Iso 27893 2011

INTERNATIONAL ISO
STANDARD 27893
First edition
2011-08-15
Vacuum technology — Vacuum

gauges — Evaluation of the uncertainties
of results of calibrations by direct
comparison with a reference gauge
Technique du vide — Manomètres à vide — Évaluation de l'incertitude
des résultats des étalonnages par comparaison directe avec un
manomètre de référence
iTeh STANDARD PREVIEW
(standards.iteh.ai)
ISO 27893:2011
https://standards.iteh.ai/catalog/standards/sist/76460e7d-01e2-4e77-b344-
1eb20cd70cf4/iso-27893-2011
Reference number
ISO 27893:2011(E)
© ISO 2011
ISO 27893:2011(E)

(standards.iteh.ai)
ISO 27893:2011
1eb20cd70cf4/iso-27893-2011
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ISO 27893:2011(E)
Contents Page
Foreword ............................................................................................................................................................ iv

1 Scope ...................................................................................................................................................... 1
2 Normative references ............................................................................................................................ 1
3 Terms and definitions ........................................................................................................................... 2
4 Symbols and abbreviated terms .......................................................................................................... 3
5 Basic concept and model ..................................................................................................................... 3
5.1 General ................................................................................................................................................... 3
5.2 Sum model ............................................................................................................................................. 4
5.3 Quotient model ...................................................................................................................................... 4
5.4 Combination of the two models ........................................................................................................... 5
6 Calculation of uncertainty in the sum model ..................................................................................... 5
6.1 Total uncertainty — Sum model .......................................................................................................... 5
6.2 Uncertainty contributions due to reference standard ....................................................................... 6
6.3 Uncertainty contributions due to unit under calibration ................................................................... 7
6.4 Uncertainty contributions due to calibration method or calibration conditions ............................ 8
6.5 iTeh STANDARD PREVIEW
Coverage factor ..................................................................................................................................... 8
7 Calculation of uncertainty in the quotient model ............................................................................... 9
(standards.iteh.ai)
7.1 Total uncertainty — Quotient model ................................................................................................... 9
7.2 Uncertainty contributions due to reference standard ....................................................................... 9
7.3 Uncertainty contributions due to the ISO unit
27893:2011
under calibration .......................................................... 10
7.4 https://standards.iteh.ai/catalog/standards/sist/76460e7d-01e2-4e77-b344-
Uncertainty contributions due to calibration method or calibration conditions .......................... 11
7.5 1eb20cd70cf4/iso-27893-2011
Coverage factor ................................................................................................................................... 12
8 Combination of the sum and quotient model for error of reading ................................................. 13
9 Reporting uncertainties ...................................................................................................................... 13
9.1 Uncertainty budget .............................................................................................................................. 13
9.2 Calibration certificate .......................................................................................................................... 14
Bibliography ...................................................................................................................................................... 15
© ISO 2011 – All rights reserved iii

ISO 27893:2011(E)
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 27893 was prepared by Technical Committee ISO/TC 112, Vacuum technology.
This first edition of ISO 27893 cancels and replaces the first edition of ISO/TS 27893:2009, which has been
technically revised.
(standards.iteh.ai)
ISO 27893:2011
1eb20cd70cf4/iso-27893-2011
iv © ISO 2011 – All rights reserved

INTERNATIONAL STANDARD ISO 27893:2011(E)
Vacuum technology — Vacuum gauges — Evaluation of the

uncertainties of results of calibrations by direct comparison
with a reference gauge
1 Scope
This International Standard gives guidelines for the determination and reporting of measurement uncertainties
arising during vacuum gauge calibration by direct comparison with a reference gauge carried out in
accordance with ISO/TS 3567.
This International Standard describes methods for uniform reporting of uncertainties in vacuum gauge
certificates. Uncertainties reported in accordance with the guidelines given in this International Standard are
transferable in the sense that the uncertainty evaluated for one result can be used as a component in the
uncertainty evaluation of another measurement or calibration in which the first result is used.
This International Standard defines two measurement models that are sufficient to cover most practical cases.
However, it is possible that the models given cannot be applied to newly developed vacuum gauges.
(standards.iteh.ai)
The final uncertainty to be reported in a certificate is evaluated from the uncertainties of the input quantities
and influence quantities. The principal quantities that can affect the result of a vacuum calibration are
described; however, a complete list of the possible quantities that can have an influence on the final result lies
ISO 27893:2011
outside the scope of https://standards.iteh.ai/catalog/standards/sist/76460e7d-01e2-4e77-b344-
this International Standard.
1eb20cd70cf4/iso-27893-2011
NOTE It is envisaged that future Technical Specifications will address the calibration of specific types of vacuum
gauges.
2 Normative references
The following referenced documents are indispensable for the application 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/TS 3567, Vacuum gauges — Calibration by direct comparison with a reference gauge
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
© ISO 2011 – All rights reserved 1

ISO 27893:2011(E)
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO/TS 3567, ISO/IEC Guide 98-3,
ISO/IEC Guide 99 and the following apply.
3.1
corrected reading
value resulting after the reading of the gauge has been corrected for systematic errors
EXAMPLE For the results given in the calibration certificate of the reference standard.
3.2
long-term instability
possible change of calibrated value after long periods of time
EXAMPLE Change resulting from transportation of the device.
NOTE Long-term instability is different from reproducibility as defined in ISO/IEC Guide 99:2007, 3.7.
3.3
model
uncertainty of measurementmathematical model set out in ISO/IEC Guide 98-3
3.4
offset
measuring instruments zero error
datum measurement error where the specified measured quantity value is zero
NOTE
(standards.iteh.ai)
Adapted from ISO/IEC Guide 99:2007, 4.28.
ISO 27893:2011
EXAMPLE The reading when there is no pressure (absolute or differential) or a pressure far below the resolution
limit applied to a vacuum gauge.
1eb20cd70cf4/iso-27893-2011
3.5
deviation of offset
Possible difference of an offset (3.4) value between the time of the measurement of the offset (3.4) and the
time when a pressure reading is taken
3.6
reference standard
reference gauge
standard, generally having the highest metrological quality available at a given location or in a given
organization, from which measurements made there are derived
NOTE Adapted from ISO/IEC Guide 99:2007, 6.6.
EXAMPLE The gauge or standard that gives traceability to the SI unit in the calibration apparatus in accordance with
ISO/TS 3567.
3.7
calibration pressure
vacuum gauges pressure evaluated from the corrected reading (3.1) of the reference standard (3.6) and
all necessary corrections at the gauge port of the unit under calibration
EXAMPLE Necessary corrections might be for known differences between gauge ports.
2 © ISO 2011 – All rights reserved

ISO 27893:2011(E)
4 Symbols and abbreviated terms
Symbol or Designation Unit

abbreviated term
UUC unit under calibration (vacuum gauge) —
e error of reading in relative units
k coverage factor to expand standard uncertainty, u 1
pUUC pressure indication of a UUC corrected for known deviations Pa 1)
pind,UUC pressure indication of a UUC not corrected for any deviation Pa
pstd pressure indication of reference gauge (reference standard) Pa

corrected for known deviations
pind,std pressure indication of reference gauge (reference standard) not Pa

corrected for any deviation
rUUC quantity determined by a calibration in the quotient model any unit
rstd the quantity that was determined for the reference standard any unit
S sensitivity of the output of a vacuum gauge any unit
u
standard uncertainty any unit
U
(standards.iteh.ai)
expanded uncertainty any unit
xUUC indication of a UUC

ISO 27893:2011 any unit
xstd indication of a 1eb20cd70cf4/iso-27893-2011
reference gauge any unit
xi (often unknown) input quantities and corrections of gauge any unit
Xi (often unknown) input quantities and corrections of calibration any unit

method or condition
p error of reading in absolute units Pa
pi deviations in the pressure unit (often unknown) Pa
xi (often unknown) deviations in the x any unit
eff effective accommodation coefficient of a spinning rotor gauge 1
5 Basic concept and model
5.1 General
In a vacuum gauge calibration carried out in accordance with ISO/TS 3567, the corrected reading of a
reference gauge gives the value of the quantity that is traceable to the SI. All vacuum gauges shall be
calibrated in terms of pressure. This means that the user of the vacuum gauge calibrated in accordance with
ISO/TS 3567 and this International Standard obtains a clear assignment of the output quantity of the gauge to
the SI unit of pressure, the pascal.
1) 1 Pa = 0,01 mbar.

ISO 27893:2011(E)
The value of pressure obtained from the corrected reading of the reference standard output can be used to
determine the pressure at the entrance port of the unit under calibration (UUC). This is referred to as
calibration pressure value. Often the corrected reading of the reference standard is identical to the calibration
pressure value and valid for all gauge ports.
The calibration pressure value can be used to determine an error of the reading, p, of the unit under
calibration. In this case, a sum model gives an adequate description of the measurement.
The calibration pressure value can also be used to determine a correction factor, a sensitivity coefficient, an
effective accommodation coefficient or a gauge constant, in which case a quotient model gives an adequate
description of the measurement.
In both models it can be assumed that all the input quantities are uncorrelated.
5.2 Sum model
In the sum model, the difference between the reading of the UUC, pind, and the “true” calibration pressure
traceable to the SI units is taken as the measurand, p. The calibration pressure is given by the reference
standard pressure value, pstd, and possibly by a correction term, pm, due to the calibration method
considering known effects like height correction, thermal transpiration, and pressure non-uniformity. The
general sum model thus becomes
p  pUUC   p std   pm  (1)
The first term refers to the UUC, the second to the reference standard, and the third to the calibration method.
The sum of the last two terms gives the calibration pressure value. All quantities shall be expressed in the SI
unit of pressure, the pascal. (standards.iteh.ai)
Each of these terms is again expressed by another model equation, which makes all necessary corrections
due to offsets, temperature corrections, deviation ISO 27893:2011 from the SI value in accordance with the
of indication
calibration certificate, etc. https://standards.iteh.ai/catalog/standards/sist/76460e7d-01e2-4e77-b344-
1eb20cd70cf4/iso-27893-2011
5.3 Quotient model
In the quotient model, the ratio of the reading of the UUC, xUUC, and the standard pressure value, pstd, is
taken as the measurand, rUUC. The general quotient model thus becomes
xUUC
rUUC 
p std  Xi (2)
i
The numerator refers to the UUC, the denominator to the reference standard, and the product to the
calibration method and conditions. The latter can also be defined by the vacuum gauges under study, e.g. the
emission current in a hot cathode ionization gauge. It is possible to express xind in any reasonable unit, e.g.
that of pressure, voltage or current. The Xi can be expressed in any meaningful physical unit or can be without
dimension.
Each of these factors is expressed by another model equation, which makes all necessary corrections due to
offsets, temperature corrections, deviation of indication in accordance with calibration certificate, etc.
Examples of rUUC are
a) f c1 the reciprocal of a dimensionless correction factor, where xUUC  pUUC and Xi  1;
b) S a sensitivity of the analogue output, VUUC, of a capacitance diaphragm gauge, where xUUC  VUUC;
c) S a sensitivity of the analogue output, VUUC, of a thermal conductivity gauge, where xUUC  VUUC;

ISO 27893:2011(E)
d) eff the effective accommodation coefficient of a spinning rotor gauge, where xUUC  pUUC, when
eff  1 was entered into the controller;
e) S a sensitivity of a Bayard-Alpert gauge with a hot cathode, where xUUC  IUUC is the positive ion
current of the collector and X1  1/Ie, where Ie is the emission current.
5.4 Combination of the two models
It is possible to evaluate some of the input quantities in each model by either of the two models. First, for
example, pstd as well as its uncertainty can be evaluated by the quotient model, thus
x
p std  std (3)
rstd
The result can then be used in Equation (1). This is unavoidable if rstd is given in the certificate applying
Equation (2) (e.g. the sensitivity of an analogue output), where rUUC is replaced by rstd.
It is, however, not recommended to combine the sum and quotient model in one equation. This task should be
left to experts, since complicated sensitivity coefficients might appear that are not covered in this International
Standard for reasons of clarity. The relative error of reading, e, however, is a common case, where an easy to
handle combination of the two methods is possible.
The error of reading, e, can be expressed mathematically as
pUUC   p std  p m 
iTeh STANDARD
p UUC PREVIEW
e  1 (4a)
 p std  p m  p  p
(standards.iteh.ai)
std m
or, if pm  0
ISO 27893:2011
p  p std p
e  UUC  UUC  1 1eb20cd70cf4/iso-27893-2011 (4b)
p std p std
See Clause 4 for the designations of pUUC, pstd, and pm. The uncertainty of e is described in Clause 8.
6 Calculation of uncertainty in the sum model
6.1 Total uncertainty — Sum model
The total uncertainty in the sum model, u(p), is given by
u( p )  u( pUUC ) 2  u( p std ) 2  u( pm ) 2 (5)
where
u(pUUC) is the standard uncertainty of the corrected indication of vacuum gauge UUC;
u(pstd) is the standard uncertainty of the value of standard pressure;
u(pm) is the standard uncertainty of the deviations due to the calibration method.

ISO 27893:2011(E)
6.2 Uncertainty contributions due to reference standard
The measurement of the standard pressure, pstd, is given by
p std  pind,std  p offs,std   p drft,std   p cal,std   p t,std   pT ,std   p els,std (6)
where
pind,std is the indication of the reference standard;
poffs,std is the offset (zero deviation) of the reference standard;
pdrft,std is the deviation of offset due to drift (in most cases, pdrft,std  0);
pcal,std is the correction in accordance with the calibration certificate;
pt,std is the deviation due to long-term instability (in most cases, pt,std  0);
pT,std is the deviation due to temperature at the calibration laboratory;
pels,std is the deviation due to other influences, e.g. inclination of device (in most cases, pels,std  0).
All quantities in Equation (6) refer to the reference standard gauge.
NOTE If the offset is deducted or adjusted to zero in the device itself, poffs,std  0.

The standard uncertainty of the standard pressure, u(pstd), is then given by
(standards.iteh.ai)
             
2 2 2 2 2 2 2
u  p std   u pind,std  u p offs,std  u p drft,std  u  p cal,std  u  p t,std  u pT ,std  u  p els,std (7)
ISO 27893:2011
where
1eb20cd70cf4/iso-27893-2011
u(pind,std) is the uncertainty originating from the dispersion of measurement values, including
dispersion due to digitizing, resolution scatter, etc.;
u(poffs,std) is the uncertainty of the offset values at measurement of the offset [without reproducibility of
the offset covered by u(pdrft,std)];
u(pdrft,std) is the uncertainty of the offset values at time of calibration due to offset drift or other
systematic dependencies, e.g. due to the frequency dependence of spinning rotor gauges;
u(pcal,std) is the uncertainty of the standard in accordance with the calibration certificate;
u(pt,std) is the uncertainty component allowing for the long-term instability;
u(pT,std) is the uncertainty component due to the temperature influence under the conditions of the
calibration laboratory;
u(pels,std) is the uncertainty due to the specific conditions at the calibration laboratory, e.g. different
mounting position of built-in devices.
For a pind,std that has not been obtained from repeated observations, estimate u(pind,std) from scientific
judgement based on all of the available information on the possible variability (including uncertainty
component due to digitizing, repeatability, etc.).
For a temperature at calibration different from that shown in the calibration certificate, u(pT,std) should be
included, if significant.

ISO 27893:2011(E)
6.3 Uncertainty contributions due to unit under calibration
The measurement of the pressure of the UUC, pUUC, is given by
pUUC  pind,UUC  p offs,UUC   p drft,UUC   p els,UUC (8)
where
pind,UUC is the indication of the UUC;
poffs,UUC is the offset (zero point deviation) of the UUC;
pdrft,UUC is the deviation of offset drift (in most cases, pdrft,UUC  0);
pels,UUC represents the deviations due to other influences, e.g. inclination (in most cases,
pres,UUC  0).
The standard uncertainty of the measurement of the pressure with UUC, u(pUUC), is then given by
       
2 2 2 2
u  pUUC   u p ind,UUC  u p offs,UUC  u  p drft,UUC  u  p els,UUC (9)
where
u(pind,UUC) is the uncertainty originating from the dispersion of measurement values of UUC, including
(standards.iteh.ai)
dispersion due to digitizing, resolution scatter, etc.;
u(poffs,UUC) is the uncertainty of the offset values of the UUC at measurement of the offset (without
ISO 27893:2011
reproducibility of the offset covered by the following quantity);
1eb20cd70cf4/iso-27893-2011
u(pdrft,UUC) is the uncertainty of the offset values of the UUC due to offset drift or other systematic
dependencies, e.g. due to speed dependence in the case of spinning rotor gauges;
u(pels,UUC) represents the other uncertainty components, which can also stem from the calibration item,
e.g. temperature influences.
For a pind,UUC that has not been obtained from repeated observations, estimate u(pind,UUC) from scientific
judgement based on all of the available information on the possible variability (including uncertainty
component due to digitizing, repeatability, etc.).
If the above-mentioned dependencies or values are not known, or cannot be estimated by the calibration
laboratory, or manufacturer's specifications are not available, carry out at least two repeat measurements on
different days. The uncertainty component of the values of the calibration item, u(pind,UUC), is then determined
from
u(pind,UUC)  u(prep,UUC) (10)
where u(prep,UUC) is the repeatability (standard deviation) of the (at least) three measurement values
determined for one pressure point or over a larger range.

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INTERNATIONAL ISO

Vacuum technology — Vacuum

iTeh STANDARD PREVIEW

COPYRIGHT PROTECTED DOCUMENT

ii © ISO 2011 – All rights reserved

Foreword ............................................................................................................................................................ iv

© ISO 2011 – All rights reserved iii

iv © ISO 2011 – All rights reserved

Vacuum technology — Vacuum gauges — Evaluation of the

© ISO 2011 – All rights reserved 1

3 Terms and definitions

EXAMPLE Change resulting from transportation of the device.

NOTE Adapted from ISO/IEC Guide 99:2007, 6.6.

2 © ISO 2011 – All rights reserved

4 Symbols and abbreviated terms

Symbol or Designation Unit

UUC unit under calibration (vacuum gauge) —

e error of reading in relative units

k coverage factor to expand standard uncertainty, u 1

pUUC pressure indication of a UUC corrected for known deviations Pa 1)

pind,UUC pressure indication of a UUC not corrected for any deviation Pa

pstd pressure indication of reference gauge (reference standard) Pa

pind,std pressure indication of reference gauge (reference standard) not Pa

rUUC quantity determined by a calibration in the quotient model any unit

S sensitivity of the output of a vacuum gauge any unit

xUUC indication of a UUC

xi (often unknown) input quantities and corrections of gauge any unit

Xi (often unknown) input quantities and corrections of calibration any unit

p error of reading in absolute units Pa

pi deviations in the pressure unit (often unknown) Pa

xi (often unknown) deviations in the x any unit

eff effective accommodation coefficient of a spinning rotor gauge 1

5 Basic concept and model

© ISO 2011 – All rights reserved 3

5.2 Sum model

p  pUUC   p std   pm  (1)

Examples of rUUC are

4 © ISO 2011 – All rights reserved

5.4 Combination of the two models

The error of reading, e, can be expressed mathematically as

6 Calculation of uncertainty in the sum model

6.1 Total uncertainty — Sum model

The total uncertainty in the sum model, u(p), is given by

u( p )  u( pUUC ) 2  u( p std ) 2  u( pm ) 2 (5)

u(pstd) is the standard uncertainty of the value of standard pressure;

© ISO 2011 – All rights reserved 5

6.2 Uncertainty contributions due to reference standard

The measurement of the standard pressure, pstd, is given by

p std  pind,std  p offs,std   p drft,std   p cal,std   p t,std   pT ,std   p els,std (6)

pind,std is the indication of the reference standard;

poffs,std is the offset (zero deviation) of the reference standard;

pcal,std is the correction in accordance with the calibration certificate;

pT,std is the deviation due to temperature at the calibration laboratory;

All quantities in Equation (6) refer to the reference standard gauge.

iTeh STANDARD PREVIEW

u(pt,std) is the uncertainty component allowing for the long-term instability;

6 © ISO 2011 – All rights reserved

6.3 Uncertainty contributions due to unit under calibration

The measurement of the pressure of the UUC, pUUC, is given by