ISO/TR 11462-3:2020

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 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

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
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
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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.
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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

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/ .
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/
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

2 © ISO 2020 – All rights reserved

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.
— 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).
— 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
4 © ISO 2020 – All rights reserved

Key
X value
Y1 absolute frequency
Y2 relative frequency in %
Figure 1 — Histogram of test data set 1
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)
6 © ISO 2020 – All rights reserved

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
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
8 © ISO 2020 – All rights reserved


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
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
10 © ISO 2020 – All rights reserved

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
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
12 © ISO 2020 – All rights reserved

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
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
()
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.
14 © ISO 2020 – All rights reserved

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 ):
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
16 © ISO 2020 – All rights reserved


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
5.2.2.5 s chart
The s control chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 14.
Key
X subgroup number
Y empirical standard deviation s value
Figure 14 — s control chart for test data set 2
The control limits are (see ISO 7870-2:2013, Table 1):
L = 0
CL
U = 0,011 083
CL
18 © ISO 2020 – All rights reserved

5.2.2.6 R chart
The R control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 15.
Key
X subgroup number
Y range R value
Figure 15 — R control chart for test data set 2
The control limits are (see ISO 7870-2:2013, Table 1):
L = 0
CL
U = 0,020 94
CL
5.2.2.7 Moving range chart
The moving range control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 16.
Key
X individuals number
Y moving range value
Figure 16 — Moving range control chart for test data set 2
The control limits are (see ISO 7870-2:2013, Table 3):
L = 0
CL
U = 0,016 80
CL
Out of control situations are given in Table 10.
Table 10 — Results of pattern tests for the moving range control chart and test data set 2
Out of control situations
Value Result/violation Value Result/violation
44 to 57 run below centreline 268 to 275 run below centreline
60 to 68 run below centreline 321 to 331 run below centreline
75 violation of U 336 violation of U
CL CL
156 to 163 run below centreline 337 violation of U
CL
166 to 174 run below centreline 408 violation of U
CL
199 to 206 trend decreasing 433 violation of U
CL
199 violation of U 465 violation of U
CL CL
201 to 211 run below centreline 468 violation of U
CL
221 to 228 run below centreline 469 violation of U
CL
229 violation of U
CL
20 © ISO 2020 – All rights reserved

5.2.2.8 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 1,43 C 0,59
p pk
C 0,59 C 2,26
pkL pkU
Because of non-normal distributed data (Weibull) M cannot be used – instead M is used.
3,5 3,1
Capability indices (calculation method M )
3,1
Process is stable (mean, R - chart) - C /C is used
p pk
C (1,59) theoretical limit C 1,83
p pk
C --- C 1,83
pkL pkU
5.3 Test data set 3
5.3.1 Test data set 3 information
This set of test data is taken from a process following a non- normal distribution with a varying
dispersion parameter σ and is for checking the accuracy of calculation for control limits, sample
statistics and process capabilities. A description of test data set 3 is given in Table 11. Figure 17 shows a
histogram and Figure 18 a probability plot of the data set with the purpose of data visualization.
Table 11 — Description of test data set 3
Description of data input
Distribution model B Resulting distribution non-normal, unimodal
Data set Annex A, Table A.1 decimal points 2
Total sample size 1 000 U 5
Size of subgroups 5 L -5
Key
Y1 absolute frequency
Y2 relative frequency in %
Figure 17 — Histogram of test data set 3
22 © ISO 2020 – All rights reserved

Key
X value
Y1 probability in %
Y2 1-probability in %
Figure 18 — Probability plot of test data set 3
NOTE The width of the class intervals is 0,74.
The class interval with the highest frequency of values is from −0,005 to 0,735.
The density plot is based on the assumption of normality and estimated parameters l = 1, d = 5.
5.3.2 Test data set 3 results
5.3.2.1 List of sample statistics
Table 12 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 12 — List of sample statistics for test data set 3
Statistic Value Reference
Location
x (l = 1) −0,002 5 ISO 22514-2:2017, Formula (11)
 0,000 0 ISO 22514-2:2017, Formula (12)
x (l = 2)
−0,002 5 ISO 22514-2:2017, Formula (13)
x (l = 3)
0,000 6 ISO 22514-2:2017, Formula (14)

x (l = 4)
Table 12 (continued)
Statistic Value Reference
Dispersion
ˆ
5,292 3 (normal distribution) ISO 22514-2:2017, Formula (15)
Δ (d = 1)
σˆ (d = 2) 0,856 1 ISO 22514-2:2017, Formula (16)
ˆ 0,759 9 ISO 22514-2:2017, Formula (17)
σ (d = 3)
σˆ (d = 4) 0,767 5 ISO 22514-2:2017, Formula (18)
σˆ (d = 5) 0,882 1 ISO 22514-2:2017, Formula (19)
s 0,714 3 ISO 7870-2:2013, 3.2
8,150 0 ISO 7870-2:2013, 3.2
R
1,785 2 ISO 7870-2:2013, 3.2
R
R 0,859 0 ISO 7870-2:2013, 3.2
m
5.3.2.2 x - chart
The x−control chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 19.
Key
X number of subgroup
Y mean value
Figure 19 — Mean control chart for test data set 3
The control limits are (see ISO 7870-2:2013, Table 1, using s )
L = −1,021 8
CL
U = 1,016 8
CL
Out of control situations are given in Table 13.
24 © ISO 2020 – All rights reserved

Table 13 — Results of pattern tests for the mean control chart and test data set 3
Out of control situations
Subgroup Result/violation Subgroup Result/violation
10 violation of U 106 violation of L
CL CL
14 violation of U 116 to 122 run below centreline
CL
16 violation of U 125 violation of U
CL CL
28 violation of U 128 violation of U
CL CL
100 violation of U 149 violation of L
CL CL
102 violation of L
CL
5.3.2.3 X chart
The individuals control chart calculated according to ISO 7870-2:2013, 6.2, is shown in Figure 20.
Key
X value number
Y individuals
Figure 20 — Individuals control chart for test data set 3
The control limits are (see ISO 7870-2:2013, Table 3):
L = −2,287 4
CL
U = 2,282 5
CL
Out of control situations are given in Table 14.
Table 14 — Results of pattern tests for the individuals control chart and test data set 3
Out of control situations
Value Result/violation Value Result/violation
12 violation of U 523 violation of U
CL CL
16 violation of L 528 violation of L
CL CL
24 to 33 run above centreline 532 violation of U
CL
48 violation of U 534 violation of L
CL CL
66 violation of U 538 violation of U
CL CL
106 to 112 run above centreline 581 violation of L
CL
113 violation of L 588 violation of L
CL CL
120 violation of L 599 to 608 run below centreline
CL
126 violation of U 622 violation of U
CL CL
150 violation of L 639 violation of U
CL CL
204 violation of U 652 violation of U
CL CL
205 to 211 run below centreline 672 violation of U
CL
222 violation of L 673 violation of U
CL CL
228 violation of L 684 violation of U
CL CL
251 to 261 run below centreline 697 to 705 run above centreline
288 to 298 run above centreline 726 violation of L
CL
504 violation of U 747 to 770 run above centreline
CL
505 to 511 run below centreline 958 violation of U
CL
507 violation of L 960 violation of U
CL CL
Because of the variation in dispersion another set of control limits can be calculated e.g. based on a
Johnson transformation.
L = −2,964 6
CL
U = 2,959 7
CL
26 © ISO 2020 – All rights reserved


5.3.2.4 x chart
The median control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 21.
Key
X subgroup number
Y median value
Figure 21 — Median control chart for test data set 3
The control limits are (see ISO 7870-2:2013, Table 4):
L = −1,233 0
CL
U = 1,234 2
CL
Out of control situations are given in Table 15.
Table 15 — Results of pattern tests for the median control chart and test data set 3
Out of control situations
Subgroup Result/violation Subgroup Result/violation
80 to 86 run below centreline 119 violation of L
CL
91 to 97 run below centreline 128 violation of U
CL
102 violation of L
CL
Because of the variation in dispersion another set of control limits can be calculated based on a Johnson
Transformation.
L = −1,377 4
CL
U = 1,372 4
CL
5.3.2.5 s chart
The s control chart calculated according to ISO 7870-2:2013, 6.1, is shown in Figure 22.
Key
X subgroup number
Y empirical standard deviation s value
Figure 22 — s control chart for test data set 3
The control limits are (see ISO 7870-2:2013, Table 1):
L = 0
CL
U = 1,492 1
CL
Out of control situations are given in Table 16.
Table 16 — Results of pattern tests for the s control chart and test data set 3
Out of control situations
Subgroup Result/violation Subgroup Result/violation
3 violation of U 108 violation of U
CL CL
14 violation of U 112 to 120 run above centreline
CL
24 violation of U 118 violation of U
CL CL
26 violation of U 124 violation of U
CL CL
27 violation of U 124 to 131 run above centreline
CL
30 violation of U 131 violation of U
CL CL
46 violation of U 133 to 140 run above centreline
CL
55 to 99 run below centreline 135 violation of U
CL
101 violation of U 142 to 148 run above centreline
CL
104 to 110 run above centreline 156 to 190 run below centreline
28 © ISO 2020 – All rights reserved

Table 16 (continued)
Out of control situations
Subgroup Result/violation Subgroup Result/violation
107 violation of U 192 violation of U
CL CL
Because of the variation in dispersion another set of control limits can be calculated (Johnson
transformation)
L = 0,139 22
CL
U = 1,806 07
CL
5.3.2.6 R chart
The R control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 23.
Key
X subgroup number
Y range R value
Figure 23 — R control chart for test data set 3
The control limits are (see ISO 7870-2:2013, Table 1):
L = 0
CL
U = 3,773 9
CL
Out of control situations are given in Table 17.
Table 17 — Results of pattern tests for the R control chart and test data set 3
Out of control situations
Subgroup Result/violation Subgroup Result/violation
3 violation of U 107 violation of U
CL CL
14 violation of U 108 violation of U
CL CL
Table 17 (continued)
Out of control situations
Subgroup Result/violation Subgroup Result/violation
24 violation of U 112 to 120 run above centreline
CL
26 violation of U 118 violation of U
CL CL
27 violation of U 124 to 131 run above centreline
CL
29 violation of U 124 violation of U
CL CL
46 violation of U 131 violation of U
CL CL
47 to 53 run below centreline 135 violation of U
CL
55 to 99 run below centreline 156 to 190 run below centreline
101 violation of U 192 violation of U
CL CL
104 to 110 run above centreline
5.3.2.7 Moving range chart
The moving range control chart calculated according to ISO 7870-2:2013, 6.3, is shown in Figure 24.
Key
X individuals number
Y moving range value
Figure 24 — Moving range control chart for test data set 3
The control limits are (see ISO 7870-2:2013, Table 3):
L = 0
CL
U = 2,806 3
CL
Out of control situations are given in Table 18.
30 © ISO 2020 – All rights reserved

Table 18 — Results of pattern tests for the moving range control chart and test data set 3
Out of control situations
Value Result/violation Value Result/violation
7 to 14 run above centreline 446 to 461 run below centreline
7 violation of U 475 to 486 run below centreline
CL
12 violation of U 502 to 509 run above centreline
CL
13 violation of U 504 violation of U
CL CL
26 to 33 run below centreline 505 violation of U
CL
36 to 47 run below centreline 523 violation of U
CL
66 violation of U 524 violation of U
CL CL
67 violation of U 533 violation of U
CL CL
113 violation of U 538 violation of U
CL CL
126 violation of U 582 violation of U
CL CL
127 violation of U 588 violation of U
CL CL
134 violation of U 589 violation of U
CL CL
141 violation of U 636 violation of U
CL CL
145 to 153 run above centreline 652 violation of U
CL
150 violation of U 672 to 678 run above centreline
CL
151 violation of U 672 violation of U
CL CL
163 violation of U 685 violation of U
CL CL
164 violation of U 694 to 700 run above centreline
CL
205 violation of U 697 violation of U
CL CL
205 violation of U 706 to 715 run above centreline
CL
222 violation of U 727 violation of U
CL CL
223 violation of U 761 to 770 run below centreline
CL
228 violation of U 786 to 804 run below centreline
CL
229 violation of U 806 to 821 run below centreline
CL
235 to 245 run below centreline 832 to 851 run below centreline
270 to 281 run below centreline 854 to 863 run below centreline
283 to 304 run below centreline 867 to 875 run below centreline
308 to 318 run below centreline 881 to 905 run below centreline
320 to 357 run below centreline 920 to 952 run below centreline
373 to 386 run below centreline 958 violation of U
CL
388 to 408 run below centreline 960 violation of U
CL
417 to 434 run below centreline 982 to 990 run below centreline
436 to 444 run below centreline 992 to 1 000 run below centreline
Because of the variation in dispersion another set of control limits can be calculated.
5.3.2.8 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 not stable (mean, R - chart) - P /P is used
p pk
P 1,89 P 1,89
p pk
P 1,89 P 1,89
pkL pkU
Because of non-normal distributed data (dispersion not stable) M cannot be used – instead M and
3,5 3,1
a Pearson or Johnson transformation is used.
Capability indices (calculation method M )
3,1
Process is not stable (mean, R - chart) - P /P is used. Calculation based on:
p pk
Pearson transformation
P 1,42 P 1,39
p pk
P 1,89 P 1,46
pkL pkU
Johnson Transformation
P 1,02 P 1,02
p pk
P 1,03 P 1,02
pkL pkU
5.4 Test data set 4
5.4.1 Test data set 4 information
This set of test data is taken from a process following a normal distribution (having changes in the
values of parameters µ and σ over time) and is for checking the accuracy of calculation for control
limits, sample
...