “operator”
replaced by “measuring personnel”]
3.18
in-situ conditions
reproducibility conditions (3.17) in the same measurement environment
Note 1 to entry: The measurement environment is influenced, for example, by the ambient temperature which
can influence the conditions of the measuring instrumentation and measurement object.
3.19
repeatability conditions
conditions where independent test results are obtained with the same method on identical test items
in the same measuring body (3.16) and measurement environment by the same member of measuring
personnel (3.15) using the same equipment within short intervals of time
[SOURCE: ISO 5725-1:1994, 3.14, modified — “Laboratory” replaced by “measuring body and
measurement environment”, “operator” replaced by “member of measuring personnel” and Note 1
deleted]
3.20
reproducibility standard deviation
measuring body standard deviation
σ
L
standard deviation (3.5) of results obtained under reproducibility conditions (3.17)
Note 1 to entry: The measuring body standard deviation is also referred to as the measuring body or laboratory
deviation or scattering.
Note 2 to entry: Depending on the measuring method, it is not always possible to create the same conditions.
For example, ISO 20643 requires three different test subjects for vibration emission measurements. The
reproducibility standard deviation then includes the test subject standard deviation.
Note 3 to entry: The measuring body standard deviation principally consists of the standard deviation of the
measuring instrument and the standard deviation that results from the measurement strategy that is used. It
therefore also includes interpretations of the measurement standard, for example with regard to the points of
the transducer coupling and locations of the measurement point.
3.21
in-situ standard deviation
σ
s
standard deviation of results obtained under in-situ conditions (3.18)
3.22
repeatability standard deviation
σ
r
standard deviation of results obtained under repeatability conditions (3.19)
Note 1 to entry: According to ISO 5349-2, at least three individual measurements should be made.
3.23
interlaboratory test
series of measurements performed by different laboratories or measuring bodies under reproducibility
conditions (3.17)
Note 1 to entry: Interlaboratory tests (sometimes referred to as “Round robin tests”) can have very different
objectives. For example, to verify a measurement method, to determine measurement uncertainties or to
benchmark for a particular measuring body.
3.24
specified value
vibration value that is specified in a technical rule or required by law or otherwise that is to be complied
with
Note 1 to entry: Depending on the context, the specified value is referred to as the limit value, action value,
guidance value or threshold limit value.
3.25
production standard deviation
standard deviation (3.5) of results obtained under the same conditions for different new products of the
same type of device or machine in a series
Note 1 to entry: With the exception of the product to be measured (for example machine or vehicle), all other
conditions (measuring instrument, measuring body, measuring personnel, test subjects, measuring conditions
and the measurement method and, if relevant, also the in-situ conditions) are the same.
Note 2 to entry: The production standard deviation is also referred to as the product scattering in EN 12096.
However, the product scattering can also include the deviation due to aging.
3.26
test subject standard deviation
standard deviation (3.5) of results obtained under the same conditions, but with different test subjects
(3.14)
Note 1 to entry: With the exception of the test subject (for example machine user or vehicle driver, all other
conditions (machine, vehicle, measuring instrument, measuring body, measuring personnel, measuring
conditions and the measurement method and, if relevant, also the in-situ conditions) are the same.
Note 2 to entry: If the individual measurements are not performed promptly, changes can occur in the same test
subject, for example change of mass, change of behaviour or improved skill.
3.27
uncertainty budget
statement summarizing the estimation of the uncertainty (3.7)
components that contributes to the uncertainty (3.7) of a result of a measurement
Note 1 to entry: The uncertainty of the result of the measurement is unambiguous only when the measurement
procedure (including the measurement object, measurand, measurement method and conditions) is defined.
Note 2 to entry: The term “budget” is used for the assignment of numerical values to the uncertainty components
and their combination and expansion, based on the measurement procedure, measurement conditions and
assumptions.
[SOURCE: ISO 14253-2:2011, 3.9]
3.28
measurand
quantity intended to be measured
EXAMPLE 1 The potential difference between the terminals of a battery may decrease when using a voltmeter
with a significant internal conductance to perform the measurement. The open-circuit potential difference can
be calculated from the internal resistances of the battery and the voltmeter.
EXAMPLE 2 The length of a steel rod in equilibrium with the ambient temperature of 23 °C will be different
from the length at the specified temperature of 20 °C, which is the measurand. In this case, a correction is
necessary.
Note 1 to entry: The specification of a measurand requires knowledge of the kind of quantity, description of the
state of the phenomenon, body, or substance carrying the quantity, including any relevant component, and the
chemical entities involved.
Note 2 to entry: In the second edition of the VIM and in IEC 60050-300:2001, the measurand is defined as the
‘quantity subject to measurement’.
Note 3 to entry: The measurement, including the measuring system and the conditions under which the
measurement is carried out, might change the phenomenon, body, or substance such that the quantity being
measured may differ from the measurand as defined. In this case, adequate correction is necessary.
[SOURCE: ISO/IEC Guide 99:2007, 2.3, modified — Note 4 to entry deleted]
4 Considerations regarding the uncertainty of vibration measurements
4.1 Measurement objectives and fixed parameters
The consideration of measurement uncertainty shall begin with a clear understanding of the objectives
of the measurements. The measurement objectives will define those parameters that are fixed and
those that contribute to the uncertainty evaluation. For example, our objectives may be any of the
following:
a) to obtain an in-use vibration value for a particular task for a particular tool or vehicle, as used by a
particular operator;
b) to obtain a typical in-use vibration value for a particular task for that particular tool or vehicle
(used by any worker);
c) to obtain a typical in-use vibration value for a particular task for that type of tool or vehicle.
NOTE The vibration value can be a vibration emission value, a vibration immission value or a vibration
exposure value.
Other objectives may also be possible, but in each case, the fixed parameters are different, and will
affect how the measurement is planned so that measurement uncertainties can be determined. For
the three scenarios above, there are two key variations, relating to the machine and to the machine
operator, which are associated with each objective.
— To achieve objective a), measurements for the specified task on the identified tool or vehicle with
the same operator are sufficient. The measurements do not require the assessment of differences
between operators or machines, they are both fixed.
— To achieve objective b), measurements for the specified task on the identified tool or vehicle are
needed with a number of machine operators. The measurements require consideration of differences
between operators, while the machine is fixed.
— To achieve objective c), measurements for the specified task of a number of samples of the tool
or vehicle types used by a number of machine operators are needed. The measurements require
consideration of differences between operators and machines.
These examples, only consider two variable parameters. It may be necessary to consider other
variables, such as machine configuration, materials, inserted tools, machine models, ages, maintenance,
road conditions. Table 1 provides more examples of factors that may need to be accounted for when
planning a measurement strategy. The examples also only consider vibration magnitude evaluation;
in many cases the measurement will be of vibration exposure, in which case consideration of exposure
time uncertainties will be required.
4.2 Types of uncertainties
It is useful to define three distinct types of uncertainty relating to vibration measurements.
a) Measurement equipment uncertainty: Uncertainties related to the system selected for the
measurement: transducer calibration, mounting, instrumentation, signal processing and data
handling.
b) Measurement procedure uncertainty: Uncertainties related to
1) decisions that have to be made when performing a measurement, such as the selection of:
transducer locations, measurement periods, test subjects, work tasks, and
2) the skill and experience of the person performing the measurements.
Uncertainties need to be distinguished from errors. Examples of typical errors are listed in Annex C
NOTE Measurement equipment uncertainty and measurement procedure uncertainty are representing the
laboratory uncertainty. Performing measurements according to a standardised procedure usually limits the
measurement uncertainty.
c) Measurement restrictions uncertainty: Depending on the objectives, uncertainties may result from
the limited access to a representative sample of measurement environments (usually issues outside
the measurer’s control). These could include restrictions on the
1) availability of work sites, tasks or machines,
2) environmental conditions (temperature, noise humidity) during measurements,
3) machine operator physical characteristics (e.g. height, mass and strength), and
4) machine operator skill, experience and behaviour.
4.3 Measurement instrumentation uncertainty sources
Measurement uncertainty connected with the measurement instrumentation is dealt with in ISO 8041-1.
5 Evaluation of the uncertainty
5.1 Evaluation of the uncertainty through mathematical modelling
For various reasons, the aim is to draw up a detailed uncertainty budget based on a mathematical model
of the evaluation of measurement, including interferences. One reason is that a budget of this kind can
be used to determine the most important uncertainty components and, if applicable, reduce them.
Furthermore, the uncertainty determined through such a mathematical model reflects the concrete
conditions that were actually present when determining the measurand. That means the uncertainty
is individually adapted to the measurand. This clause provides instructions for determining such
uncertainty budgets.
Examples of models for measuring procedures are provided in Annex B.
The functional relation f between input and output quantity is often not known. In such cases, it can
be assumed that the individual, uncorrelated variables X have a linear relation to the output quantity
i
and the associated sensitivity coefficients, c = 1. The following is one possible formulation of this
i
assumption:
Yy=+ X (11)
∑
i
i
In Formula (11), the input quantities X are random numbers that are obtained from a distribution with
i
a given standard deviation, s and the mean value x = 0 . If no other information is available, it can be
i i
assumed that the input quantities have a normal (Gaussian) distribution. Formula (9) for the combined
standard uncertainty, then simplifies to
L
uy()= ux() (12)
∑
c i
i=1
The terms of Formula (12) can be determined according to two types of evaluation (Type A and Type B
evaluation, see ISO/IEC Guide 98-3).
The term that describes the variance for repeated measurements in Formula (12) is determined
according to the Type A method. For n repeated measurements, the variance is described by the
standard deviation of the mean value sx() . For measurement series with less than about 30 repeated
i
measurements, the standard deviation of the mean value should still be corrected using the Bayes term.
n−1
sx()= sx() (13)
corr ii
n−3
The uncertainty in this case is equal to u(x ) = s .
repeat corr
All other uncertainties u(x ) can be calculated according to the Type B method. Two cases frequently
i
occur.
a) If an estimated value and its uncertainty u(x ) are known (e.g. from a calibration report), this
i
uncertainty is used. A normal distribution is assumed.
b) If it is known that the estimated value is between two values, a rectangular distribution can be
assumed. For a symmetrical distribution of the input quantities around the mean value, i.e.
Xx=±a , the uncertainty is
ii
a
ux()= (14)
i
Besides this analytical approach to the combined standard uncertainty via Formula (9), a numerical
approach can also be selected (see ISO/IEC Guide 98-3:2008/Suppl.1). If it is assumed that the input
quantities are uncorrelated random numbers, the uncertainty of the output quantity can be determined
using a Monte Carlo calculation. In this case, in contrast to Formula (9), it is possible to use any
distributions and standard deviations of any magnitude.
5.2 Determination of the uncertainty from interlaboratory tests
If the uncertainty is only limited to the reproducibility standard deviation, σ and the repeatability
L
standard deviation, σ , the combined standard uncertainty u from an interlaboratory test can be stated
r c
as standard deviation σ .
R
u ==σσ +σ (15)
c RL r
The fundamental concept and the method for determining these standard deviations are described
in ISO 5725-1 and ISO 5725-2. Both standard deviations are determined in interlaboratory tests, in
which as many measuring bodies as possible should participate, in order to gain reliable results. The
reproducibility and repeatability standard deviations describe the combined standard uncertainty
linked to a method. This combined standard uncertainty is associated with all results that were
determined using the same specified method. It can therefore also be used as estimated value for an
in-situ standard deviation.
The method for which the reproducibility or repeatability standard deviation is to be determined shall
be described exactly. Each participating measuring body shall apply the method in such a way that in
the repeated measurements as many of the possibilities are covered as possible. For example, in many
situations the vibration transducers should be recoupled for each repetition.
The measurement results shall not be subject to any preselection by the measuring bodies.
NOTE The choice of test object for an interlaboratory test not only depends on the measurand to be
determined, but also on the specified boundary conditions, such as setup and operating conditions. Practical
aspects can also be considered. Ideally, the same test object can be used by all measuring bodies, which is
examined by the first measuring body for possible changes at the end of the interlaboratory test (“round robin
test”). However, it is also possible that all participants receive nominally identical test objects, for example from
one production batch. In this case, a consistency test can be conducted to investigate factors such as ageing or
maintenance before and possibly also after the interlaboratory test.
5.3 Determination (estimation) of uncertainties from field measurements
If the uncertainty of a measurement and the mathematical model is not known, uncertainties determined
from other investigations can be applied to the task under consideration as being indicative. In some
cases such values are specified in standards for example for hand-held motor-operated tools (see series
IEC 60745) and transportable motor-operated electric tools (see series IEC 61029), a constant value
is specified for the expanded uncertainty, to which an emission measurement is assigned. EN 12096
specifies an estimated value for the expanded uncertainty for the production standard deviation.
If estimating uncertainty from comparative data, the accuracy of the uncertainty estimate is largely
dependent on how many conditions are the same between the new measurements under consideration
and the comparison data set used for the estimation. Influencing factors are listed in Table 1. Table 1
illustrates possible considerations for two example cases where comparison data are being considered.
A detailed example with values can be found in Annex A.
Table 1 illustrates factors which may be significant. However, many other conditions can be included in
the analysis, such as the age and condition of the machine and its engine or power supply, and inserted
tool or attachments used, the workpiece or vehicle loading, measurement environment, measuring
personnel, machine operators and measuring instrument.
NOTE The referred vibration quantities are usually the vibration accelerations directly measured at the
interfaces between the human body and a tool, a machine, a vehicle, or a workpiece using a method defined in an
ISO standard, or those derived or calculated using the accelerations defined in the standard. The general concepts
and methods described in this document can also be optionally applicable to help analyse the uncertainty of the
vibration quantities or biodynamic responses measured at or on the human body.
Table 1 — Illustration of influencing factors for uncertainty data
Examples
Hand-arm vibration Whole-body vibration
Example case: Uncertainty of vibration measure- Uncertainty of vibration measure-
ment of an angle grinder cutting steel ment of a forklift truck in a ware-
pipe in a workplace house
Influencing factors Is the comparison data set based on measurement:
Measurands are identical. i.e.: the — in accordance with ISO 5349-2, — in accordance with ISO 2631-1,
measured values are evaluated ac- for example using the W for example using W & W
h k d
cording to the same specification. frequency weighting frequency weightings
The measurements to determine — on machine handles, at the — on the vehicle seat, during
the measurand are transferable. centre of the gripping zone periods of representative
during periods of representative driving
cutting
The measured objects (machines) — grinder of identical make and — vehicle of identical make and
should be identical as far as possible model or similar specification, model or similar specification,
in terms of vibration generation, size, power and cutting wheel load capacity and power
size and coupling to the environ-
— suspension seat of identical
ment.
make and model or similar
performance category
The work processes of the meas- — during cutting (rather than — driving on warehouse style
ured objects are transferable. grinding) a similar material road surface at speeds similar
to those in a warehouse
The machine operator, measure- — with similar forces, posture, — handling similar loads with
ment duration and number of hand position and cutting rates similar travel distances and
measurements for determining the loading rates
measured values are comparable.
The environment — temperature, location (inside, — weather conditions, surface
outside), weather conditions conditions
6 Presentation of results
Vibration quantities shall be given with their physical units, such as m/s .
The uncertainty information shall include
a) an uncertainty value, reported either using the physical unit of the output quantity (e.g. as m/s ) or
as a percentage,
b) the coverage factor of the uncertainty value,
c) any relevant additional information, such as use of non-Gaussian distributions.
The uncertainty value of the measurand (the expanded uncertainty) is dependent on the combined
standard uncertainty u determined according to Clause 5 and on the selected one- or two-sided
c
coverage probability, taking into account the coverage factor k required by the application.
A one-sided coverage probability is considered when it is necessary to ensure that the expected value
y of the measurand does not exceed a limit value y (or does not fall below a limit value y ). For a p,
max min
the expected value is only above the upper limit value (or below the lower limit value) with a probability
of 1 − p.
A two-sided coverage probability is assumed, if the expected value y of the measurand for a coverage
probability, p, has to lie within a symmetrical interval around the mean value of the measured values.
In the case of a distribution density function assumed to be symmetrical, the expected value y only lies
above the upper interval limit or below the lower interval limit with a probability of 1 − p/2 in each
case.
The coverage factor, k, is e.g. 1,0 or 1,3 etc., depending on the desired coverage probability for two-sided
and for one-sided tests, see Table 2.
EXAMPLE For a typical measurement of a hand-held drilling tool a coverage probability of 95 % is commonly
used, which results in a coverage factor of 1,6 for one-sided tests and a coverage factor of 2,0 for two-sided tests.
For the statistical background see Annex D.
Table 2 — Coverage factor for different coverage probabilities during one-sided and two-sided
tests with normal distribution
Coverage probability, p Coverage probability, p
Coverage factor (rounded)
for two-sided tests for one-sided tests
k % %
1,0 68 84
1,3 80 90
1,6 90 95
2,0 95 97,5
The measurement result shall be stated as follows.
a) For a two-sided test:
ˆˆ
YU=±yy=±ku (16)
c
where
Y is the measurand;
ˆy is the best estimated value determination on the basis of measurements;
U is the expanded uncertainty, see Formula (10).
2 2
EXAMPLE For a measured value of 12,5 m/s and a determined combined standard uncertainty of 0,9 m/s
in a two-sided test at a selected coverage probability of 95 %, the following result is obtained:
a =±12,,51 8 m / s
()
hw
Thus, the expanded uncertainty is U = 1,8 m/s with the coverage factor, k = 2 (see Table 2).
b) For a one-sided test (see also 7.2):
— If the aim is to comply with a specified value:
YU=+ˆˆyy=+ku (17)
c
— If the aim is to exceed a specified value:
ˆˆ
YU=−=−yy ku (18)
c
NOTE The above instructions apply to a positive specified value.
EXAMPLE For a measured (positive) value of 12,5 m/s and a determined combined standard uncertainty of
0,9 m/s in a one-sided test at a selected coverage probability of 95 %, the following result is obtained according
to Formula (17):
a =±12,,51 44 m / s
()
hw
Thus the expanded uncertainty is U = 1,44 m/s with the coverage factor, k = 1,6 (see Table 2). A
specified value of 13,94 m/s would be met with a coverage probability of 95 %.
The complete measurement result therefore consists of the estimated value for the measurand and its
expanded measurement uncertainty.
ˆ
NOTE Indication of the best estimated value y without an expanded uncertainty, as was previously typical
practice, is equivalent to a coverage probability of just 50 %.
7 Use of uncertainties
7.1 General
Whether and how uncertainty is used can be defined by statutory provisions or contractual agreements.
The use of uncertainty is determined by the purpose of the measurement.
7.2 Use of uncertainties in comparisons
When comparing results with specified values, uncertainty plays a significant role, for example when
evaluating measurement results. The use of uncertainty is typically required by a standard or other
technical rule or regulation. A distinction can be made between the following cases with regard
to deciding whether the result determined according to a specified method, taking into account the
expanded uncertainty U, complies with a specified value Y (for example a limit value), whereby the
req
uncertainty is used as an increased or reduced allowance.
— The decision “specified value complied with” is reached reliably when the result plus uncertainty
does not exceed the specified value:
yU+≤Y (19)
req
— The decision “Specified value exceeded” is reached reliably when the result minus uncertainty
exceed the specified value:
yU−>Y (20)
req
NOTE The above instructions apply to a positive specified value.
Annex A
(informative)
Uncertainty in the measurement of hand-arm vibration at the
workplace — Example for determination of the measurement
uncertainty of the vibration exposure during task-based
measurements according to ISO 5349-2
A.1 Introduction
This annex is concerned with the uncertainty of the measurement of hand-arm vibration at the
workplace using mathematical modelling according to 5.1. Results from interlaboratory tests are also
applied in this case (see 5.2).
Uncertainty based on empirical values according to 5.3 can be applied for an initial rough estimation
2 2
from the illustrative values according to EN 12096 for measured values between 2,5 m/s and 5 m/s
to be 50 % and for measured values > 5 m/s to be 40 %. Emission measurement standards frequently
only give conventions for estimating the expanded uncertainty; these conventions are designated as K
values.
A.2 Principles of the calculation
A.2.1 General
The uncertainty when recording the longer-term typical vibration exposure is derived based on the
random sample linked to the measurement (limited measu
...