ISO/TS 27893:2009

TECHNICAL ISO/TS
SPECIFICATION 27893
First edition
2009-02-01

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




Reference number
ISO/TS 27893:2009(E)
©
ISO 2009

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ISO/TS 27893:2009(E)
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ISO/TS 27893:2009(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 Sum model .4
5.2 Quotient model .4
5.3 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 Coverage factor .8
7 Calculation of uncertainty in the quotient model.9
7.1 Total uncertainty (quotient model) .9
7.2 Uncertainty contributions due to reference standard .9
7.3 Uncertainty contributions due to the unit under calibration .10
7.4 Uncertainty contributions due to calibration method or calibration conditions .11
7.5 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

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ISO/TS 27893:2009(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.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of document:
— an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
— an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
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/TS 27893 was prepared by Technical Committee ISO/TC 112, Vacuum technology.

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TECHNICAL SPECIFICATION ISO/TS 27893:2009(E)

Vacuum technology — Vacuum gauges — Evaluation of the
uncertainties of results of calibrations by direct comparison
with a reference gauge
1 Scope
This Technical Specification gives guidelines for the determination and reporting of measurement
uncertainties arising during vacuum gauge calibration by direct comparison with a reference gauge in
accordance with ISO/TS 3567. It describes methods for uniform reporting of uncertainties in vacuum gauge
certificates. Uncertainties reported in accordance with this Technical Specification 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 specification 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.
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 may affect the result of a vacuum calibration are
described; however, a complete list of the possible quantities that may have an influence on the final result
lies outside the scope of this Technical Specification.
NOTE It is intended to give such details in Technical Specifications for 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 98-3:2008, 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)
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ISO/TS 27893:2009(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 (e.g. 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 that has resulted 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
zero error (of a measuring instrument)
datum measurement error where the specified measured quantity value is zero
NOTE Adapted from ISO/IEC Guide 99:2007, 4.28.
EXAMPLE The reading when there is no pressure (absolute or differential) or a pressure far below the resolution
limit applied to a vacuum gauge.
3.5
deviation of offset
The possible difference of an offset (3.4) value at the time of the measurement of the offset (3.4) and the
time when a pressure reading is taken
3.6
reference gauge
reference standard
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 of the reference standard and all necessary
corrections (e.g. for known differences between gauge ports) at the gauge port of the unit under calibration
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ISO/TS 27893:2009(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
1)
p pressure indication of a UUC Pa
ind
p pressure indication of reference gauge (reference standard) Pa
std
corrected for known deviations
r the quantity determined by a calibration in the quotient model
S a sensitivity of the output of a vacuum gauge
x indication of a UUC any unit
ind
X (often unknown) input quantities and corrections
i
∆p error of reading in absolute units
δp (often unknown) deviations in the pressure unit Pa
i
σ the effective accommodation coefficient of a spinning rotor gauge
eff
5 Basic concept and model
In a vacuum gauge calibration 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
Technical Specification obtains a clear assignment of the output quantity of the gauge to the SI unit of
pressure, the pascal.
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.

1) 1 Pa = 0,01 mbar.
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ISO/TS 27893:2009(E)
5.1 Sum model
In the sum model, the difference between the reading of the UUC, p , and the “true” calibration pressure
ind
traceable to the SI units is taken as the measurand, ∆p. The calibration pressure is given by the reference
standard pressure value, p , and possibly by a correction term, δp , due to the calibration method
std m
considering known effects like height correction, thermal transpiration, and pressure non-uniformity. The
general sum model thus becomes
∆=ppp− +δp (1)
()
ind std m
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.
Each of these terms is again expressed by another model equation, which makes all necessary corrections
due to offsets, temperature corrections, deviation of indication from the SI value in accordance with the
calibration certificate, etc.
5.2 Quotient model
In the quotient model, the ratio of the reading of the UUC, x , and the standard pressure value, p , is taken
ind std
as the measurand, r. The general quotient model thus becomes
x
ind
rX= (2)
∏ i
p
std
i
The numerator refers to the UUC, the denominator to the reference standard, and the product to the
calibration method and conditions. The latter may be 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 x in any reasonable unit,
ind
e.g. that of pressure, voltage or current. The X may be expressed in any meaningful physical unit or be
i
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 r are
−1
a) f the reciprocal of a dimensionless correction factor, where x = p and X = 1;
c
ind ind i
b) S a sensitivity of the analogue output, V , of a capacitance diaphragm gauge, where x = V ;
ind ind ind
c) S a sensitivity of the analogue output, V , of a thermal conductivity gauge, where x = V ;
ind ind ind
d) σ the effective accommodation coefficient of a spinning rotor gauge, where x = p , when σ = 1
eff ind ind eff
was entered into the controller;
e) S a sensitivity of a Bayard-Alpert gauge with a hot cathode, where x = I is the positive ion current
ind ind
of the collector and X = 1/I , where I is the emission current.
1 e e
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ISO/TS 27893:2009(E)
5.3 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, p as well as its uncertainty can be evaluated by the quotient model, thus
std
x
ind
p = (3)
std
r
The result can then be used in Equation (1). This is unavoidable, if r is given in the certificate applying
Equation (2) (e.g. the sensitivity of an analogue output).
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 may appear that are not covered in this Technical
Specification 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
ppp−+δ
()
ind std m
e =
pp+δ
()
std m
(4a)
p
ind
=−1
pp+δ
std m
or, if δp = 0
m
pp−
ind std
e =
p
std
(4b)
p
ind
=−1
p
std
See Clause 4 for the designations of p , p , and δp . The uncertainty of e is described in Clause 8.
ind std m
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
22 2
up(∆=) u(p ) +u()p +u()δp (5)
ind std m
where
u(p ) is the standard uncertainty of the indication of vacuum gauge UUC;
ind
u(p ) is the standard uncertainty of the value of standard pressure;
std
u(δp ) is the standard uncertainty of the deviations due to the calibration method.
m
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ISO/TS 27893:2009(E)
6.2 Uncertainty contributions due to reference standard
The measurement of the standard pressure, p , is given by
std
pp= −p +δp +δp +δp +δp +δp (6)
std ind,std offs,std drft,std cal,std tT,std ,std res,std
where
p is the indication of the reference standard;
ind,std
p is the offset (zero deviation) of the reference standard;
offs,std
δp is the deviation of offset due to drift (in most cases, δp = 0);
drft,std drft,std
δp is the correction in accordance with the calibration certificate;
cal,std
δp is the deviation due to long-term instability (in most cases, δp = 0);
t,std t,std
δp is the deviation due to temperature at the calibration laboratory;
T,std
δp is the deviation due to other influences (e.g. inclination of device) (in most cases,
res,std
δp = 0).
res,std
All quantities in Equation (6) refer to the r
...