# ISO/TR 11462-3:2020

(Main)## Guidelines for implementation of statistical process control (SPC) — Part 3: Reference data sets for SPC software validation

## Guidelines for implementation of statistical process control (SPC) — Part 3: Reference data sets for SPC software validation

This document describes examples for software validation for SPC software implementing the standards of the ISO 7870 series on control charts and the ISO 22514 series on capability and performance. In detail ISO 7870‑2, ISO 22514‑2 and ISO 22514‑8 are covered. It provides data sets and test results for testing the implementation of the evaluation methods described in these standards. This includes the detection of out of control situations as well as the calculation of sample statistics and process capability indices. The test examples cover the following situations: a) General: — different sample and subgroup sizes, accuracy of calculation for large/small numbers; b) ISO 22514 series: — calculation of sample statistics for location and dispersion; — different distribution models; c) ISO 7870‑2: — calculation of control limits; — visualization of data (histogram, control charts); — detection of out of control situations.

## Lignes directrices pour la mise en œuvre de la maîtrise statistique des processus (MSP) — Partie 3: Jeux de données de référence pour la validation de logiciels pour MSP

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TECHNICAL ISO/TR

REPORT 11462-3

First edition

2020-06

Guidelines for implementation of

statistical process control (SPC) —

Part 3:

Reference data sets for SPC software

validation

Lignes directrices pour la mise en œuvre de la maîtrise statistique des

processus (MSP) —

Partie 3: Jeux de données de référence pour la validation de logiciels

pour MSP

Reference number

ISO/TR 11462-3:2020(E)

©

ISO 2020

---------------------- Page: 1 ----------------------

ISO/TR 11462-3:2020(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2020

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.

ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

ii © ISO 2020 – All rights reserved

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ISO/TR 11462-3:2020(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

4 Overview of the test examples . 3

5 Reference data sets description and evaluation . 4

5.1 Test data set 1 . 4

5.1.1 Test data set 1 information . 4

5.1.2 Test data set 1 results . 6

5.2 Test data set 2 .13

5.2.1 Test data set 2 information .13

5.2.2 Test data set 2 results .14

5.3 Test data set 3 .21

5.3.1 Test data set 3 information .21

5.3.2 Test data set 3 results .23

5.4 Test data set 4 .32

5.4.1 Test data set 4 information .32

5.4.2 Test data set 4 results .34

5.5 Test data set 5 .43

5.5.1 Test data set 5 information .43

5.5.2 Test data set 5 results .45

5.6 Test data set 6 .53

5.6.1 Test data set 6 information .53

5.6.2 Test data set 6 results .55

5.7 Test data set 7 .63

5.7.1 Test data set 7 information .63

5.7.2 Test data set 7 results .65

5.8 Test data set 8 .73

5.8.1 Test data set 8 information .73

5.8.2 Test data set 8 results .75

5.9 Test data set 9 .82

5.9.1 Test data set 9 information .82

5.9.2 Test data set 9 results .85

5.10 Test data set 10 .92

5.10.1 Test data set 10 information .92

5.10.2 Test data set 10 results .95

5.11 Test data set 11 .102

5.11.1 Test data set 11 information .102

5.11.2 Test data set 11 results .103

Annex A (informative) Test data values .105

Bibliography .129

© ISO 2020 – All rights reserved iii

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ISO/TR 11462-3:2020(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 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.

iv © ISO 2020 – All rights reserved

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ISO/TR 11462-3:2020(E)

Introduction

The test examples given in this document were developed for the assessment of statistical process

control (SPC) systems. They allow SPC 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 the widest possible spectrum, 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 Annex A. An

electronic version is available at https:// standards .iso .org/ iso/ tr/ 11462/ -3/ ed -1/ en/ .

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TECHNICAL REPORT ISO/TR 11462-3:2020(E)

Guidelines for implementation of statistical process

control (SPC) —

Part 3:

Reference data sets for SPC software validation

1 Scope

This document describes examples for software validation for SPC software implementing the standards

of the ISO 7870 series on control charts and the ISO 22514 series on capability and performance. In

detail ISO 7870-2, ISO 22514-2 and ISO 22514-8 are covered.

It provides data sets and test results for testing the implementation of the evaluation methods described

in these standards. This includes the detection of out of control situations as well as the calculation of

sample statistics and process capability indices.

The test examples cover the following situations:

a) General:

— different sample and subgroup sizes, accuracy of calculation for large/small numbers;

b) ISO 22514 series:

— calculation of sample statistics for location and dispersion;

— different distribution models;

c) ISO 7870-2:

— calculation of control limits;

— visualization of data (histogram, control charts);

— detection of out of control situations.

2 Normative references

There are no normative references in this document.

3 Terms and definitions, and symbols and abbreviated terms

3.1 Terms and definitions

No terms and definitions are listed in this document.

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 http:// www .electropedia .org/

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ISO/TR 11462-3:2020(E)

3.2 Symbols and abbreviated terms

Symbols used in this document are identical to the symbols used in ISO 22514-2 and ISO 7870-2:

C process capability index

p

C minimum process capability index

pk

C upper process capability index

pkU

C lower process capability index

pkL

U upper control limit

CL

L lower control limit

CL

m number of subgroups

n sample size of each subgroup

P machine performance index

m

P minimum machine performance index

mk

P upper machine performance index

mkU

P lower machine performance index

mkL

P process performance index

p

P minimum process performance index

pk

P upper process performance index

pkU

P lower process performance index

pkL

T Centreline (target value) for the respective characteristic in the control charts

U upper specification limit

L lower specification limit

U upper specification limit, transformed values

tr

L lower specification limit, transformed values

tr

Abbreviated terms:

SPC statistical process control

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ISO/TR 11462-3:2020(E)

4 Overview of the test examples

See Table 1 for an overview of the test examples.

Table 1 — Overview of test examples

Test data Distri- Resulting Total Subgroup

Decimal

set Subclause bution distribu- sample sample Description of data set

points

number model tion size size

Data follows a normal distribu-

1 5.1 A1 normal 4 125 5

tion with no outliers

Correct calculations for a

2 5.2 A2 Weibull 3 600 3 sample following a Weibull

distribution

Normal distribution with time

3 5.3 B non-normal 2 1 000 5

dependent shift of mean

Location: random normally dis-

4 5.4 C1 normal 2 1 000 5

tributed; dispersion: constant

Location: random non-nor-

mally distributed; dispersion:

5 5.5 C2 non-normal 2 1 000 5

constant; resulting distribu-

tion: non-normal

Capability indices for trend

6 5.6 C3 non-normal 2 600 6

production (tool wear)

Capability indices for fix tool-

7 5.7 C4 non-normal 2 500 5

ing (tool change)

Systematic and random chang-

8 5.8 D non-normal 3 500 5 es in location and dispersion

- non-normal

Correct calculations for a

9 5.9 A2 Rayleigh 3 500 5 sample following a Rayleigh

distribution

Correct calculations for a

10 5.10 A2 Weibull 0 200 5 sample following a Weibull

distribution

ISO 22514-8 capability of mul-

11 5.11 C2 normal 1 30 (10)

ti-state production processes

NOTE

— The decision which distribution model fits the data and its use is up to the statistical expert. Within this

document distribution models for each example are therefore assumed. The procedure to select a statistical

distribution is not part of this document.

— According to ISO 22514-2 the calculation method d = 5 for the dispersion is not suited for non-normal

distributions. It is calculated and given in this document even for non-normal distributions for the purpose

of validating the implementation of the calculation method of d = 5.

— The resulting distributions for test 2, 9 and 10 are pre-selected models and with no means the "best natural"

resulting distribution models for the same reason no goodness of fit statistics are given, knowing they will

lead to reject H for the pre-selected distribution models.

0

— Two more decimal places for sample statistics and control limits than digits of the input values. Resulting

values are rounded (ISO/IEC/IEEE 60559, rounded-to-the-nearest).

— Capability index are always given with 2 digits (rounded).

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ISO/TR 11462-3:2020(E)

— Control limits were calculated using all values in the test data set.

— All control limits were calculated using tabulated correction factors in ISO 7870-2. Using the exact quantiles

of the corresponding distribution functions instead can lead to a deviation in the results <0,1 %.

— The centrelines for the control charts were chosen according to the respective statistics given by

ISO 7870-2:2013, 6.1 to 6.3

— The histogram plot is not part of the validation, since the procedure is not specified in ISO 7870 series nor in

ISO 22514 series. Histograms are for visualization purposes only.

— No units are given, no unit conversion has to be done.

— Time-dependent distribution models A-D are specified in ISO 22514-2.

— Internally a precision of 15 digits is used, when already calculated values are used again in further calculations.

— If the data are not normal distributed an individual chart and a MR chart cannot be used.

5 Reference data sets description and evaluation

5.1 Test data set 1

5.1.1 Test data set 1 information

This set of test data is taken from a process following a normal distribution and is for checking the

accuracy of calculation for control limits, sample statistics and process capabilities. A description of

test data set 1 is given in Table 2. Figure 1 shows a histogram and Figure 2 a probability plot of the test

data set 1 with the purpose of data visualization.

Table 2 — Description of test data set 1

Description of data input

Distribution model A1 Resulting distribution Normal

Data set Annex A, Table A.1 decimal points 4

Total sample size 125 U 14,075

Size of subgroups 5 L 14,060

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Key

X value

Y1 absolute frequency

Y2 relative frequency in %

Figure 1 — Histogram of test data set 1

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ISO/TR 11462-3:2020(E)

Key

X value

Y1 probability in %

Y2 1-probability in %

Figure 2 — Probability plot of test data set 1

NOTE The width of the class intervals is 0,000 7.

The class interval with the highest frequency of values is from 14,067 95 to 14,068 02.

The density plot is based on the assumption of normality and estimated parameters l = 1, d = 5.

5.1.2 Test data set 1 results

5.1.2.1 List of sample statistics

Table 3 lists all sample statistics which are necessary to calculate the target values and control limits

for the control charts described in ISO 7870-2 as well as the estimators for location and dispersion

given in ISO 22514-2 for the calculation of the process capability indices.

Table 3 — List of sample statistics for test data set 1

Statistic Value Reference

Location

x (l = 1) 14,067 958 ISO 22514-2:2017, Formula (11)

14,068 000 ISO 22514-2:2017, Formula (12)

x (l = 2)

14,067 958 ISO 22514-2:2017, Formula (13)

x (l = 3)

14,067 828 ISO 22514-2:2017, Formula (14)

x (l = 4)

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ISO/TR 11462-3:2020(E)

Table 3 (continued)

Statistic Value Reference

Dispersion

ˆ

0,007 240 (normal distribution) ISO 22514-2:2017: Formula (15)

Δ (d = 1)

σˆ (d = 2) 0,001 187 ISO 22514-2:2017, Formula (16)

ˆ 0,001 200 ISO 22514-2:2017, Formula (17)

σ (d = 3)

σˆ (d = 4) 0,001 180 ISO 22514-2:2017, Formula (18)

σˆ (d = 5) 0,001 207 ISO 22514-2:2017, Formula (19)

s 0,001 128 ISO 7870-2:2013, 3.2

0,005 900 ISO 7870-2:2013, 3.2

R

0,002 744 ISO 7870-2:2013, 3.2

R

R 0,001 379 ISO 7870-2:2013, 3.2

m

5.1.2.2 x chart

The xcontrol chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 3.

Key

X number of subgroup

Y mean value

Figure 3 — Mean control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 1, using s ):

L = 14,066 349

CL

U = 14,069 568

CL

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ISO/TR 11462-3:2020(E)

5.1.2.3 X chart

The individuals control chart calculated according to ISO 7870-2:2013, 6.2, is shown in Figure 4.

Key

X value number

Y individuals

Figure 4 — Individuals control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 3):

L = 14,064 29

CL

U = 14,071 63

CL

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ISO/TR 11462-3:2020(E)

5.1.2.4 x chart

The median control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 5.

Key

X subgroup number

Y median value

Figure 5 — Median control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 4):

L = 14,065 93

CL

U = 14,069 72

CL

Out of control situations are given in Table 4.

Table 4 — Results of pattern tests for the median control chart and test data set 1

Out of control situations

Subgroup Result/violation Subgroup Result/violation

6 Violation of L

CL

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ISO/TR 11462-3:2020(E)

5.1.2.5 s chart

The s control chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 6.

Key

X subgroup number

Y empirical standard deviation s value

Figure 6 — s control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 1):

L = 0

CL

U = 0,002 356

CL

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ISO/TR 11462-3:2020(E)

5.1.2.6 R chart

The R control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 7.

Key

X subgroup number

Y range R value

Figure 7 — R control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 1):

L = 0

CL

U = 0,005 801

CL

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ISO/TR 11462-3:2020(E)

5.1.2.7 Moving range chart

The moving range control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 8.

Key

X individuals number

Y moving range value

Figure 8 — Moving range control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 3):

L = 0

CL

U = 0,004 51

CL

Out of control situations are given in Table 5.

Table 5 — Results of pattern tests for the moving range control chart and test data set 1

Out of control situations

Value Result/violation Value Result/violation

77 to 84 run below centreline

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ISO/TR 11462-3:2020(E)

5.1.2.8 Process capability

The process capability is calculated according to ISO 22514-2:2017, Clause 6, with calculation method

l = 3 for the location estimator and calculation method d = 5 for the dispersion estimator.

Capability indices (calculation method M )

3,5

Process is stable (mean, R - chart) - C /C is used

p pk

C 2,07 C 1,95

p pk

C 2,20 C 1,95

pkL pkU

5.2 Test data set 2

5.2.1 Test data set 2 information

This set of test data is taken from a process following a non-normal distribution and is for checking the

accuracy of calculation for control limits, sample statistics and process capabilities. A description of

test data set 2 is given in Table 6. Figure 9 shows a histogram and Figure 10 a probability plot of the test

data set 2 with the purpose of data visualization.

Table 6 — Description of test data set 2

Description of data input

Distribution model A2 Resulting distribution Weibull

Data set Annex A, Table A.1 decimal points 3

Total sample size 600 U 0,04

Size of subgroups 3 L 0

Key

X value

Y1 absolute frequency

Y2 relative frequency in %

Figure 9 — Histogram of test data set 2

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ISO/TR 11462-3:2020(E)

Key

X value

Y1 probability in %

Y2 1-probability in %

Figure 10 — Probability plot of test data set 2

NOTE The width of the class intervals is 0,003.

The class interval with the highest frequency of values is from 0,003 5 to 0,006 5.

The density plot is based on the assumption of a two parametric Weibull distribution with estimated parameters

scale a = 0,009 39 and shape b = 1,897 82. Both estimators have been calculated using the method of Maximum

Likelihood.

The 0,135 %- and the 99,865 %-percentiles are calculated using the inverse distribution function of the Weibull

distribution

1

−1

()

Fp()|,ab =×ap[]−−ln()1

b

X = 0,000 29

0,135 %

X = 0,025 39

99,865 %

5.2.2 Test data set 2 results

5.2.2.1 List of sample statistics

Table 7 lists all sample statistics which are necessary to calculate the target values and control limits

for the control charts described in ISO 7870-2 as well as the estimators for location and dispersion

given in ISO 22514-2 for the calculation of the process capability indices.

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ISO/TR 11462-3:2020(E)

Table 7 — List of sample statistics for test data set 2

Statistic Value Reference

Location

x (l = 1) 0,008 29 ISO 22514-2:2017, Formula (11)

x (l = 2) 0,007 00 ISO 22514-2:2017, Formula (12)

0,008 29 ISO 22514-2:2017, Formula (13)

x (l = 3)

0,007 51 ISO 22514-2:2017, Formula (14)

x (l = 4)

Dispersion

ˆ

0,025 11 (Weibull using parameters in 5.2.1) ISO 22514-2:2017, Formula (15)

Δ (d = 1)

σˆ (d = 2) 0,004 88 ISO 22514-2:2017, Formula (16)

σˆ (d = 3) 0,004 87 ISO 22514-2:2017, Formula (17)

ˆ 0,004 81 ISO 22514-2:2017, Formula (18)

σ (d = 4)

σˆ (d = 5) 0,004 67 ISO 22514-2:2017, Formula (19)

s 0,004 32 ISO 7870-2:2013, 3.2

R 0,026 00 ISO 7870-2:2013, 3.2

0,008 13 ISO 7870-2:2013, 3.2

R

R 0,005 14 ISO 7870-2:2013, 3.2

m

5.2.2.2 x chart

The xcontrol chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 11.

Key

X number of subgroup

Y mean value

Figure 11 — Mean control chart for test data set 2

The control limits are (see ISO 7870-2:2013, Table 1, using s ):

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ISO/TR 11462-3:2020(E)

L = −0,000 15 (The calculated lower control limit is negative and the dataset is one-sided against

CL

0 limited characteristic. Therefore, the lower control limit is not shown, L = ----)

CL

U = 0,016 72

CL

5.2.2.3 X chart

The individuals control chart calculated according to ISO 7870-2:2013, 6.2, is shown in Figure 12.

Key

X value number

Y individuals

Figure 12 — Individuals control chart for test data set 2

The control limits are (see ISO 7870-2:2013, Table 3):

L = −0,005 39

CL

U = 0,021 96

CL

Out of control situations are given in Table 8.

Table 8 — Results of pattern tests for the individuals control chart and test data set 2

Out of control situations

Value Result/violation Value Result/violation

75 violation of U 433 violation of U

CL CL

155 to 163 run below centreline 435 to 441 run below centreline

222 to 228 run below centreline 464 violation of U

CL

367 violation of U 468 violation of U

CL CL

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ISO/TR 11462-3:2020(E)

5.2.2.4 x chart

The median control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 13.

Key

X subgroup number

Y median value

Figure 13 — Median control chart for test data set 2

The control limits are (see ISO 7870-2:2013, Table 4):

L = −0,002 15

CL

U = 0,017 17

CL

Out of control situations are given in Table 9.

Table 9 — Results of pattern tests for the median control chart and test data set 2

Out of control situations

Subgroup Result/violation Subgroup Result/violation

91 to 97 run below centreline 155 violation of U

CL

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ISO/TR 11462-3:2020(E)

5.2.2.5 s

**...**

TECHNICAL ISO/TR

REPORT 11462-3

First edition

Guidelines for implementation of

statistical process control (SPC) —

Part 3:

Reference data sets for SPC software

validation

Lignes directrices pour la mise en œuvre de la maîtrise statistique des

processus (MSP) —

Partie 3: Jeux de données de référence pour la validation de logiciels

pour MSP

PROOF/ÉPREUVE

Reference number

ISO/TR 11462-3:2020(E)

©

ISO 2020

---------------------- Page: 1 ----------------------

ISO/TR 11462-3:2020(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2020

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.

ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Fax: +41 22 749 09 47

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

ii PROOF/ÉPREUVE © ISO 2020 – All rights reserved

---------------------- Page: 2 ----------------------

ISO/TR 11462-3:2020(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

4 Overview of the test examples . 3

4.1 Overview . 3

5 Reference data sets description and evaluation . 4

5.1 Test data set 1 . 4

5.1.1 Test data set 1 information . 4

5.1.2 Test data set 1 results . 6

5.2 Test data set 2 .13

5.2.1 Test data set 2 information .13

5.2.2 Test data set 2 results .14

5.3 Test data set 3 .21

5.3.1 Test data set 3 information .21

5.3.2 Test data set 3 results .23

5.4 Test data set 4 .32

5.4.1 Test data set 4 information .32

5.4.2 Test data set 4 results .34

5.5 Test data set 5 .43

5.5.1 Test data set 5 information .43

5.5.2 Test data set 5 results .45

5.6 Test data set 6 .53

5.6.1 Test data set 6 information .53

5.6.2 Test data set 6 results .55

5.7 Test data set 7 .63

5.7.1 Test data set 7 information .63

5.7.2 Test data set 7 results .65

5.8 Test data set 8 .73

5.8.1 Test data set 8 information .73

5.8.2 Test data set 8 results .75

5.9 Test data set 9 .82

5.9.1 Test data set 9 information .82

5.9.2 Test data set 9 results .85

5.10 Test data set 10 .92

5.10.1 Test data set 10 information .92

5.10.2 Test data set 10 results .95

5.11 Test data set 11 .102

5.11.1 Test data set 11 information .102

5.11.2 Test data set 11 results .103

Annex A (normative) Test data values .105

Bibliography .129

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ISO/TR 11462-3:2020(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.

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Subcommittee SC 4, Applications of statistical methods in process management.

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Introduction

The test examples given in this document were developed for the assessment of SPC systems. They

allow SPC 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 Annex A.

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TECHNICAL REPORT ISO/TR 11462-3:2020(E)

Guidelines for implementation of statistical process

control (SPC) —

Part 3:

Reference data sets for SPC software validation

1 Scope

This document describes examples for software validation for SPC software implementing the standards

of the ISO 7870 series on control charts and the ISO 22514 series on capability and performance. In

detail ISO 7870-2, ISO 22514-2 and ISO 22514-8 are covered.

It provides data sets and test results for testing the implementation of the evaluation methods described

in these standards. This includes the detection of out of control situations as well as the calculation of

sample statistics and process capability indices.

The test examples cover the following situations:

a) General:

— different sample and subgroup sizes accuracy of calculation for large/small numbers;

b) ISO 22514 series:

— calculation of sample statistics for location and dispersion;

— different distribution models;

c) ISO 7870-2:

— calculation of control limits;

— visualization of data (histogram, control charts);

— detection of out of control situations.

2 Normative references

There are no normative references in this document.

3 Terms and definitions, and symbols and abbreviated terms

3.1 Terms and definitions

No terms and definitions are listed in this document.

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 http:// www .electropedia .org/

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3.2 Symbols and abbreviated terms

Symbols used in this document are identical to the symbols used in ISO 22514-2 and ISO 7870-2:

C process capability index

p

C minimum process capability index

pk

C upper process capability index

pkU

C lower process capability index

pkL

U upper control limit

CL

L lower control limit

CL

m number of subgroups

n sample size of each subgroup

P machine performance index

m

P minimum machine performance index

mk

P upper machine performance index

mkU

P lower machine performance index

mkL

P process performance index

p

P minimum process performance index

pk

P upper process performance index

pkU

P lower process performance index

pkL

T Centreline (target value) for the respective characteristic in the control charts

U upper specification limit

L lower specification limit

U upper specification limit, transformed values

tr

L lower specification limit, transformed values

tr

Abbreviated terms:

SPC statistical process control

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4 Overview of the test examples

4.1 Overview

See Table 1 for an overview of the test examples.

Table 1 — Overview of test examples

Test data Distri- Resulting Total Subgroup

Decimal

set Subclause bution distribu- sample sample Description of data set

points

number model tion size size

Data follows a normal distribu-

1 5.1 A1 normal 4 125 5

tion with no outliers

Correct calculations for a

2 5.2 A2 Weibull 3 600 3 sample following a Weibull

distribution

Normal distribution with time

3 5.3 B non-normal 2 1 000 5

dependent shift of mean

Location: random normally dis-

4 5.4 C1 normal 2 1 000 5

tributed; dispersion: constant

Location random non-normally

distributed; dispersion con-

5 5.5 C2 non-normal 2 1 000 5

stant; resulting distribution

non-normal

Capability indices for trend

6 5.6 C3 non-normal 2 600 6

production (tool wear)

Capability indices for fix tool-

7 5.7 C4 non-normal 2 500 5

ing (tool change)

Systematic and random chang-

8 5.8 D non-normal 3 500 5 es in location and dispersion

- non-normal

Correct calculations for a

9 5.9 A2 Rayleigh 3 500 5 sample following a Rayleigh

distribution

Correct calculations for a

10 5.10 A2 Weibull 0 200 5 sample following a Weibull

distribution

ISO 22514-8 capability of mul-

11 5.11 C2 normal 1 30 (10)

ti-state production processes

NOTE

— The decision which distribution model fits the data and is used is up to the statistical expert. Within this

document distribution models for each example are therefore assumed. The procedure to select a statistical

distribution is not part of this document.

— According to ISO 22514-2 the calculation method d = 5 for the dispersion is not suited for non-normal

distributions. It is calculated and given in this document even for non-normal distributions for the purpose

of validating the implementation of the calculation method of d = 5.

— The resulting distributions for test 2, 9 and 10 are pre-selected models and with no means the "best natural"

resulting distribution models for the same reason no goodness of fit statistics are given, knowing they will

lead to reject H for the pre-selected distribution models.

0

— Two more decimal places for sample statistics and control limits than digits of the input values. Resulting

values are rounded (ISO/IEC/IEEE 60559, rounded-to-the-nearest).

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ISO/TR 11462-3:2020(E)

— Capability index are always given with 2 digits (rounded).

— Control limits were calculated using all values in the test data set.

— All control limits were calculated using tabulated correction factors in ISO 7870-2. Using the exact quantiles

of the corresponding distribution functions instead can lead to a deviation in the results <0,1 %.

— The centrelines for the control charts were chosen according to the respective statistics given by

ISO 7870-2:2013, 6.1 to 6.3

— The histogram plot is not part of the validation, since the procedure is not specified in ISO 7870 series nor in

ISO 22514 series. Histograms are for visualization purposes only.

— No units are given, no unit conversion has to be done.

— Time-dependent distribution models A-D are specified in ISO 22514-2.

— Internally a precision of 15 digits is used, when already calculated values are used again in further calculations.

— If the data are not normal distributed an individual chart and a MR chart cannot be used.

5 Reference data sets description and evaluation

5.1 Test data set 1

5.1.1 Test data set 1 information

This set of test data is taken from a process following a normal distribution and is for checking the

accuracy of calculation for control limits, sample statistics and process capabilities. A description of

test data set 1 is given in Table 2. Figure 1 shows a histogram and Figure 2 a probability plot of the test

data set 1 with the purpose of data visualization.

Table 2 — Description of test data set 1

Description of data input

Distribution model A1 Resulting distribution Normal

Data set Annex A, Table A.1 decimal points 4

Total sample size 125 U 14,075

Size of subgroups 5 L 14,060

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Key

X value

Y1 absolute frequency

Y2 relative frequency in %

Figure 1 — Histogram of test data set 1

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Key

X value

Y1 probability in %

Y2 1-probability in %

Figure 2 — Probability plot of test data set 1

NOTE The width of the class intervals is 0,000 7.

The class interval with the highest frequency of values is from 14,067 95 to 14,068 02.

The density plot is based on the assumption of normality and estimated parameters l = 1, d = 5.

5.1.2 Test data set 1 results

5.1.2.1 List of sample statistics

Table 3 lists all sample statistics which are necessary to calculate the target values and control limits

for the control charts described in ISO 7870-2 as well as the estimators for location and dispersion

given in ISO 22514-2 for the calculation of the process capability indices.

Table 3 — List of sample statistics for test data set 1

Statistic Value Reference

Location

x (l = 1) 14,067 958 ISO 22514-2:2017, Formula (11)

14,068 000 ISO 22514-2:2017, Formula (12)

x , (l = 2)

14,067 958 ISO 22514-2:2017, Formula (13)

x (l = 3)

14,067 828 ISO 22514-2:2017, Formula (14)

x (l = 4)

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Table 3 (continued)

Statistic Value Reference

Dispersion

ˆ

0,007 240 (normal distribution) ISO 22514-2:2017: Formula (15)

Δ (d = 1)

σˆ (d = 2) 0,001 187 ISO 22514-2:2017, Formula (16)

ˆ 0,001 200 ISO 22514-2:2017, Formula (17)

σ (d = 3)

σˆ (d = 4) 0,001 180 ISO 22514-2:2017, Formula (18)

σˆ (d = 5) 0,001 207 ISO 22514-2:2017, Formula (19)

s 0,001 128 ISO 7870-2:2013, 3.2

0,005 900 ISO 7870-2:2013, 3.2

R

0,002 744 ISO 7870-2:2013, 3.2

R

R 0,001 379 ISO 7870-2:2013, 3.2

m

5.1.2.2 x chart

The xcontrol chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 3.

Key

X number of subgroup

Y mean value

Figure 3 — Mean control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 1, using s ):

L = 14,066 349

CL

U = 14,069 568

CL

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5.1.2.3 X chart

The individuals control chart calculated according to ISO 7870-2:2013, 6.2, is shown in Figure 4.

Key

X value number

Y individuals

Figure 4 — Individuals control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 3):

L = 14,064 29

CL

U = 14,071 63

CL

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5.1.2.4 x chart

The median control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 5.

Key

X subgroup number

Y median value

Figure 5 — Median control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 4):

L = 14,065 93

CL

U = 14,069 72

CL

Out of control situations are given in Table 4.

Table 4 — Results of pattern tests for the median control chart and test data set 1

Out of control situations

Subgroup Result/violation Subgroup Result/violation

6 Violation of L

CL

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5.1.2.5 s chart

The s control chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 6.

Key

X subgroup number

Y empirical standard deviation s value

Figure 6 — s control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 1):

L = 0

CL

U = 0,002 356

CL

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5.1.2.6 R chart

The R control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 7.

Key

X subgroup number

Y range R value

Figure 7 — R control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 1):

L = 0

CL

U = 0,005 801

CL

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5.1.2.7 Moving range chart

The moving range control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 8.

Key

X individuals number

Y moving range value

Figure 8 — Moving range control chart for test data set 1

The control limits are (see ISO 7870-2:2013, Table 3):

L = 0

CL

U = 0,004 51

CL

Out of control situations are given in Table 5.

Table 5 — Results of pattern tests for the moving range control chart and test data set 1

Out of control situations

Value Result/violation Value Result/violation

77 to 84 run below centreline

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5.1.2.8 Process capability

The process capability is calculated according to ISO 22514-2:2017, Clause 6, with calculation method

l = 3 for the location estimator and calculation method d = 5 for the dispersion estimator.

Capability indices (calculation method M )

3,5

Process is stable (mean, R - chart) - C /C is used

p pk

C 2,07 C 1,95

p pk

C 2,20 C 1,95

pkL pkU

5.2 Test data set 2

5.2.1 Test data set 2 information

This set of test data is taken from a process following a non-normal distribution and is for checking the

accuracy of calculation for control limits, sample statistics and process capabilities. A description of

test data set 2 is given in Table 6. Figure 9 shows a histogram and Figure 10 a probability plot of the test

data set 2 with the purpose of data visualization.

Table 6 — Description of test data set 2

Description of data input

Distribution model A2 Resulting distribution Weibull

Data set Annex A, Table A.1 decimal points 3

Total sample size 600 U 0,04

Size of subgroups 3 L 0

Key

X value

Y1 absolute frequency

Y2 relative frequency in %

Figure 9 — Histogram of test data set 2

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Key

X value

Y1 probability in %

Y2 1-probability in %

Figure 10 — Probability plot of test data set 2

NOTE The width of the class intervals is 0,003.

The class interval with the highest frequency of values is from 0,003 5 to 0,006 5.

The density plot is based on the assumption of a two parametric Weibull distribution with estimated parameters

scale a = 0,009 39 and shape b = 1,897 82. Both estimators have been calculated using the method of Maximum

Likelihood.

The 0,135 %- and the 99,865 %-percentiles are calculated using the inverse distribution function of the Weibull

distribution

1

−1

()

Fp()|,ab =×ap[]−−ln()1

b

X = 0,000 29

0,135 %

X = 0,025 39

99,865 %

5.2.2 Test data set 2 results

5.2.2.1 List of sample statistics

Table 7 lists all sample statistics which are necessary to calculate the target values and control limits

for the control charts described in ISO 7870-2 as well as the estimators for location and dispersion

given in ISO 22514-2 for the calculation of the process capability indices.

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Table 7 — List of sample statistics for test data set 2

Statistic Value Reference

Location

x (l = 1) 0,008 29 ISO 22514-2:2017, Formula (11)

x , (l = 2) 0,007 00 ISO 22514-2:2017, Formula (12)

0,008 29 ISO 22514-2:2017, Formula (13)

x , (l = 3)

0,007 51 ISO 22514-2:2017, Formula (14)

x , (l = 4)

Dispersion

ˆ

0,025 11 (Weibull using parameters in 5.2.1) ISO 22514-2:2017, Formula (15)

Δ (d = 1)

σˆ (d = 2) 0,004 88 ISO 22514-2:2017, Formula (16)

σˆ (d = 3) 0,004 87 ISO 22514-2:2017, Formula (17)

ˆ 0,004 81 ISO 22514-2:2017, Formula (18)

σ (d = 4)

σˆ (d = 5) 0,004 67 ISO 22514-2:2017, Formula (19)

s 0,004 32 ISO 7870-2:2013, 3.2

R 0,026 00 ISO 7870-2:2013, 3.2

0,008 13 ISO 7870-2:2013, 3.2

R

R 0,005 14 ISO 7870-2:2013, 3.2

m

5.2.2.2 x chart

The xcontrol chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 11.

Key

X number of subgroup

Y mean value

Figure 11 — Mean control chart for test data set 2

The control limits are (see ISO 7870-2:2013, Table 1, using s ):

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L = −0,000 15 (The calculated lower control limit is negative and the dataset is one-sided against

CL

0 limited characteristic. Therefore, the lower control limit is not shown, L = ----)

CL

U = 0,016 72

CL

5.2.2.3 X chart

The individuals control chart calculated according to ISO 7870-2:2013, 6.2, is shown in Figure 12.

Key

X value number

Y individuals

Figure 12 — Individuals control chart for test data set 2

The control limits are (see ISO 7870-2:2013, Table 3):

L = −0,005 39

CL

U = 0,021 96

CL

Out of control situations are given in Table 8.

Table 8 — Results of pattern tests for the individuals control chart and test data set 2

Out of control situations

Value Result/violation Value Result/violation

75 violation of U 433 violation of U

CL CL

155 to 163 run below centreline 435 to 441 run below centreline

222 to 228 run below centreline 464 violation of U

CL

367 violation of U 468 violation of U

CL CL

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5.2.2.4 x chart

The median control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 13.

Key

X subgroup number

Y median value

Figure 13 — Median control chart for test data set 2

The control limits are (see ISO 7870-2:2013, Table 4):

L = −0,002 15

CL

U = 0,017 17

CL

Out o

**...**

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