INTERNATIONAL ISO

STANDARD 2360
Fourth edition
2017-07

Non-conductive coatings on non-

magnetic electrically conductive base
metals — Measurement of coating
thickness — Amplitude-sensitive
eddy-current method
Revêtements non conducteurs sur matériaux de base non
magnétiques conducteurs de l’électricité — Mesurage de l’épaisseur
de revêtement — Méthode par courants de Foucault sensible aux
variations d’amplitude

Reference number
ISO 2360:2017(E)

© ISO 2017
ISO 2360:2017(E)

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ii © ISO 2017 – All rights reserved

 ISO 2360:2017(E)

Contents Page
Foreword ........................................................................................................................................................................................................................................ iv
1 Scope ................................................................................................................................................................................................................................. 1
2 Normative references ...................................................................................................................................................................................... 1
3 Terms and definitions ..................................................................................................................................................................................... 1
4 Principle of measurement .......................................................................................................................................................................... 2
5 Factors affecting measurement uncertainty ........................................................................................................................... 3
5 .1 B as ic influence o f the co ating thicknes s ........................................................................................................................... 3
5.2 Electrical properties of the base metal .............................................................................................................................. 3
5 .3 Geo metry: B as e metal thicknes s .............................................................................................................................................. 4
5 .4 Geo metry: E dge e ff .................................................................................................................................................................... 4
ects

5 .5 f
Geo metry: S ur ace curvature ...................................................................................................................................................... 4
5.6 Surface roughness ................................................................................................................................................................................ 4
5.7 Cleanliness: Lift-off effect .............................................................................................................................................................. 5
5.8 Probe pressure ........................................................................................................................................................................................ 5
5.9 Probe tilt ....................................................................................................................................................................................................... 5
5.10 Temperature effects ............................................................................................................................................................................ 5
5.11 Intermediate coatings ....................................................................................................................................................................... 6
5 .1 2 E xternal electro magnetic fields ................................................................................................................................................ 6
6 Calibration and adjustment of the instrument ..................................................................................................................... 6
6.1 General ........................................................................................................................................................................................................... 6
6.2 f
Thicknes s re erence s tandards ................................................................................................................................................. 6
6.3 Methods of adjustment .................................................................................................................................................................... 7
7 Measurement procedure and evaluation .................................................................................................................................... 8
7.1 General ........................................................................................................................................................................................................... 8
7.2 Number of measurements and evaluation ...................................................................................................................... 8
8 Uncertainty of the results ............................................................................................................................................................................ 8
8.1 General remarks .................................................................................................................................................................................... 8
8.2 Uncertainty o f the calib ratio n o f the ins trument ...................................................................................................... 9
8.3 Stochastic errors ................................................................................................................................................................................. 10
8.4 Uncertainties caus ed by f acto rs s ummarized in Clause 5 .............................................................................. 10
8.5 C o mb ined uncertainty, exp anded uncertainty and final res ult .................................................................. 11
9 Precision .................................................................................................................................................................................................................... 11
9.1 General ........................................................................................................................................................................................................ 11
9.2 Rep eatab ility ( r) .................................................................................................................................................................................. 11
9.3 Rep ro ducib ility limit ( R) .............................................................................................................................................................. 12
10 Test report................................................................................................................................................................................................................ 12
Annex A (informative) Eddy-current generation in a metallic conductor .................................................................. 14
Annex B (informative) Basics of the determination of the uncertainty of a measurement of
the used measurement method corresponding to ISO/IEC Guide 98-3 ................................................... 18
Annex C (informative) Basic performance requirements for coating thickness gauges which
are based on the amplitude-sensitive eddy-current method described in this document .. 20
Annex D (informative) Examples for the experimental estimation of factors affecting the
measurement accuracy............................................................................................................................................................................... 22
Annex E (informative) Table of the student factor .............................................................................................................................. 27
Annex F (informative) Example of uncertainty estimation (see Clause 8) ................................................................ 28
Annex G (informative) Details on precision ............................................................................................................................................... 30
Bibliography ............................................................................................................................................................................................................................. 34

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ISO 2360:2017(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work o f 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 o f
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
di fferent types o f ISO documents should be noted. This document was dra fted 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 o f the elements o f this document may be the subject o f
patent rights. ISO shall not be held responsible for identi fying any or all such patent rights. Details o f
any patent rights identified during the development o f 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 in formation given for the convenience o f users and does not
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expressions related to con formity assessment, as well as in formation about ISO’s adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: www.iso .org/iso/foreword .html.
This document was prepared by Technical Committee ISO/TC 107, Metallic and other inorganic coatings.
This fourth edition cancels and replaces the third edition (ISO 2360:2003), which has been technically
revised.

iv © ISO 2017 – All rights reserved

INTERNATIONAL STANDARD ISO 2360:2017(E)

Non-conductive coatings on non-magnetic electrically

conductive base metals — Measurement of coating
thickness — Amplitude-sensitive eddy-current method
1 Scope
This document specifies a method for non-destructive measurements o f the thickness o f non-conductive
coatings on non-magnetic electrically conductive base metals, using amplitude-sensitive eddy-current
instruments.
In this document, the term “coating” is used for materials such as, for example, paints and varnishes,
electroplated coatings, enamel coatings, plastic coatings, claddings and powder coatings. This method
is particularly applicable to measurements o f the thickness o f most oxide coatings produced by
anodizing, but is not applicable to all conversion coatings, some o f which are too thin to be measured by
this method (see Clause 6).
This method can also be used to measure non-magnetic metallic coatings on non-conductive base
materials. However, the phase-sensitive eddy-current method specified in ISO 21968 is particularly
usable to this application and can provide thickness results with a higher accuracy (see Annex A).
This method is not applicable to measure non-magnetic metallic coatings on conductive base metals.
The phase-sensitive eddy-current method specified in ISO 21968 is particularly use ful for this
application. However, in the special case o f very thin coatings with a very small conductivity, the
amplitude-sensitive eddy-current method can also be used for this application (see Annex A).
Although the method can be used for measurements o f the thickness o f coatings on magnetic base
metals, its use for this application is not recommended. In such cases, the magnetic method specified
in ISO 2178 can be used. Only in case o f very thick coatings above approximately 1 mm, the amplitude-
sensitive eddy-current method can also be used for this application (see Annex A).

2 Normative references
The following documents are re ferred to in the text in such a way that some or all o f their content
constitutes requirements o f this document. For dated re ferences, only the edition cited applies. For
undated re ferences, the latest edition o f the re ferenced document (including any amendments) applies.
ISO 2064, Metallic and other inorganic coatings — Definitions and conventions concerning the measurement
of thickness

ISO 4618, Paints and varnishes — Terms and definitions

ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)

3 Terms and definitions

For the purposes o f this document, the terms and definitions given in ISO 2064 and ISO 4618 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia .org/
— ISO Online browsing platform: available at http://www.iso .org/obp
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ISO 2360:2017(E)

3.1
adjustment of a measuring system
set o f operations carried out on a measuring system so that it provides prescribed indications
corresponding to given values o f a quantity to be measured
Note 1 to entry: Adjustment o f a measuring system can include zero adjustment, o ffset adjustment, and span
adjustment (sometimes called gain adjustment).
Note 2 to entry: Adjustment o f a measuring system should not be con fused with calibration, which is a
prerequisite for adjustment.
Note 3 to entry: A fter an adjustment o f a measuring system, the measuring system must usually be recalibrated.
Note 4 to entry: Colloquially, the term “calibration” is frequently, but falsely, used instead o f the term “adjustment”.
In the same way, the terms “verification” and “checking” are o ften used instead o f the correct term “calibration”.
[SOURCE: ISO/IEC Guide 99:2007, 3.11 (also known as “VIM”)]
3.2
calibration
operation that, under specified conditions, in a first step, establishes a relation between the quantity
values with measurement uncertainties provided by measurement standards and corresponding
indications with associated measurement uncertainties and, in a second step, uses this information to
establish a relation for obtaining a measurement result from an indication
Note 1 to entry: A calibration may be expressed by a statement, calibration function, calibration diagram,
calibration curve, or calibration table. In some cases, it may consist o f an additive or multiplicative correction o f
the indication with associated measurement uncertainty.
Note 2 to entry: Calibration should not be con fused with adjustment o f a measuring system, o ften mistakenly
called “sel f-calibration”, nor with verification o f calibration.
Note 3 to entry: O ften, the first step alone in the above definition is perceived as being calibration.
[SOURCE: ISO/IEC Guide 99:2007, 2.39 (also known as “VIM”)]

4 Principle of measurement
Eddy-current instruments work on the principle that a high frequency electromagnetic field generated
by the probe system o f the instrument will produce eddy-currents in the base metal beneath the
coating on which the probe is placed (see Figure 1). These induced currents cause a change of the
electromagnetic field surrounding the probe coil and there fore result in a change o f the amplitude
o f the probe coil impedance. The induced eddy-current density is a function o f the distance between
the generating coil and the base metal sur face. Consequently, this impedance change can be used as
a measure o f the thickness o f the coating on the conductor by means o f a calibration with re ference
standards (see also Annex A).
In order to measure a change o f the coil impedance amplitude, the test coil is usually part o f an oscillator
circuit with a resonant frequency determined by the coil inductance and resistance. A change of the coil
impedance amplitude results in a shi ft o f the resonant frequency. Consequently, the measured resonant
frequency is a measure o f the coating thickness. The values are either pre-processed by digital means
or are directly displayed on a use fully scaled gauge.
The probe and measuring system/display may be integrated into a single instrument.
NOTE 1 Annex C describes the basic performance requirements of the equipment.
NOTE 2 Factors a ffecting measurement accuracy are discussed in Clause 5.

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 ISO 2360:2017(E)

Key
1 ferrite core of the probe 5 induced eddy- current

2 f high requency electro magnetic field ~

I exciting current
3 non-conductive coating t co ating thicknes s

4 base metal U = f(t) measurement signal

Figure 1 — Amplitude-sensitive eddy-current method

5 Factors affecting measurement uncertainty

5 . 1 B a s i c i n fl u e n c e o f th e c o a ti n g th i c kn e s s

T he s en s itivity o f a prob e, i . e . the me as u rement e ffe c t, de cre as e s with i nc re as i ng th ickne s s with i n the

me as u rement range o f the prob e . I n the lower me as u rement range, th i s me as u rement uncer ta i nty (i n

ab s olute term s) i s con s tant, i ndep endent o f the co ati ng th ickne s s . T he ab s olute va lue o f th i s u ncer tai nty

dep end s on the prop er tie s o f the prob e s ys tem and the s ample materi a l s , e . g. the homo geneity o f the

b a s e me ta l conduc tivity, the b as e me ta l rough ne s s and the s a mple s ur face rough nes s . I n the upp er

me as u rement range, the u ncer ta i nty b e come s approxi mately a con s tant frac tion of the co ati ng

th ickne s s .

5.2 Electrical properties of the base metal

T he conduc tivity o f the b as e me ta l de term i ne s the i nduce d e ddy- c u rrent den s ity for a given prob e

s ys tem and fre quenc y. C on s e quently, the b as e me ta l conduc tivity c au s e s the me a s urement e ffe c t for
th i s me tho d . T he relation sh ip b e twe en co ati ng th ickne s s a nd the me a s u re d va lue dep end s s trongly

on the conduc tivity of the base me ta l . C on s e quently, ca l ibration pro ce du re s and me a s urements

shall be made on the same material. Different materials with different conductivities as well as local
fluc tuation s o f the conduc tivity or variation s b e twe en d i fferent s ample s c an c au s e (more or les s) errors

i n the th ickne s s re ad i ng.

NO TE T here a re i n s tr u ments a nd p ro b e s ava i l ab le th at a re c ap ab le o f auto m atic a l l y comp en s ati ng the b a s e

me ta l conduc tivity i n fluence thu s avoid i n g the re s u lti n g th ickne s s er ro r.

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ISO 2360:2017(E)

5.3 Geometry: Base metal thickness

Generation o f eddy currents by the coil’s magnetic field in the depth o f the base metal is obstructed
i f the base metal thickness is too small. This influence can only be neglected above a certain critical
minimum base metal thickness.
There fore, the thickness o f the base metal should always be higher than this critical minimum base
metal thickness. An adjustment o f the instrument can compensate for errors caused by thin base metal.
However, any variation in thickness o f the base metal can cause increased uncertainty and errors.
The critical minimum base metal thickness depends on both the probe system (frequency, geometry)
and the conductivity o f the base metal. Its value should be determined experimentally, unless otherwise
specified by the manu facturer.
NOTE A simple experiment to estimate the critical minimum base metal thickness is described in D.3.
However, in the absence o f any other in formation, the required minimum base metal thickness, tmin ,
can be estimated from Formula (1).
t min = 3 ⋅ δ 0 (1)
where
δ0 is the standard penetration depth of the base metal (see A.1).
5.4 Geometry: Edge effects
The induction o f eddy currents is obstructed by geometric limitations o f the base metal (e.g. edges,
drills and others). There fore, measurements made too near to an edge or corner may not be valid unless
the instrument has been specifically adjusted for such measurements. The necessary distance in order
to avoid an impact o f the edge e ffect depends on the probe system (field distribution).
NOTE 1 A simple experiment to estimate the edge effect is described in D.2.
NOTE 2 When compared with the phase-sensitive method o f ISO 21968, the amplitude-sensitive eddy-current
instruments can be substantially more a ffected by edge e ffects.

5.5 Geometry: Surface curvature

The propagation o f the magnetic field and consequently the induction o f eddy currents are a ffected
by the sur face curvature o f the base metal. This influence becomes more pronounced with decreasing
radius o f the curvature and decreasing coating thickness. In order to minimize this influence, an
adjustment should be per formed on a base metal with the same geometry.
The influence o f sur face curvature depends considerably on the probe geometry and can be reduced
by reducing the sensitive area o f the probe. Probes with very small sensitive areas are o ften called
microprobes.
NOTE 1 There are instruments and probes available that are capable o f automatically compensating the base
metal sur face curvature influence thus avoiding the resulting thickness error.
NOTE 2 A simple experiment to estimate the effect of surface curvature is described in D.4.
5.6 Surface roughness
Measurements are influenced by the sur face topography o f the base metal and the coating. Rough
sur faces can cause both systematic and random errors. Random errors can be reduced by making
multiple measurements, each measurement being made at a different location, and then calculating the
average value of that series of measurements.

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 ISO 2360:2017(E)

In order to reduce the influence o f roughness, a calibration should be carried out with an uncoated base
metal with a roughness equivalent to the coated sample base metal.
I f necessary, the definition o f the average coating thickness that is used should be stated between the
supplier and client.
NOTE When compared with the phase-sensitive method o f ISO 21968, the amplitude-sensitive eddy-current
measurement can be more a ffected by base metal roughness.

5.7 Cleanliness: Lift-off effect

I f the probe is not placed directly onto the coating, the gap between the probe and coating (li ft-o ff)
will a ffect the measurement as i f it were an additional coating. Li ft-o ff can be produced unintentionally
due to the presence o f small particles between the probe and coating. The probe tip shall frequently be
checked for cleanliness.

5.8 Probe pressure

The pressure that the probe exerts on the test specimen can a ffect instrument reading and shall always
be the same during adjustment and measurements.
The influence o f the probe pressure is more pronounced in case o f so ft coatings because the probe tip
can be indented into the coating. Therefore, the probe pressure should be as small as possible. Most
commercially available instruments are equipped with spring loaded probes, which ensure a constant
pressure during the placement. A suitable auxiliary device should be used in case the probe is not
spring loaded.
NOTE 1 The contact pressure and the probe tip indentation depth can be reduced by reducing the applied load
force or by using a probe with a larger diameter o f the probe tip.

NOTE 2 An indentation o f the probe tip into so ft coatings can be reduced by placing a protective foil with
known thickness onto the coated sur face. In this case, the coating thickness is the measured thickness minus
the foil thickness. This procedure is not applicable when measuring non-magnetic metallic coatings on non-
conductive base materials.
5.9 Probe tilt
Unless otherwise instructed by the manu facturer, the probe shall be applied perpendicularly to the
coating sur face as tilting the probe away from the sur face normal can cause measurement errors.
The risk o f inadvertent tilt can be minimized by the probe design or by the use o f a probe-holding jig.
NOTE Most commercially available instruments are equipped with spring loaded probes, which ensure a
perpendicular placement on the sample surface.
5.10 Temperature effects
As temperature changes a ffect the characteristics o f the probe, it should be used under approximately
the same temperature conditions as when the instrument was calibrated.
NOTE 1 The influence o f temperature variations can be reduced by a temperature compensation o f the probe.
The manu facturer’s specification is taken into account.
NOTE 2 Temperature differences between the probe, electronics of the instrument, environment and sample
can cause large thickness errors. One example is the thickness measurement o f hot coatings.
Most metals change their electrical conductivity with temperature. Because the measured coating
thickness is influenced by changes in the electrical conductivity o f the base metal, large temperature
changes should be avoided (see 5.2).

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ISO 2360:2017(E)

5.11 Intermediate coatings

T he pre s ence o f an i nterme d iate co ati ng c an a ffe c t the me as u rement o f the co ati ng th ickne s s i f the

electrical characteristics of that intermediate coating differ from those of the coating or base metal. If
a diff ff
erence do e s exi s t, then the me a s urements wi l l, i n add ition, b e a e c te d b y an i nterme d i ate co ati ng

f
th ickne s s o tmin f les s tha n tmin , then the intermediate coating, if non-
. I the th ickne s s i s gre ater than

magnetic, can be treated as the base metal (see 5.3).

5 . 1 2 E x te r n a l e l e c tro m a g n e ti c fi e l d s

T he me as u rement re s u lts c an be i n fluence d by s trong ele c tromagne tic i nter feri ng field s . In cases

showi ng u ne xp e c te d re s u lts or a s trong variation o f re s u lts , wh ich c an no t b e e xplai ne d b y o ther fac tors ,
th i s i n fluence shou ld b e ta ken i nto accou nt. I n th i s s ituation, a comp a ri s on me as u rement s hou ld b e

ca rrie d out at a lo c ation without i nter feri ng field s .

6 Calibration and adjustment of the instrument

6.1 General
P rior to u s e, ever y i n s tru ment s ha l l b e c a l ibrate d or adj u s te d accord i ng to the i n s tr uc tion s o f the

manu fac tu rer by me an s o f s u itable th ickne s s re ference s tandard s a nd base me ta l . T he materi a l,

ge ome tr y, a nd s u r face prop er tie s o f the b as e me ta l us e d for c a l ibration or adj u s tment shou ld b e s i m i lar

to tho s e for the te s t s p e ci men s i n order to avoid deviation s c au s e d by the fac tors de s c rib e d i n Clause 5.
O ther wi s e, the s e i n fluence s sha l l b e con s idere d i n the e s ti mation o f the me a s u rement u ncer ta i nty.

During calibration or adjustment, the instruments, standards and base metal should have the same
temperature as the test specimens to minimize temperature induced differences.
I n order to avoid the i n fluence o f i n s tr ument d ri ft, p erio d ic control me a s u rements with re ference

standards or control samples are recommended. If required, the instrument has to be re-adjusted.
NO TE M o s t i n s tr u ments auto m atic a l l y adj u s t them s el ve s du r i n g a fu nc tio n c a l le d “c a l ib ration”, c a r r ie d out

b y the op erato r, where a s the re s u lt o f the c a l ib ratio n i s o ften no t ob viou s .

6.2 Thickness reference standards

T h ickne s s re ference s tandard s for c a l ibration and adj u s tment a re either co ate d b as e me ta l s or foi l s ,
which are placed onto uncoated base metals.
Foi l s a nd co ati ngs sh a l l b e non- conduc ti ve and non-magne ti z able . T h ickne s s va lue s o f the re ference

s ta nda rd s and thei r as s o ci ate d u ncer tai ntie s s ha l l b e known a nd u nambiguou sly do c umente d . T he

s u r face are a for wh ich the s e va lue s are va l id s ha l l b e marke d . T he th ickne s s va lue s s hou ld b e trace able

to cer ti fie d re ference s ta nda rd s .

T he uncer ta i ntie s s ha l l b e do c u mente d with thei r con fidence level, e . g. U (9 5 %) , i . e . the prob abi l ity, th at

the “tr ue” va lue i s with i n the rep or te d u ncer tai nty i nter va l arou nd the do c u mente d th ickne s s va lue, i s

minimum 95 %.
P rior to u s e, foi l s a nd co ati ngs are to b e che cke d vi s ua l ly for damage or me ch an ic a l we ar as th i s wou ld

cau s e an i ncorre c t adj u s tment a nd thu s s ys tematic devi ation o f a l l me as u rement va lues .

In most cases, the foil material is plastic. In contrast to the magnetic method (see ISO 2178), conductive
materia l s , e . g. copp er a l loys , c an no t b e u s e d b e c au s e i n s uch foi l s , e ddy c u rrents c an b e i nduce d . T hey

wou ld a ffe c t the me a s u rement a nd cau s e th ickne s s errors .

NOTE When measuring non-magnetic metallic coatings on non-conductive base materials, the situation is
“inverted”.

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 ISO 2360:2017(E)

The use o f foils as re ference standards, compared to selected coated base metals, benefits from the
possibility o f placing the foils directly on each base metal. The geometry influence and other factors are
already considered within the adjustment.
However, by placing the probe on foils, elastic or plastic de formation may occur, which can a ffect the
measurement result. Moreover, any gap between the pole o f the probe, foil and base metal has to be
avoided. Especially for concave specimens, or i f the foil is wrinkled or bent, the usually low pressure o f
the spring loaded guiding sleeve o f the probe may not be su fficient to ensure there is no gap.
Possible elastic or even plastic deformation of a reference foil depends on the applied force of the
probe and the probe tip diameter (see 5.9). Consequently, the calibration of such reference foils should
be carried out with comparable values of the applied force and tip diameter to avoid indentation
di fferences during the probe calibration. In this way, respective indentation errors are already taken
into account in the foil thickness value, i.e. this value can be smaller than the una ffected geometric
thickness. The values o f both the applied force and the tip diameter used at the foil calibration should
be known from the re ference foil manu facturer so that possible thickness errors can be estimated.

6.3 Methods of adjustment

Adjustment o f the coating thickness gauges is executed by placing the probes on uncoated and/or one
or more coated pieces o f base metal with known coating thickness. Depending on the instrument types,
instructions of the manufacturer and on the functional range of the instrument under use, adjustments
can be carried out on the following items:
a) a piece of uncoated base metal;
b) a piece o f uncoated base metal and a piece o f coated base metal with defined coating thickness;
c) a piece o f uncoated base metal and several pieces o f coated base metal with defined but di fferent
coating thickness;
d) several pieces o f coated base metal with defined but di fferent coating thickness.
According to 6.2, the term “coated base metal” includes foils placed onto uncoated base metal.
The stated adjustment methods may lead to di fferent accuracies o f the measuring results. Thus,
a method that best fits the given application and leads to the desired accuracy should be used. The
measuring uncertainty that can be achieved by the di fferent adjustment methods depends on the
evaluation algorithm o f the gauges as well as on the material, geometry and sur face condition o f the
standards and o f the base metals to be measured. I f the desired accuracy is not achieved by one method,
a di fferent adjustment method may lead to better results. In general, the measuring uncertainty can be
reduced by increasing the number o f adjustment points and the better and closer the adjustment points
cover the expected thickness interval o f the coating to be measured.
NOTE 1 The process that is used to adapt the probe to the given base metal by placing the probe onto the
uncoated base metal, is often called “zeroing” or “zero point calibration”. However, even this procedure is an
“adjustment” or part o f an adjustment process as defined by this document.
NOTE 2 Depending on how many pieces o f coated and uncoated base metals are used to adjust the instrument,
the corresponding adjustment method is often called “single-point”, “two-point” or “multiple-point adjustment”.
The measurement uncertainty resulting from an adjustment o f the instrument cannot be generalized
to all subsequent measurements. In each case, all specific and additional influencing factors need to be
considered in detail, see Clause 5 and Annex D.
NOTE 3 Some types o f gauges permit resetting the instrument to an original adjustment o f the manu facturer.
This adjustment is valid for the manu facturer’s uncoated or coated re ference standards only. I f these standards
or the same types o f standards are used to check the instrument a fter a period o f use, any deterioration o f gauge
and probes, e.g. wear o f the probe by abrasion o f the contact pole, can be recognized by observing deviations o f
the measuring results.

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ISO 2360:2017(E)

7 Measurement procedure and evaluation

7.1 General
Every instrument shall be operated according to the manu facturer’s instructions especially considering
the factors a ffecting measurement accuracy discussed in Clause 5.
Be fore using the instrument and a fter changes a ffecting the measurement accuracy (see Clause 5), the
adjustment o f the instrument shall be checked.
To ensure that the instrument measures correctly, it shall be calibrated with valid standards at the
place of inspection each time:
a) the instrument is put into operation,
b) material and geometry o f the test specimens are changed, or
c) other conditions o f the inspection have changed (e.g. temperature) whose e ffects are not known.
As not all changes o f measurement conditions and their influences on the measurement accuracy can
be immediately recognized (e.g. dri ft, wear o f the probe), the instrument should be calibrated at regular
time intervals while in use.
7.2 Number of measurements and evaluation
The coating thickness should be determined as the arithmetic mean o f several single values, which
are measured in a defined area o f the coating sur face. In addition to the mean, the standard deviation
should be reported (see Annex B). The random part o f the measurement uncertainty can be reduced by
increasing the number o f measurements. I f not otherwise specified or agreed upon, it is recommended
to measure at least five single values (depending on the application).
NOTE 1 From the standard deviation, a variation coe fficient V can be calculated. V corresponds to the relative
standard deviation (e.g. in percent) and enables a direct comparison of the standard deviation for different
thicknesses.
NOTE 2 The total scatter of the measurement is composed of the scatter of the instrument itself and the
scatter caused by the test specimen. The standard deviation o f the operator and probe in the measured thickness
range is determined by repeated measurements at the same location, i f necessary with the help o f an auxiliary
device for placing the probe.
When measuring on rough coating sur faces or on test specimens with known large thickness gradients
(e.g. due to their size and/or their shape), the reason for deviations between the single measurements
should be determined by a series o f measurements.

8 Uncertainty of the results

8.1 General remarks
A complete evaluation o f the uncertainty o f the measured thickness shall be carried out in accordance
with ISO/IEC Guide 98-3. Details o f the background o f the expression o f the uncertainty are summarized
in Annex B and a typical example of this calculation is described in Annex F.
Uncertainty o f the thickness measuring result is a combination o f uncertainties from a number o f
different sources. Important sources that should be considered include the following:
a) uncertainty o f the calibration o f the instrument;
b) stochastic influences a ffecting the measurement;
c) uncertainties caused by factors summarized in Clause 5;

8 © ISO 2017 – All rights reserved

 ISO 2360:2017(E)

d) further influences, dri fts, digitalization e ffects and other e ffects.

All uncertainty components shall be estimated and summarized to the combined standard uncertainty
as described in ISO/IEC Guide 98-3, see Annex B.
A possible procedure for the estimation o f the uncertainty is given in the following simplified approach
(see 8.2 to 8.5).
The single uncertainty components o f the listed sources are dependent on the respective measurements,
the properties of the samples measured, the instrument, the environmental condition, etc. and can
show large di fferences for di fferent applications. There fore, the single uncertainty components shall
be estimated for each measurement in all detail. The quality o f the uncertainty is determined by
the quality o f the estimation o f all uncertainty components. Missing components result in incorrect
uncertainty estimations and consequently in incorrect thickness results.
In particular, the factors listed in Clause 5 can result in large uncertainty values and should be
minimized by an adjustment i f possible.
NOTE In addition to the need to express the uncertainty in the result, the analysis o f possible uncertainty
components provides detailed information in order to improve the measurement.
8.2 Uncertainty of the calibration of the instrument
I f no other in formation is given, the current uncertainty o f an instrument can be estimated within a
limited thickness range by realization o f n repeated measurements on a given reference standard with
known thickness, tr, and uncertainty, Ur (k = 2). The measurement result is the arithmetic mean value,
t m , o f the measured thickness values with the standard deviation, s(tm). The quality o f the calibration

is determined by the ratio, E, of the resulting difference, t m − t r , and the combined uncertainty o f the
calibration measurement. This uncertainty (denominator o f E, k = 2) is considered to be caused by the
stochastic error of the measurement with n repeats (compare to 8.3) and the given reference standard
uncertainty, Ur. In case of E ≤ 1, the calibration is valid and cannot be further improved by means o f this
re ference standard, i.e. the di fference cannot be distinguished from the uncertainty. There fore, the
standard uncertainty o f the calibration, ucal (k = 1), is given by the combined uncertainty o f the
verification measurement but with respect to the 1 sigma level (k = 1).
However, in the case of E > 1, a significant deviation of the calibration within the uncertainty is detected
and an adjustment o f the instrument should be carried out in order to improve the calibration accuracy.
See Formulae (2) and (3):
t r − tm
E=
2 × u cal
(2)

s (t ) 
2

u cal =  t ( 68 , 27 %, n − 1 ) × m  +  0 , 5 × U r 
2
(3)
 n 
NOTE 1 In case the tolerance, T, of the reference standard is given instead of Ur, i.e. (tr ± T), for example in a
certificate o f a certified re ference material, the respective standard uncertainty (for 68,3 % confidence level) can
be calculated as U r = T and the expanded uncertainty (for 95,4 % confidence level) as U r ( k = 2 ) = 1 , 653 × T
3 3
. The deviation from the usual factor 2 for normal distribution is due to the fact that tolerances follow rectangular
distributions.
The calibration uncertainty ucal is only valid in a small thickness range around tr. In the case of a larger
thickness range o f interest, the uncertainty ucal should be estimated on both sides o f the thickness
range. The linear interpolation between both values gives the uncertainty o f interest as a function o f
the thickness.

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ISO 2360:2017(E)

Very o ften, the accuracy o f the calibration is limited by the given uncertainty o f the re ference standard,
as the uncertainty o f the calibration cannot be smaller than the uncertainty o f the re ference standard
used. In order to improve the calibration, a re ference standard with a smaller uncertainty is necessary.
Usually, a normalization or zeroing on an uncoated base metal is recommended by the manu facturer
at the beginning o f a measurement. The resulting uncertainty o f this normalization is considered to be
already included in ucal .
NOTE 2 t(68,27 %, n – 1): student factor (degrees of freedom f = n - 1 and level o f confidence with P = 68,27 %).
Respective values are summarized in Annex E.
8.3 Stochastic errors
In general, repeated measurements are recommended in order to improve the accuracy o f the arithmetic
mean value, t , of the thickness values measured (see 7.2 ), i.e. to reduce the uncertainty of the thickness
result. In the case of n repeated measurements, the standard uncertainty, usto (k = 1), of the arithmetic
mean, t , can be estimated by using Formula (4) (Type A):
u sto = t ( 68 , 27 %, n − 1 ) ×
()
s t
(4)
n

The standard uncertainty, u sto , is a measure of all errors arising from unpredictable or stochastic
temporal and spatial variations o f influence quantities.
NOTE 1 The standard uncertainty, u sto , can be reduced by increasing the number o f repeated measurements.
This can be important, e.g. in case of rough sample surfaces.
NOTE 2 Not all contributions to the uncertainty, u sto , are o f random nature (Type A). This depends on the
design o f the experiment. For example, the measured thickness o f a larger sample with a thickness gradient
results in a high uncertainty, u sto , because o f the systematic thickness variation. In the case o f a reduced
measurement area, usto is reduced and the arithmetic mean value, t , gives a better description of the local
thickness.
Care should be taken to address the risk that Type B standard uncertainties (see 8.4), which might
contribute to Type A standard uncertainties, are not counted twice.

8.4 Uncertainties caused by factors summarized in Clause 5

The influence o f the factors summarized in Clause 5 should be minimized by means o f an adjustment
whenever this is possible. Very o ften, these influences can only be estimated and the resulting
uncertainty shall be considered as a component o f the combined uncertainty o f the measurement.
Simple experiments to estimate the uncertainty o f some o f these factors are described in Annex D.
Usually, the influence o f these factors, and there fore the resulting uncertainties, are a function o f
thickness. Consequently, in order to estimate the uncertainty for a given thickness or for, at least, a
small thickness range, the experiments shall be carried out with samples with the thickness o f interest.
For example, the variation o f the conductivity properties o f the base metal is considered (conductivity
variation). As described in D.5 , the expected variation should be estimated for the thickness of interest.
The resulting thickness variation with respect to the selected re ference base metal should be

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 ISO 2360:2017(E)

∆t bm = abs ( t min − t r ) or ∆t bm = abs ( t max − t r ) . This gives the standard uncertainty caused by the
variation of the base metal properties ubm(k = 1) as shown in Formula (5):
∆t bm
u bm = (5)
3
The same estimation o f the standard uncertainty shall be carried out for all relevant factors listed in
Clause 5. For example, in the case of an expected variation of the surface curvature resulting in ∆t cs
with respect to D.4, the standard uncertainty can be estimated as ucs(k = 1) as shown in Formula (6):
∆t cs
u cs = (6)
3
In case the influence o f a factor is minimized by means o f an adjustment, the remaining uncertainty
shall be considered.
Some o f these factors influencing the accuracy can be minimized by means o f flexible foils as re ference
standards, e.g. base metal properties (5.3) or surface curvature (5.5), if the calibration is carried out
with foils on the base metal with identical material and curvature properties as the sample of interest
shows. In this case, only expected variations o f the sample properties shall be considered.

8 . 5 C o m b i n e d u n c e r ta i n ty, e x p a n d e d u n c e r ta i n ty a n d fi n a l re s u l t

The combined uncertainty summarizes all standard uncertainty components (8.2, 8.3, 8.4 and any
potential others). In the simplified approach described, when estimating the uncertainties for a given
thickness, or a very small thickness range, the sensitivity coe fficients can be considered to be equal to 1
(see Annex B). This results in the combined uncertainty, uc , as shown in Formula (7):
2 2 2 2 (7)
u c= u cal + u sto + u bm + u cs + ...
As the final result, the expanded uncertainty U(k = 2) is calculated (2-sigma level, 95,45 %) as shown in
Formula (8):
U ( k = 2 ) = 2uc (8)
And the complete result o f the measurement with the thickness value, t , is calculated as shown in
Formula (9):
t = t ±U(k = 2) (9)

9 Precision

9.1 General
See Annex G for further information on determining precision.
9.2 Repeatability (r)
Repeatability, r, is the value less than or equal to which the absolute difference between two test results
obtained under repeatability conditions may be expected to be, with a probability o f 95 % (according to
ISO 5725-1:1994, 3.16). The repeatability limit, r, in accordance with this document and calculated with
a probability o f 95 %, is given in Table 1.

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ISO 2360:2017(E)

Table 1 — Repeatability limit (r)

Coating thickness R e p e a t a b i l i t y l i m i t o f fi r s t Repeatability limit of all
measuring point (triple fi ve m e a s u r i n g p o i n t s

measurement)
rx
1 rx
approx. µm µm µm
12 1,0 1,0
25 1,7 2,3
125 2,7 12,5
9.3 Reproducibility limit (R)
Repro ducibi l ity l i m it, R, is the value less than or equal to which the absolute difference between two
te s t re s u lts ob tai ne d u nder repro ducibi l ity cond ition s may b e exp e c te d to b e, with a prob abi l ity o f 9 5 %

R, in accordance with this document and

(accord i ng to I S O 5 7 2 5 -1 : 19 9 4, 3 . 2 0) . T he repro ducibi l ity l i m it,

ca lc u late d with a prob abi l ity o f Table 2.

9 5 % , i s given i n

Table 2 — Reproducibility limit (R)

Coating thickness Reproducibility limit of Reproducibility limit of all
fi r s t m e a s u r i n g p o i n t fi ve m e a s u r i n g p o i n t s

(triple measurement)
Rx
1 Rx
approx. µm µm µm
12 –a –a
25 5,0 5,3
125 6,0 13,0
a No calculation of R x1 and R x re p ro duc ib i l i ty co u ld b e do ne i n re s p e c t o f o n l y o ne s a mp le .

10 Test report
The test report shall include the following information:
a) a l l i n formation ne ce s s ar y for the identi fic ation o f the te s t s p e ci men;

b) a re ference to th i s do c u ment, i nclud i ng its ye ar o f publ ication, i . e . I S O 2 3 6 0 : 2 017;

c) the sizes of the test areas over which the measurements were made in square millimetres (mm 2 );
NOTE Other units of measurement can be used, with agreement between the supplier and client.
d) the location(s) of the test area(s) on each specimen;
e) the number of test specimens measured;
f) an identi fic ation o f the i n s tr ument, prob e and s ta nda rd s u s e d for the te s t, i nclud i ng re ference to

any va l idation cer ti fic ation o f the e qu ipment;

g) the re s u lts o f the te s t, rep o r te d a s the me a s u re d th ickne s s e s , i n m ic ro me tre s , at e ach a re a at

which the test was carried out, including the results of the individual determinations and their
arithmetic mean;
h) the name of the operator and testing organization;

12 © ISO 2017 – All rights reserved

 ISO 2 3 60: 2 01 7(E)

i) a ny u nu s ua l fe atu res ob s er ve d and any ci rc u m s ta nce s or cond ition s that a re l i kely to a ffe c t the

re s u lts or thei r va l id ity;

j) a ny deviation from the me tho d s p e c i fie d;

k) d ate o f the te s t.

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ISO 2360:2017(E)

Annex A
(informative)
Eddy-current generation in a metallic conductor

A.1 General
E ddy- c u rrent i n s tr uments work on the pri nciple that a h igh fre quenc y ele c tromagne tic field generate d

by the prob e s ys tem o f the i n s trument pro duce e ddy c u rrents i n a n ele c tric a l conduc tor on wh ich the

prob e i s place d . T he s e i nduce d e ddy c u rrents c au s e a cha nge o f the ele c tromagne tic field s u rrou nd i ng

the prob e coi l s ys tem a nd there fore re s u lt i n a ch ange o f the ampl itude a nd/or the ph as e o f the prob e

coi l i mp e dance, wh ich c a n b e u s e d as a me a s u re o f the th ickne s s o f the co ati ng on the conduc tor (s e e

A.2 and A.5) or of the conductor itself (see A.3 and A.4).
T he e ddy- c u rrent generation i n a me ta l conduc tor i s shown i n Figure 1.
J(δ
T he e ddy- c u rrent den s ity, ) , cha nge s its magn itude with i ncre a s i ng d i s tance, δ , from the s u r face o f

the conductor (depth). At the depth, δ0 (s tandard p ene tration dep th) , the ele c tromagne tic field a nd

J ( δ 0 ) = 1 . In principle, this standard penetration depth is

J (0 )
con s e quently the c u rrent den s ity d rop s to
e

de term i ne d b y the s a mple conduc ti vity and the p erme abi l ity a nd the fre quenc y o f the prob e coi l

s ys tem; s e e Figure A.1.

a) high frequency or/and high conductivity b) low frequency or/and low conductivity
Key
1 probe δ0 standard depth of penetration
2 eddy currents δ depth
J(δ) dens ity

F i g u r e A . 1 — S c h e m a t i c t o s h o w t h e i n f l u e n c e o ff r e q u e n c y a n d c o n d u c t i v i t y o n t h e s t a n d a r d

penetration depth

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 ISO 2360:2017(E)

The standard penetration depth, δ0 , is a useful value for some important rough estimations. It may be
calculated, in mm, using Formula (A.1):
δ =
503 × F (A.1)
0 p
f ×σ × µ r

where
f is the probe operating frequency, in Hertz;
σ is the electrical conductivity o f the conductor, in megasiemens per metre;
μ r is the relative permeability o f the conductor (for non-magnetic materials μ r = 1);

p is a correction factor determined by the geometry o f the probe.

F

The amplitude-sensitive eddy-current method is best suited to the measurement o f non-conductive

coatings on non-magnetic base metals (see A.2) but also to the measurement of bare non-magnetic
metallic coatings on non-conductive base metals (see A.3 ). The phase-sensitive eddy-current method
(see ISO 21968) is best suited to the measurement of non-magnetic metallic coatings on metallic or non-
metallic base metals (see A.2 and A.3 ) especially i f the metallic coating has to be measured through
paint or i f a contactless measurement is necessary, i.e. a “li ft-o ff” compensation is necessary.

A.2 Example 1: Non-conductive coating on a conductive base metal

In this case, the eddy-current density is only determined by the distance between the probe and the
base metal, i.e. the coating thickness (see Figure A.2 ). A larger coating thickness results in a reduced
interaction o f the magnetic field o f the probe with the base metal and consequently in a reduced eddy-
current density. This e ffect can be used as a measure o f the coating thickness.

Key
1 probe
2 non-conductive coating
3 conductive base metal
Figure A.2 — Schematic of the eddy-current density in the case of non-conductive coating on a
conductive base metal

To establish that the eddy-current density is a unique measure o f the coating thickness, this density
should not be a ffected or limited by the base metal thickness. In order to achieve this, the base metal
shall be thicker than the minimum base metal thickness. This minimum thickness, tmin , in mm, can be
estimated as shown in Formula (A.2) (see 5.3):
t min = 3 δ 0 (A.2)

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ISO 2360:2017(E)

NOTE tmin is very o ften called “saturation thickness”. I f the base metal thickness is lower than this minimum
thickness, tmin , the measured value o f the coating thickness will be a ffected and the value o f the thickness that is
obtained is too high.
However, in the special case o f very thin coatings with a very small conductivity, the amplitude-sensitive
eddy-current method can also be applied, because this coating is considered as non-conductive. A
typical example is thin chromium coating plated on copper with a coating thickness below 10 µm. In
this situation, the impact o f the eddy currents induced in the coating can be neglected. However, a
larger thickness results in an increasing eddy-current density in the coating resulting in an increasing
thickness error, although the conductivity o f the chromium coating is small. The possible thickness
error should be determined or estimated to decide whether this method is applicable or not.
A.3 Example 2: Conductive coating on a non-conductive base material
In this case, the eddy-current density is determined only by the thickness o f the conductive coating (see
Figure A.3 ). A larger coating thickness results in an increased interaction of the magnetic field of the
probe with the conductive coating and consequently in an increased eddy-current density. This e ffect
can be used as a measure o f the coating thickness.

Key
1 probe
2 conductive coating
3 non-conductive base metal
Figure A.3 — Schematic of the eddy-current density in the case of conductive coating on a non-
conductive material

The approximate maximum measurable thickness, tmax, in mm, may be calculated from Formula (A.3):
max = 0,8 δ0
t (A.3)
For example, the thickness range is limited by the penetration depth, δ0 . If the conductive coating
thickness is increased further, the resulting increase o f the generated eddy-current density starts to
become smaller, i.e. the measurement sensitivity will be reduced.
The amplitude-sensitive eddy-current method is only capable o f measuring a conductive coating on top
of a non-conductive material. In the case of a conductive coating on top of a conductive base metal,
the amplitude-sensitive method cannot distinguish between the coating and the base metal, i.e. the
entire eddy-current density generated in the coating and the base metal would be used to determine
the coating thickness. This results in incorrect thickness values.

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 ISO 2360:2017(E)

A.4 Example 3: Conductive coating on a conductive and/or magnetic base metal

In this case, as shown in Figure A.4 , the generate d e ddy- c urrent den s ity i s de term i ne d b y the th ickne s s

and conduc tivity o f the co ati ng and the conduc tivity and p erme abi l ity o f the b a s e me ta l . T he co ati ng

th ickne s s c an on ly b e me as u re d b y me a n s o f the pha s e - s en s itive e ddy- c u rrent me tho d . D e tai l s are

given in ISO 21968.

Key
1 probe
2 conductive coating
3 conductive base metal
Figure A.4 — Schematic of the eddy-current density in the case of conductive coating on a
conductive and/or magnetic base metal

A.5 Example 4: Non-conductive coating on a magnetic base metal

I n th i s c a s e, the e ddy- c urrent den s ity i s on ly de term i ne d b y the d i s tance b e twe en the prob e and the

b a s e me ta l, i . e . the co ati ng th ickne s s (s e e Figure A.2). However, the probe impedance is also affected
by the magne tic prop er tie s o f the b a s e me ta l, re s u lti ng i n th ickne s s errors . T h i s add itiona l me a s u ri ng

e ffe c t i s opp o s ite to the e ffe c t o f the e ddy c urrents . Fu r thermore, the ampl itude - s en s itive e ddy- c u rrent

me tho d i s ver y s en s itive to cha nges or fluc tuation s o f the p erme abi l ity o f the b a s e me ta l, i . e . even when

the magne tic b a s e me ta l wa s ta ken i nto accou nt i n the c a l ibration, the th ickne s s res u lts a re exp e c te d

to show strong variations on different magnetic base metals and also at different locations on one
b a s e me ta l (e . g. s te el) . C on s e quently, the magne tic me tho d s p e c i fie d i n I S O 2 178 s hou ld b e u s e d i n th i s

situation.
O n ly i n the c a s e o f ver y th ick co ati ngs ab ove approxi mately 1 m m, the a mpl itude - s en s itive e ddy- c u rrent

method can also be used for this application. There are two reasons for this:
a) for s uch th ick co ati ngs , the relative i mp ac t o f the p erme abi l ity o f the b a s e me ta l i s s trongly re duce d;

b) i n order to me a s u re s uch th ick co ati ngs , the e ddy- c urrent prob e coi l shows a la rge d ia me ter and

con s e quently, the ac tive a re a o f the co ati ng i nclude d i n the me as u rement i s i ncre a s e d . I n th i s way,

the prob e i nte grate s va ri ation s o f the p erme abi l ity over the enti re ac tive are a, re s u lti ng i n more

stable results.
T he m i n i mu m th ickne s s o f the co ati ng ne ce s s ar y to u s e th i s me tho d for the s e appl ic ation s shou ld b e

de term i ne d with res p e c t to the exp e c te d accep table rep e atabi l ity a nd truene s s o f the me a s u rement.

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ISO 2360:2017(E)

Annex B
(informative)
Basics of the determination of the uncertainty of a measurement
of the used measurement method corresponding to ISO/
IEC Guide 98-3

B.1 General
Coating thicknesses are generally determined as the mean value o f several single measurements that
are carried out at a fixed section o f the layer’s sur face.
On the basis o f these measurements, a mean value is allocated to the measurand “coating thickness”. An
uncertainty value is assigned which provides in formation about the reliability o f the allocated value.
Analysis is carried out progressively and begins by drawing up a model equation that shows the
functional correlation between the indicated output value, t, and all the relevant influence quantities,
Hi , as shown in Formula (B.1):

t = F(H H H 0
H H )
,
1
,
2
, ...
i
...
n
(B.1)
To every influence quantity belongs a sensitivity coe fficient, ci , which indicates how strong a
modification Δ Hi affects the result t.
When the function, F, is given as analytic expression, the sensitivity coefficients may be calculated by
partial derivation; see Formula (B.2):
δt
c i = δH (B.2)
i
I f the kind o f the functional correlation in unknown, an approximation by means o f polynomial
functions is recommended.
In many practical cases, this formulation is expressed by a linear dependence, i.e. the sensitivity
coe fficients become constant. This situation arises, for example, in sections o f limited coating thickness.
In order to summarize the uncertainties o f various error influences appropriately, all single uncertainty
components may be re ferred to a level o f confidence o f 68,27 %, the so-called “standard uncertainty”.
There are two types o f uncertainties: Type A (see B.2 ) and Type B (see B.3).

B.2 Type A
The standard uncertainty o f Type A is a measure o f all random errors arising from unpredictable or
stochastic temporal and spatial variations o f influence quantities.
The standard uncertainty corresponds to the point o f confidence o f the mean value; see Formula (B.3)
and Formula (B.4):
u s to = t( 68 , 2 7 % , n − 1 ) ×
s( t )
(B.3)
n

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 ISO 2360:2017(E)

∑( x − x )2 j

s=
j= 1 (B.4)
(n − 1 )
where
s is the empirical standard deviation of the repetition measurement n, and
t (68,27 %, n – 1) is the student factor (degrees of freedom f = n – 1 and level of confidence with
p = 68,27 %).

Respective values are summarized in Annex E.

B.3 Type B
Many influencing factors or errors are not to be described by Type A, e.g. influencing factors o f Clause 5.
These are classified as Type B.
In order to realize a balanced combination o f those error influences with the uncertainties o f Type A,
the ad hoc probability factors are allocated. In many practical cases, the influencing factors treated
here are to be described by a uni form distribution (rectangle distribution).
I f an influence quantity fluctuates within a section Δ Hi , the resulting uncertainty can be calculated as
shown in Formula (B.5):
t max − t min (B.5)
u B=
12
These fluctuations are generally estimated or determined experimentally (see Annex D).
In many applications, known uncertainties can be used for the uncertainty determination. A typical
example is a given uncertainty o f a thickness re ference standard. To release this, take into consideration
that these statements o f uncertainty are converted into the standard uncertainty, e.g. for U(k = 2),
follow the standard uncertainty shown in Formula (B.6):

u ( 68 , 27 %) = U( 95 2, 45 %) (B.6)
In order to summarize all investigated uncertainties, the so-called “combined uncertainty” is calculated.
This is done by multiplying all standard uncertainties by their sensitivity coe fficients and adding them
up squared. In a simplified case, the sensitivity coe fficients are equally one; see Formula (B.7):

u= ∑ (ciui ) 2 (B.7)
i

Multiplying with an indicated coverage factor o f k ≥ 2 results in an expanded uncertainty, which should
be indicated in the actual result; see Formula (B.8):
U = k⋅u (B.8)

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ISO 2360:2017(E)

Annex C
(informative)
Basic performance requirements for coating thickness gauges
which are based on the amplitude-sensitive eddy-current method
described in this document

C . 1 Te c h n i c a l s p e c i fi c a ti o n

T he manu fac tu rer ’s te ch n ic a l s p e c i fic ation s hou ld at le as t provide the fol lowi ng te ch n ic a l i n formation

for instruments and probes:

a) principle of measurement;
b) measuring range;
c) b as ic i n formation on me as u ri ng u ncer tai nty or p erm i s s ible error o f me as u rement i f me as u ri ng i s

c arrie d out u nder cond ition s s p e ci fie d b y the manu fac turer;

d) i n formation on how me a s u ri ng re s u lts a re i n fluence d b y the materi a l, c ur vatu re a nd th ickne s s o f

the b a s e me ta l and b y the e dge e ffe c t (me a s u rements clo s e to a n e dge) ;

e) b atter y op erati ng ti me;

f) function of an undervoltage monitor and automatic undervoltage switch-off;

g) permissible operating temperature;
h) permissible storage temperature;
i) available methods for calibration and adjustment;
j) contact force of probes with spring loaded guiding sleeves;
k) avai labi l ity o f temp eratu re comp en s ation;

l) measuring rate;
m) data memor y (de s ign, c ap acity, data com mu n ic ation) ;

n) size and weight of instrument (with batteries) and probes.

C . 2 C h e c k/ ve r i fi c a ti o n o f i n s tr u m e n ts a n d p ro b e s

C.2.1 Prior to the supply, after repair and at regular intervals after use
After the instruments and probes have been adjusted according to the manufacturer’s instructions,
the me as u ri ng acc u rac y shou ld b e che cke d and veri fie d b y u s i ng a plane and u nco ate d b a s e me ta l

and a representative number of coated calibration standards or calibration foils, whose coating or foil
th ickne s s e s shou ld b e e qua l ly d i s tribute d with i n the me a s uri ng ra nge o f the res p e c tive prob e .

T he a i m o f the che ck/veri fic ation o f the i n s tru ments i s to en s u re that the th ickne s s devi ation s a re

with i n the manu fac tu rer ’s te ch n ic a l s p e ci fic ation .

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 ISO 2360:2017(E)

C.2.2 Performed on site

The accuracy o f the instruments and probes should be verified daily. A fter the instrument has been
adjusted according to the manu facturer’s instructions, make a verification with an appropriate number
o f coated calibration standards made from the same base metal as the items to be measured or by
means o f calibration foils put onto the base metal to be measured. Their thicknesses should cover the
expected coating thickness range. I f curved coated items need to be measured, verification shall be
executed on items o f the same base metal, geometry and curvature as the items to be measured.
The aim o f the check/verification o f the instruments is to ensure that the thickness deviations are
within the manu facturer’s technical specification.

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ISO 2360:2017(E)

Annex D
(informative)
Examples for the experimental estimation of factors affecting the
measurement accuracy

D.1 General
Factors a ffecting the measurement accuracy are summarized and described in Clause 5. In practical
measurements, it is important to estimate the influence o f these factors or the resulting uncertainty.
Therefore, some examples of simple experiments are described in this annex in order to show how the
influence o f these factors can be estimated. These experiments also provide a basis for estimating the
respective uncertainty.
The factors described in D.2 to D.5 can cause di fferently pronounced influences for an instrument
working with combined measuring principles in one probe. Consequently, the factors should be
estimated separately for each measuring principle.

D.2 Edge effect

A simple edge e ffect test, to assess the e ffect o f the proximity o f an edge, consists o f using a clean,
uncoated and even sample of the base metal and follows the procedure described in Step 1 to Step 4
below. The procedure is illustrated in Figure D.1.
Step 1
Place the probe on the sample, su fficiently away from the edge.
Step 2
Adjust the instrument to read zero.
Step 3
Progressively bring the probe towards the edge and note where a change o f the instrument reading
occurs with respect to the expected uncertainty or to the given thickness tolerance.
Step 4
Measure the distance, d, from the probe to the edge (see Figure D.1).
The instrument may be used without correction provided that the probe is further from the edge than
the distance as measured above. If the probe is used closer to the edge, a special adjustment is required
or the additional resulting uncertainty for the used distance needs to be considered. I f necessary, re fer
to the manufacturer’s instructions.

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 ISO 2360:2017(E)

Key
d distance from the probe to the edge
Figure D.1 — Schematic representation of the test for edge effect

D.3 Base metal thickness

A simple test to prove that the base metal thickness, t0 , is larger than the critical minimum base metal
thickness, t0 crit, consists of using two (or more) clean, uncoated and even samples of the base metal with
the thickness o f interest and follows the procedure described in Step 1 to Step 4 below. The procedure
is illustrated in Figure D.2.
Step 1
Place the probe on the first sample. It should be proven that the reading is not a ffected by the edges o f
the sample (see D.2).
Step 2
Adjust the instrument to read zero.
Step 3
Place the second sample beneath the first one, place the probe on top o f this stack and check the
instrument reading. I f the instrument reading is still zero with respect to the expected uncertainty,
the base metal thickness, t0 , is larger than the critical minimum base metal thickness, t0 crit, and no
additional uncertainty needs to be considered. I f the instrument reading changes negatively with
respect to the expected uncertainty, t0 , is smaller than t0 crit, i.e. the measurement is a ffected by the too
small base metal thickness.
Step 4
If t0 is smaller than t0 crit, place a third sample beneath the stack of Step 3, place the probe on top of this
stack and check the instrument reading. I f the instrument reading is still the same as in Step 3 with
respect to the uncertainty, the critical minimum base metal thickness lies within t0 < t0 crit < 2 t0 . If the
instrument reading shows a larger negative value than in Step 3, then two times of t0 is still smaller
than t0 crit. Continue to stack further samples in order to estimate t0 crit.
The instrument may be used without correction provided that the base metal thickness t0 is larger than
t0 crit . If t0 is smaller than t0 crit , a special calibration correction is required and it shall be considered
that possible base metal variations cause an increase o f the respective thickness uncertainty.
The experimentally determined critical minimum base metal thickness, t0 crit, can be used to estimate
the resulting uncertainty.
In order to improve the accuracy o f the estimation o f t0 crit, samples with smaller thickness than t0
should be used.

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ISO 2360:2017(E)

I f the instrument does not display negative values, it is recommended to use a thin foil (e.g. 10 µm)
between the probe and base metal to observe the decrease o f the thickness.
NOTE The procedure to stack several samples in order to simulate an increase o f the base metal thickness
allows a good estimation of t0 crit because the impact o f the air gap between the samples on the eddy-current
generation in the sample stack in comparison to the respective homogeneous material is almost negligible (eddy-
current flow is perpendicular to the probe axis). There fore, this simplified procedure can be carried out more
easily with good results instead o f producing base metals with variable thickness.

Figure D.2 — Schematic representation of the test for base metal thickness

D.4 Surface curvature

A simple test to assess the e ffect o f the influence o f the sample sur face curvature uses a clean uncoated
sample o f the base metal with di fferent curvature diameters (e.g. cylinder) and follows the procedure
described in Step 1 to Step 4 below. All used samples should provide the same material properties as
the base metal. The procedure is illustrated in Figure D.3 using the example of a convex curvature.
Step 1
Place the probe on an even sample (no curvature). It should be proven that the reading is not affected
by the edges o f the sample (see D.2 ) and that the base metal thickness o f the sample is larger than the
critical minimum base metal thickness (see D.3).
Step 2
Adjust the instrument to read zero.
Step 3
Place the probe on each sample starting with the largest available diameter and then continue the
test with decreasing sample diameters. Note the diameter where a change of the instrument reading
(positive increase) occurs with respect to the expected uncertainty or to the given thickness tolerance.
The instrument may be used without correction provided that the sample o f interest shows a larger
diameter than the noted one. If the diameter is smaller, an adjustment or special calibration correction
is required or the additional resulting uncertainty for the used distance can be considered. I f necessary,
refer to the manufacturer’s instructions.
In practical situations, the diameter o f the samples o f interest varies very o ften. In this situation, the
smallest and the largest diameter expected should be estimated and the instrument should be adjusted
on an uncoated sample close to the average diameter. As a result, the measured deviation for the
smallest and largest diameter can be estimated from the described procedure and used to estimate the
uncertainty. Take this uncertainty into account during the measurement.

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 ISO 2360:2017(E)

In order to improve the accuracy o f the estimation o f the curvature influence, increase the number o f
samples with different diameters.
NOTE The same procedure can be used in cases where the samples show a concave curvature, however, this
concave curvature results in negative thickness readings. I f the instrument does not display negative values, it
is recommended to use a thin foil (e.g. 10 µm) between the probe and base metal to observe the decrease of the
thickness.

Figure D.3 — Schematic representation of the test for curvature effect

D.5 Conductivity of the base metal

In practical situations, the conductivity o f the base metal varies very o ften. A simplified procedure
described in Step 1 to Step 5 below helps to reduce this influence and estimate the resulting uncertainty.
This procedure requires several uncoated, clean and even samples representing approximately the
expected variation of the base metal. The procedure is illustrated in Figure D.4.
Step 1
Place the probe on one o f the samples. It should be proven that the reading is not a ffected by the edges
of the sample (see D.2 ), that the base metal thickness of the sample is larger than the critical minimum
base metal thickness (see D.3) and that the sample is even (no curvature, see D.4).
Step 2
Adjust the instrument to read zero.
Step 3
Place the probe on each o f the samples and notice the reading. It is recommended to carry out repeated
measurements on each sample and to use the average value in the next steps.
Step 4
Calculate the average of the readings of all samples and select the sample with the smallest deviation
from this average.
Step 5
Use this selected sample as a re ference base metal to carry out the zero adjustment for all measurements.
The instrument may be used without correction provided that the deviation o f the sample with the
smallest reading (or with the largest reading) from the calculated average value is smaller than the
expected uncertainty or the given thickness tolerance.
If there are larger variations, the selected sample should be used as a reference base metal and the
estimated deviation o f the readings o f the described procedure can be used to estimate the uncertainty.
Take this uncertainty into account during the measurements.

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ISO 2360:2017(E)

Figure D.4 — Schematic representation of the test for base metal conductivity test

26 © ISO 2017 – All rights reserved

 ISO 2360:2017(E)

Annex E
(informative)
Table of the student factor

Table E.1 — Student factor

Number of Fraction p in percent
measurements
n 68,27 % 95,45 %
2 1,84 13,97
3 1,32 4,53
4 1,20 3,31
5 1,14 2,87
6 1,11 2,65
7 1,09 2,52
8 1,08 2,43
9 1,07 2,37
10 1,06 2,32
11 1,05 2,28
12 1,05 2,25
13 1,04 2,23
14 1,04 2,21
15 1,04 2,20
16 1,03 2,18
17 1,03 2,17
18 1,03 2,16
19 1,03 2,15
20 1,03 2,14
∞ 1,00 2,00

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ISO 2360:2017(E)

Annex F
(informative)
Example of uncertainty estimation (see Clause 8)

F.1 Sample details

The example sample to be measured is as follows:
— p ai nt/a lu m i nium ( p ar t o f a c ar b o dy) ;

— e xp e c te d th ickne s s: arou nd 2 5 µm;

— the b a s e me ta l i s no t acce s s ib le , b ut p o s s ib le th ickne s s va r i atio n s c au s e d b y the u s e d a lu m i n iu m

lo ts (co nduc ti vity va r i atio n s) h ave b e en de ter m i ne d b y a n e xp er i ment (s e e D.5): measurement of

u nco ate d a lu m i n iu m p a r ts fro m car b o dy p ro duc tio n rep re s enti ng the va r i ab i l i ty of used

a lu m i n iu m fro m d i fferent s up p l iers , p ro duc tio n lo ts e tc . , re s u l ti ng co mp le te th ickne s s va r i atio n

range at t = 25 µm : ∆t bm = ±1 , 2 µm
F.2 Steps

F.2.1 The examp le s amp le is meas ured by fo llo wing thes e s tep s .

a) Veri fy the prob e ca l ibration:

1) 10 repeated measurements with a reference foil of t r = 25 , 2 µm on base metal (including

zeroing on base metal)
2) The given tolerance of the reference foil: T = ± 0 , 5 µm .
3) The used base metal is a selected reference base metal (see D.5).
4) The result is ( n = 10 ): t = 24 , 06µm and s( t ) = 0 , 11µm .
5) E (see 8.2):
C a lc u late the u ncer tai nty and

i) T he s tandard u ncer tai nty o f the re ference foi l i s:

ur =
T 0 , 5 µm = 0 , 29 µm
=
3 3
i i) T he s tandard u ncer tai nty o f the veri fic ation me as u rement (on ly the s to chas tic comp onent

is considered) is:
u sto = t ( 68 , 27 %, n − 1 ) ×
s (t )
= 1 , 06 ×
0 , 11 µm = 0 , 04 µm
n 10
2 2
i i i) T he combi ne d uncer ta i nty i s u c = ( 0 , 04 µm ) + ( 0 , 29 µm ) = 0 , 29 µm
iv) T he e xp ande d u ncer ta i nty i s U cal ( k = 2 ) = 2 × u c = 0 , 58 µm
t − tr
v) The result is E = U =
1 , 14 µm
= 1 , 96
cal (k = 2) 0 , 58 µm

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 ISO 2 3 60: 2 01 7(E)

vi) Calibration is not correct. A significant deviation has been detected, because E = 1 , 96 > 1 ,
i.e. the difference between the measured value, t , and the given reference foil value,
t − t r , is larger than U cal ( k = 2 ) = 0 , 58 µm ; consequently the calibration accuracy can be

improved by means o f this re ference foil.

b) Adjust the instrument with the reference foil.
c) Veri fy the improved probe calibration.
1) 10 repeated measurements (repeat Step a)
2) Result ( n = 10 ): t = 24 , 87µm and s( t ) = 0 , 11µm
3) Calibration is correct, because E = 0 , 56 < 1 , i.e. the difference, t − tr , is smaller than
U cal ( k = 2 ) = 0 , 58µm , no significant deviation can be proven now.

d) Calculate the uncertainty o f the probe calibration (result o f Step c).

1) u c = ( 0 , 03 µm ) 2 + ( 0 , 29 µm ) 2 = 0 , 29 µm : u cal = 0 , 29 µm
e) Measure the sample.
1) Seven repeated measurements within the given measurement area of the sample.
2) Result ( n = 7 ): t = 22 , 8µm and s( t ) = 0 , 76µm
f ) Calculate all measurement uncertainty components and the combined uncertainty.

1) Stochastic uncertainty (see 8.3): u sto = t ( 68 , 27 %, n − 1 ) ×

()
s t 0 , 76 µm
= 1 , 09 × = 0 , 31 µm
n 7
2) Standard uncertainty caused by possible base metal deviation from calibration (expected
thickness variation range) (see 8.4): ∆t bm ( 25 µm ) = ± 1 , 2 µm : u bm = 0 , 69 µm
3) Combined uncertainty (see 8.5):
2 2 2 2 2 2
c = u cal + u sto + u bm = ( 0 , 29 µm ) + ( 0 , 31 µm ) + ( 0 , 69 µm ) = 0 , 81 µm
u

g) Calculate the expanded uncertainty and expression o f the result.

1) Expanded uncertainty (see 8.5): 2 ) = 2 × u c = 1 , 6 µm
(
U k=

2) Final result of the measurement: t = 23 µm ± 1 , 6µm

F.2 .2 All other possible factors affecting the measurement accuracy are considered to be negligible in
this example (edge e ffect, base metal thickness, curvature, temperature dri ft, etc.).

F.2 .3 Further conclusions: it is obvious that the resulting uncertainty is limited by the largest
uncertainty component, in this case, the possible base metal property variation (conductivity variation).
Therefore, an increase of the number of repeated measurements would reduce usto, however, the
combined uncertainty would not be strongly affected in this way.

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ISO 2360:2017(E)

Annex G
(informative)
Details on precision

G.1 General notes on the round-robin test

A round-robin test was carried out to determine the precision data using amplitude-sensitive eddy-
current method gauges for measuring the coating thickness.
Twelve laboratories participated in the round-robin test.
G.2 Samples
For the round-robin test, six different coatings on different aluminium-substrates were prepared (see
Table G.1).
To define the measurement, five measuring points were assigned on each sample.

Table G.1 — Samples

Sample Substrate Coating Coating Calibration
number thickness foil
approx. µm µm
P02 Aluminium Red car repair finish coating 80 125
P07 Aluminium Green electro deposition coating (ED) 20 25
P08 Aluminium ED coat + base coat + clear coat 120 125
P11 Aluminium Anodized coating 9 12
P12 Aluminium Blue anodized coating 17 25
P13 Aluminium Chromium deposit 17 25

G.3 Film thickness gauges

For the round-robin test, thickness gauges with di fferent types o f probes from di fferent manu facturers
were used.
G.4 Calibration
A two point calibration, respectively, adjustment o f the gauges was done (zero point and thickness o f
calibration foil).
Two di fferent calibration methods with certified plastic foils were executed. The measurements were
based on these calibrations:
— Reference method – R: calibration and adjustment with the foil on uncoated original samples
respectively back side o f the sample. This method is pre ferred (see 5.2) and additional uncertainties
are avoided;
— Standard method – S: calibration and adjustment with the foil on an uncoated aluminium standard
panel. Within this method, additional uncertainties caused by the deviations o f the sample’s base
metal from the uncoated standard panel are to be expected.
30 © ISO 2017 – All rights reserved
 ISO 2360:2017(E)

The thicknesses o f the calibration foils were: 12 µm, 25 µm and 125 µm.
Coating thickness measurements were done directly a fter every calibration and adjustment.

G.5 Number of measurements

For the calculation o f the repeatability limit, the measurements on the first marked point were carried
out in triplicate.
A fterwards, the other four marked points were measured.

G.6 Evaluation
G.6.1 General
The statistical evaluation was carried out following ISO 5725-2 and ISO/TR 22971.
Evaluation was carried out for each calibration method.
G.6.2 Evaluation o f first measuring point
The repeatability limit, rx1 , and the reproducibility limit, Rx
1 , were calculated from the first measuring
point measured in triplicate.
G.6.3 Evaluation o f all five measuring points
The repeatability limit, rx , and the reproducibility limit, R x , were calculated from all five measuring
points. For the first measuring point, the arithmetic mean from the triple measurements is used.
Table G.2 contains the results for repeatability limits and reproducibility limits calculated from the
first measuring point in comparison to the respective limits calculated from all five measuring points.

Table G.2 — Repeatability limit, r, and reproducibility limit, R

Calibration methods rx
1? Rx
1 rx Rx

µm µm µm µm
12-R 1,0 _a 1,5 _a
12-S 1,0 _a 1,5 _a
25-R 1,6 4,1 2,2 3,7
25-S 1,7 5,0 2,3 5,3
125-R 2,7 5,6 12,3 12,3
125-S 2,3 6,0 12,5 13,0
rx
1 and Rx
1 Repeatability limit and reproducibility limit o f first measuring point (triple measurement).
rx and R x Repeatability limit and reproducibility limit o f all five measuring points.
a No calculation of R x1 and R x reproducibility could be done in respect o f only one sample.

NOTE The greater result o f the repeatability limit, rx

1 , at 125-R compared to 125-S could have several
reasons.

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ISO 2360:2017(E)

Figure G.1 to Figure G.3 s how the res u lts o f th icknes s me a s urements b as e d on the th re e d i fferent

th ickne s s c a l ibration foi l s ,

where
R is the reference method, and
S is the standard method (see also G.4).

Key
SD-12-R
SD-12-S
Figure G.1 — Comparison of reference and standard method calibration with 12 µm foil

32 © ISO 2017 – All rights reserved

 ISO 2360:2017(E)

Key
SD-25-R
SD-25-S
Figure G.2 — Comparison of reference and standard method calibration with 25 µm foil

Key
SD-125-R
SD-125-S
Figure G.3 — Comparison of reference and standard method calibration with 125 µm foil

© ISO 2017 – All rights reserved 33

ISO 2360:2017(E)

Bibliography

[1] Non-magnetic coatings on magnetic substrates — Measurement of coating thickness —

I S O 2 178 ,

Magnetic method

[2 ] ISO 2 3 61 , Electrodeposited nickel coatings on magnetic and non-magnetic substrates —

Measurement of coating thickness — Magnetic method

[3 ] ISO 2808, Paints and varnishes — Determination o f film thickness

[4] I S O 57 2 5 -1 :19 9 4, Accuracy (trueness and precision) of measurement methods and results — Part 1:

General principles and definitions

[4] ISO 5725-2, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic
method for the determination ofrepeatability and reproducibility ofa standard measurement method

[5 ] I S O 2 19 6 8 , Non-magnetic metallic coatings on metallic and non-metallic basis materials —

Measurement of coating thickness — Phase-sensitive eddy-current method

[6] I S O/I E C Guide 9 9 : 2 0 0 7, International vocabulary of metrology — Basic and general concepts and
associated terms (VIM)

[7 ] Accuracy (trueness and precision) of measurement methods and results — Practical

I S O/ T R 2 2 9 71 ,

guidance for the use of ISO 5725-2:1994 in designing, implementing and statistically analysing
interlaboratory repeatability and reproducibility results

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ISO 2 3 60: 2 01 7(E)

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