# ISO/TR 11462-4:2022

(Main)## Guidelines for implementation of statistical process control (SPC) — Part 4: Reference data sets for measurement process analysis software validation

## Guidelines for implementation of statistical process control (SPC) — Part 4: Reference data sets for measurement process analysis software validation

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/IECGuide 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.

## 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

### General Information

### Standards Content (Sample)

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 2022

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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

**...**

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