ISO/TR 11462-4:2022

TECHNICAL ISO/TR
REPORT 11462-4
First edition
2022-02
Guidelines for implementation of
statistical process control (SPC) —
Part 4:
Reference data sets for measurement
process analysis software validation
Lignes directrices pour la mise en œuvre de la maîtrise statistique des
processus (MSP) —
Partie 4: Jeu de données pour la validation des logiciels d'analyse de
processus de mesure
Reference number
ISO/TR 11462-4:2022(E)
© ISO 2022

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ISO/TR 11462-4:2022(E)
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ISO/TR 11462-4:2022(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions, and symbols and abbreviated terms . 1
3.1 Terms and definitions . 1
3.2 Symbols and abbreviated terms . 2
3.3 Abbreviated terms . 4
4 Overview of the test examples . 4
4.1 Overview . 4
4.2 Notes . 5
4.2.1 Notes on the accuracy of the test examples and results . 5
4.2.2 Note on outlier detection . 5
4.2.3 Note on capability indices . 5
4.2.4 Note on the model of the measurement and correlations . 5
4.2.5 Note on other reference data sets . 5
4.2.6 Note on systematic errors . 6
5 Reference data sets description and evaluation . 6
5.1 Test data set 1 – example of linearity study with at least three standards . 6
5.1.1 Test data set 1 – information . 6
5.1.2 Test data set 1 – data, calculations and results. 6
5.2 Test data set 2 – attribute measurement process – operator influence (ISO 22514-7) .12
5.2.1 Test data set 2 – information .12
5.2.2 Test data set 2 – data, calculations and results.12
5.3 Test data set 3 – attributive measurements – capability calculations using
reference values – calculation of the uncertainty range (ISO 22514-7) .13
5.3.1 Test data set 3 – information . 13
5.3.2 Test data set 3 – data, calculations and results.13
5.4 Test data set 4 – measurement process capability with three reference standards
(VDA 5) . 16
5.4.1 Test data set 4 – information . 16
5.4.2 Test data set 4 – data, calculations and results. 16
5.5 Test data set 5 – Measurement Process Capability of a CMM (VDA 5 and ISO 15530-
3) . 19
5.5.1 Test data set 5 – information . 19
5.5.2 Test data set 5 – data, calculations and results. 20
5.6 Test data set 6 – measurement process capability of automated test device .23
5.6.1 Test data set 6 – information . 23
5.6.2 Test data set 6 – data, calculations and results.23
5.7 Test data set 7 – measurement process capability of a multiple-point measuring
Instrument (VDA 5) . 27
5.7.1 Test data set 7 – information . 27
5.7.2 Test data set 7 – data, calculations and results. 27
Bibliography .32
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ISO/TR 11462-4:2022(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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 4, Applications of statistical methods in product and process management.
A list of all parts in the ISO 11462 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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ISO/TR 11462-4:2022(E)
Introduction
The test examples were developed for the assessment of systems performing a measurement system
analysis (MSA). They allow MSA software developers to evaluate their systems. Thus, the end user of
those systems can be sure that the data sets are evaluated correctly with a high level of reliability.
In order to cover as wide a spectrum as possible, suitable data sets were prepared individually for
various constellations. The evaluation results of those data sets are documented and commented on
the following pages.
The results were verified multiple times using different computer programs. This turns the data sets
and the results into references for validation of the software. The data sets are listed in the related
clauses of this document or can be accessed via https://standards.iso.org/iso/tr/11462/-4/ed-1/en.
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TECHNICAL REPORT ISO/TR 11462-4:2022(E)
Guidelines for implementation of statistical process
control (SPC) —
Part 4:
Reference data sets for measurement process analysis
software validation
1 Scope
This document describes examples for software validation for software implementing the standards of
ISO 22514-7 on the capability of measurement processes. In detail, the following standards are covered:
— ISO 22514-7.
It provides data sets and test results for testing the implementation of the evaluation methods described
in these standards. This includes:
a) the calculation of standard uncertainties from other sources (other than experiments – type B –
ISO/IEC Guide 98-3);
b) the estimation of uncertainty components using repeated measurements on reference parts;
c) the estimation of uncertainty components using repeated measurements on multiple parts with
different operators and their evaluation using the ANOVA method;
d) the combination of uncertainty components using the Gaussian law of uncertainty propagation;
e) the calculation of measurement process capability indices;
f) the influence of operators on attributive measurements;
g) the uncertainty range and capability indices for attributive measurements.
The test examples are intended to cover the calculation of the measuring system capability and
measurement process capability according to ISO 22514-7.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 22514-2, Statistical methods in process management — Capability and performance — Part 2: Process
capability and performance of time-dependent process models
3 Terms and definitions, and symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 22514-2 apply.
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ISO/TR 11462-4:2022(E)
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.2 Symbols and abbreviated terms
Symbols used in this standard are identical to symbols used in ISO 22514-7.
a half width of a distribution of possible values of input quantity
a maximal form deviation
OBJ
α significance level
B bias
i
C capability index for attributive measurement
attr
C measurement process capability index
MP
C measuring system capability index
MS
d average interval
d interval from the last reference value, for which all operators have assessed the result as
LR
unsatisfied to the first reference value, for which all operators have the result as approved
d interval from the last reference value, for which all operators have assessed the result as
UR
approved to the first reference value, for which all operators have the result as unsatisfied
e residuals
nj
K number of repeatability measurements
k coverage factor
k coverage factor from the calibration certificate
CAL
L lower specification limit
l measured length
M the number of subgroups
M maximum permissible error (of the measuring system) (MPE-value)
PE
m frequencies in Bowker-test
ij
N number of standards
n sample size of each subgroup
Q attributive measurement process capability ratio
attr
Q measurement process capability ratio
MP
Q measuring system capability ratio
MS
Q capability ratio limit for measuring system
MS_max
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ISO/TR 11462-4:2022(E)
Q capability ratio limit for measurement process
MP_max
R resolution of measuring system
E
ˆ
σ
sample standard deviation
T temperature
U upper specification limit
U uncertainty on the calibration of standards
CAL
u standard uncertainty on the coefficient of expansion
α
u standard uncertainty from the operator´s repeatability
AV
u standard uncertainty from the measurement bias
BI
u calibration standard uncertainty on a standard
CAL
u standard uncertainty from maximum value of repeatability or resolution
EV
u standard uncertainty from repeatability on standards
EVR
u standard uncertainty from repeatability on test parts
EVO
u standard uncertainty from reproducibility of the measuring system
GV
u standard uncertainty from interactions
IAi
u standard uncertainty from linearity of the measuring system
LIN
u standard uncertainty calculated based on maximum permissible error
MPE
u combined standard uncertainty from other influence components not included in the analysis
MS-REST
of the measuring system
u standard uncertainty from test part inhomogeneity
OBJ
u standard uncertainty from resolution of measuring system
RE
u standard uncertainty from other influence components not included in the analysis of the
REST
measurement process
u standard uncertainty from the stability of measuring system
STAB
u standard uncertainty from temperature
T
u standard uncertainty from temperature expansion coefficients
TA
u standard uncertainty from temperature difference between workpiece and measuring system
TD
U expanded measurement uncertainty on an attributive measurement
attr
u combined standard uncertainty of attributive measuring
attr
U expanded measurement uncertainty of the measuring system
MS
u combined standard uncertainty on measuring system
MS
U expanded measurement uncertainty of the measurement process
MP
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ISO/TR 11462-4:2022(E)
u combined standard uncertainty on measurement process
MP
u standard uncertainty from effect of spindle clamping
MX
u standard uncertainty from resolution
RA
u standard uncertainty from repeatability
RE
th
x
i reference quantity value
i
x reference quantity value of the standard (master) at the upper specification limit
mU
x reference quantity value of the standard (master) in the centre of the specification
mm
x reference quantity value of the standard (master) at the lower specification limit
mL
x
arithmetic mean of the conventional true values
th
y
j measurement value
j
y
arithmetic mean of the measured values
3.3 Abbreviated terms
ANOVA analysis of variance
MSA measurement systems analysis
MPE maximum permissible error
4 Overview of the test examples
4.1 Overview
For an overview of the test examples see Table 1.
Table 1 — List of the test data sets
Test
Sub- Character- Decimal Source/ Refer-
data set Description of data set
clause istics type points ence
number
All uncertainty components mentioned in the
22514-7 are covered. Combination of type A ISO 22514-7
1 5.1 Variable 2
and type B evaluation, including Linearity + additions
and GRR studies
Test on influence of operators based on ex-
2 5.2 Attributive --- ISO 22514-7
perimental data
Calculation of uncertainty range and capabil-
3 5.3 Attributive --- (6) ity of the attributive measurement process ISO 22514-7
based on experimental data
Measurement process capability with three
reference standards
Linearity study, GRR with ANOVA
4 5.4 Variable 4 VDA 5
Multiple uncertainty components: resolu-
tion, calibration, repeatability, linearity, bias,
operators, part-interaction
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ISO/TR 11462-4:2022(E)
Table 1 (continued)
Test
Sub- Character- Decimal Source/ Refer-
data set Description of data set
clause istics type points ence
number
Measurement process capability of a CMM
Repeatability and bias with one standard
VDA 5 and
5 5.5 Variable 4
Multiple uncertainty components: resolu- ISO 15530-3
tion, calibration, repeatability, linearity, bias,
temperature
Measurement process capability of automat-
ed test device
Multiple measurements on one standards and
6 5.6 Variable 4 10 parts VDA 5
Multiple uncertainty components: resolu-
tion, calibration, repeatability, linearity, bias,
MPE(gauge)
Measurement process capability of a multi-
ple-point measuring instrument
GRR with ANOVA
7 5.7 Variable 4 Multiple uncertainty components: resolution, VDA 5
calibration, repeatability, linearity, bias, MPE
(sensor), reproducibility, part-interaction,
temperature, error of temperature compen-
sation
4.2 Notes
4.2.1 Notes on the accuracy of the test examples and results
Capability indices are always given with two digits (rounded).
4.2.2 Note on outlier detection
Each test data set was tested for outliers using Grubbs’ test for outliers (according to ISO 5725-2) with a
level of significance of 1 % and no outliers were detected.
4.2.3 Note on capability indices
There are various different capability indices given in the relevant different standards and guidelines.
All are based on the ratio of the specification interval and the measurement uncertainty. Only the
expansion factors and limit values vary. In this standard only the capability indices according to
ISO 22514-7 are used.
4.2.4 Note on the model of the measurement and correlations
Although ISO/IEC Guide 98-3 provides the possibility of including non-linear models and correlations
between input quantities, correlations and non-linearities are not covered by the ISO 22514-7.
Therefore, only a linear model with sensitivity coefficients of one for every input quantity as well as no
correlations are considered in this standard and its examples.
4.2.5 Note on other reference data sets
[1]
ISO/TR 12888 provides multiple examples especially for the case of GRR studies .
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ISO/TR 11462-4:2022(E)
4.2.6 Note on systematic errors
According to ISO/IEC Guide 98-3 any systematic error is compensated and the uncertainty of the
systematic error is included into the measurement budget and is part of the combined uncertainty.
5 Reference data sets description and evaluation
5.1 Test data set 1 – example of linearity study with at least three standards
5.1.1 Test data set 1 – information
Test data set for ISO 22514-7 capability of measurement processes with a linearity and ANOVA study.
This example has been taken from ISO 22514-7:2021, Annex A (the data originally come from ISO 11095).
The uncertainties arising from the object and the temperature were added.
5.1.2 Test data set 1 – data, calculations and results
5.1.2.1 Calculation of the measuring system capability
5.1.2.1.1 Components of type B which are not taken into account by experiments
Resolution
The uncertainty component caused by resolution is u =0,001 μ44 m .
RE
The uncertainty component u is much smaller than u , see behind Table 4. Therefore, the
RE EVR
component u is not used.
RE
Object
The maximum expected error due to the clamping of the part during the measurement is
a =0,001 5 μm .
OBJ
The uncertainty component is therefore:
a
OBJ
u = =0,000 μ866 m
OBJ
√3
Calibration
It is assumed according to the calibration certificate that the calibration uncertainty u is 0,005 μm.
CAL
5.1.2.1.2 Components of Type A which are derived from a linearity study with at least 3
standards
An experiment is carried out on an imaging system (an optical microscope with a measuring device).
The data listed in Table 2 are measured values and true values of intervals in the range of 0,5 μm to
12 μm.
Table 2 — Values from repeated measurements on reference materials
Values y from K = 4 repeatability measurements on N = 10 reference
nj
Conventional true values x of
n materials
the 10 reference materials
y y y y
n1 n2 n3 n4
6,19 6,31 6,27 6,31 6,28
9,17 9,27 9,21 9,34 9,23
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ISO/TR 11462-4:2022(E)
Table 2 (continued)
Values y from K = 4 repeatability measurements on N = 10 reference
nj
Conventional true values x of
n
materials
the 10 reference materials
y y y y
n1 n2 n3 n4
1,99 2,21 2,19 2,22 2,20
7,77 8,00 7,81 7,95 7,84
4,00 4,27 4,15 4,15 4,15
10,77 10,93 10,73 10,92 10,89
4,78 4,95 4,87 5,00 5,00
2,99 3,24 3,17 3,21 3,21
6,98 7,14 7,07 7,18 7,20
9,98 10,23 10,02 10,07 10,17
Data in Table 2 are plotted in Figure 1.
Key
X reference value (µm)
Y measured value (µm)
Figure 1 — Plot of measured and true values
5.1.2.1.3 Calculation of means and residuals
For each reference material the mean value y , the bias B and the residuals e to e are calculated.
n i,n n1 n4
See Table 3 for the calculated values.
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ISO/TR 11462-4:2022(E)
Table 3 — Calculation of means and residuals
Conventional true Residuals
Mean values
values x of the 10 B
i,n
n
y e e e e
reference materials n n1 n2 n3 n4
6,19 6,292 5 0,102 5 0,017 5 −0,022 5 0,017 5 −0,012 5
9,17 9,262 5 0,092 5 0,007 5 −0,052 5 0,077 5 −0,032 5
1,99 2,205 0 0,215 0 0,005 0 −0,015 0 0,015 0 −0,005 0
7,77 7,900 0 0,130 0 0,100 0 −0,090 0 0,050 0 −0,060 0
4,00 4,180 0 0,180 0 0,090 0 −0,030 0 −0,030 0 −0,030 0
10,77 10,867 5 0,097 5 0,062 5 −0,137 5 0,052 5 0,022 5
4,78 4,955 0 0,175 0 −0,005 0 −0,085 0 0,045 0 0,045 0
2,99 3,207 5 0,217 5 0,032 5 −0,037 5 0,002 5 0,002 5
6,98 7,147 5 0,167 5 −0,007 5 −0,077 5 0,032 5 0,052 5
9,98 10,122 5 0,142 5 0,107 5 −0,102 5 −0,052 5 0,047 5
Data in Table 3 are plotted in Figure 2.
Key
X value of reference part
Y bias
1 mean bias over all reference parts
2 uncertainty from linearity
individual error
mean bias of the reference part
Figure 2 — Plot of deviations and conventional true values
5.1.2.1.4 ANOVA table
Given values:
N = 10       Number of standards (Factor A)
K = 4        Number of repeatability measurements
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ISO/TR 11462-4:2022(E)
Calculated values:
B =0,152  Arithmetic mean of all biases.
i
The components are calculated by an ANOVA, see Table 4.
Table 4 — ANOVA table
Sum of Degrees of Mean Estimated Test sta- Critical
Estimator
squares freedom squares variance tistic value
Source
2
σ
SS ν MS S F F
0
Factor A 0,077 39 9 0,008 599 0,001 121 2,089 6 2,210 7 0,033 480 9
Residual error 0,123 45 30 0,004 115 0,004 115 0,064 148 3
Total 0,200 84 39 --
5.1.2.1.5 Estimation of uncertainty components
Estimated uncertainties from Table 4 and mean bias:
Bi
uncertainty due to bias                          u ==0,087 76
BI
3
ˆ
uncertainty due to linearity                      u ==σ 0,033 48
LINA
uncertainty due to repeatability on references    u ==σˆ 0,064 15
EVRRES
5.1.2.1.6 Determination of the combined and expanded uncertainty
The uncertainty components of the measuring system are listed in Table 5 where the standard
uncertainty of the measuring system is calculated as the Euclidian distance of the following components:
22 22
uu=+ uu++ u
MS CALEVR LINBI
Because u << u the standard uncertainty of the resolution u is excluded from the calculation of
RE EVR RE
u .
MS
Table 5 — Uncertainty budget of the measuring system
u
Uncertainty component Symbol Type Remark Rank
μm
Resolution of the measuring system B (0,001 44) 5
u << u
RE EVR
Calibration uncertainty u B 0,005 00 4
CAL
Repeatability on reference standard A 0,064 15 2
u
EVR
Uncertainty from linearity u A 0,033 48 3
LIN
Uncertainty from Bias A 0,087 76 1
u
BI
Measuring system 0,113 85
u
MS
The combined uncertainty of the measuring system: u =0,114 μm
MS
and the expanded uncertainty: U =0,228 μm .
MS
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ISO/TR 11462-4:2022(E)
5.1.2.2 Experimental determination of the measurement process uncertainty
In addition to the estimated uncertainty components from the measuring system found in Table 4, it
can be useful to determine some additional uncertainty components ( uu,, u ) from the
EVOAVIAi
measurement process by the evaluation of the results from this process under the real conditions. In
this example (estimation of uncertainty components from different operators, repeatability and
interaction between operators) the following data are collected, see Table 6.
Table 6 — ANOVA test data set in µm
Operator 1 Operator 2 Operator 3
Part
Measure- Measure- Measure- Measure- Measure- Measure- Measure- Measure- Measure-
no.
ment 1 ment 2 ment 3 ment 1 ment 2 ment 3 ment 1 ment 2 ment 3
1 8,120 8,435 8,480 8,200 8,290 8,245 8,525 8,435 8,345
2 7,445 6,815 7,490 7,300 7,120 7,075 7,535 7,355 7,085
3 9,965 10,010 9,560 9,660 9,340 9,250 9,830 9,695 9,515
4 6,140 5,960 6,365 6,095 6,185 6,185 6,140 6,140 6,050
5 5,690 5,600 5,780 5,080 5,340 5,440 5,780 5,735 5,555
6 2,855 2,450 2,585 2,315 2,585 2,315 2,630 2,360 2,585
7 10,685 10,595 10,775 10,450 10,840 11,050 10,865 11,000 11,180
8 6,725 6,275 6,545 6,240 6,120 6,300 6,590 6,500 6,725
9 4,970 5,105 5,510 5,015 5,285 5,150 5,060 5,195 5,105
10 9,875 10,100 9,875 10,080 9,800 9,970 10,190 9,785 9,965
From the measurements in Table 6 the following analysis of variance table can be calculated, see Table 7.
Table 7 — ANOVA table
Degrees of Sum of Mean Estimated Test sta- Critical
Uncertainty
freedom squares Square variance tistic value
Uncertainty
F
component
0


ν SS MS F
σ ²
u =+ σ ²
i
i i
α = 5 %
Operator 2 0,519 1 0,259 5 0,007 38 0,085 91 6,810 3,150
Part to part 9 526,877 5 58,541 9 6,500 43 n/a 1 536,234 2,040
Interaction be-
tween operator 18 0,685 9 0,038 1 0,002 05 0,045 29 1,193 1,778
and part
Reproducibility 60 1,917 3 0,032 0 0,031 95 0,178 76 --- ---
Since the interaction between operator and part is not significant (F < F ) pooling is used. Then a
0
modified variance table can be developed there, see Table 8
Table 8 — Modified ANOVA table
Degrees of Sum of Mean Estimated Test sta- Critical
Uncertainty
freedom squares Square variance tistic value
Uncertainty
c
...