ISO 7870-3:2020
(Main)Control charts — Part 3: Acceptance control charts
Control charts — Part 3: Acceptance control charts
This document gives guidance on the uses of acceptance control charts and establishes general procedures for determining sample sizes, action limits and decision criteria. An acceptance control chart should be used only when: a) the within subgroup variation is in-control and the variation is estimated efficiently; b) a high level of process capability has been achieved. An acceptance control chart is typically used when the process variable under study is normally distributed; however, it can be applied to a non-normal distribution. The examples provided in this document illustrate a variety of circumstances in which this technique has advantages; these examples provide details of the determination of the sample size, the action limits and the decision criteria.
Cartes de contrôle — Partie 3: Cartes de contrôle pour acceptation
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 7870-3
Second edition
2020-05
Control charts —
Part 3:
Acceptance control charts
Cartes de contrôle —
Partie 3: Cartes de contrôle pour acceptation
Reference number
©
ISO 2020
© 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 © ISO 2020 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 2
4.1 Symbols . 2
4.2 Abbreviated terms . 3
5 Description of acceptance control chart practice . 3
6 Acceptance control of a process . 5
6.1 Plotting the chart . 5
6.2 Interpreting the chart . 5
7 Specifications . 5
8 Calculation procedures . 6
8.1 Selection of pairs of elements . 6
8.1.1 Defining elements APL and RPL . 6
8.1.2 Defining elements APL, α, β and n . 9
8.2 Frequency of sampling . 9
9 Examples .10
9.1 Example 1 (see also Figures A.3 and A.4) .10
9.2 Example 2 (see also Figure A.5) .12
10 Factors for acceptance control limits .13
11 Modified acceptance control charts .14
Annex A (normative) Nomographs for acceptance control chart design .15
Bibliography .21
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.
This second edition cancels and replaces the first edition (ISO 7870-3:2012), of which it constitutes a
minor revision with the following changes:
— typo corrections in 9.1, example 1;
— editorial updates.
A list of all parts in the ISO 7870 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
An acceptance control chart combines consideration of control implications with elements of acceptance
sampling. It is an appropriate tool for helping to make decisions with respect to process acceptance.
The bases for the decisions may be defined in terms of
a) whether or not a designated percentage of units of a product or service derived from that process
will satisfy specification requirements;
b) whether or not a process has shifted beyond some allowable zone of process level locations.
A difference from most acceptance sampling approaches is the emphasis on process acceptability rather
than on product disposition decisions.
A difference from usual control chart approaches is that the concept of process acceptance is introduced
in the process control. The process usually does not need to be in control about a single standard
process level; as long as the within-subgroup variability remains in control and is much smaller than
the tolerance spread, it can (for the purpose of acceptance) run at any level or levels within a zone of
process levels which would be acceptable in terms of tolerance requirements. Thus, it is assumed that
some assignable causes will create shifts in the process levels which are small enough in relation to
requirements that it would be uneconomical to attempt to control them too tightly for the purpose of
mere acceptance.
The use of an acceptance control chart does not, however, rule out the possibility of identifying and
removing assignable causes for the purpose of continuing process improvement.
A check on the inherent stability of the process is required. Therefore, variables are monitored using
Shewhart-type range or sample standard deviation control charts to confirm that the variability
inherent within rational subgroups remains in a steady state. Supplementary examinations of the
distribution of the encountered process levels form an additional source of control information. A
preliminary Shewhart control chart study should be conducted to verify the validity of using an
acceptance control chart.
INTERNATIONAL STANDARD ISO 7870-3:2020(E)
Control charts —
Part 3:
Acceptance control charts
1 Scope
This document gives guidance on the uses of acceptance control charts and establishes general
procedures for determining sample sizes, action limits and decision criteria. An acceptance control
chart should be used only when:
a) the within subgroup variation is in-control and the variation is estimated efficiently;
b) a high level of process capability has been achieved.
An acceptance control chart is typically used when the process variable under study is normally
distributed; however, it can be applied to a non-normal distribution. The examples provided in this
document illustrate a variety of circumstances in which this technique has advantages; these examples
provide details of the determination of the sample size, the action limits and the decision criteria.
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 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2 and the
following apply.
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/
3.1
acceptable process
process which is represented by a Shewhart control chart with a central line within the acceptable
process zone
Note 1 to entry: Ideally, the average value X of such a control chart would be at the target value.
Note 2 to entry: The acceptable process zone is shown in Figure 1. Information on the Stewhart control chart can
be found in ISO 7870-2.
Key
1 rejectable processes
2 indifference zone
3 acceptable processes
4 target level
upper RPL line
R
PL
U
upper APL line
A
PL
U
lower APL line
A
PL
L
lower RPL line
R
PL
L
Figure 1 — Two-sided specification limits: Upper and lower APL and RPL lines in relation to
processes of acceptable, rejectable, and indifference (borderline) quality
4 Symbols and abbreviated terms
NOTE The ISO/IEC Directives makes it necessary to depart from common SPC usage in respect to the
differentiation between abbreviated terms and symbols. An abbreviated term and its symbol can differ in
appearance in two ways: by font and by layout. To distinguish between abbreviated terms and symbols,
abbreviated terms are given in Arial upright and symbols in Times New Roman or Greek italics, as applicable.
Whereas abbreviated terms can contain multiple letters, symbols consist only of a single letter. For example, the
conventional abbreviation of acceptable process limit, APL, is valid but its symbol in equations becomes A . The
PL
reason for this is to avoid misinterpretation of compound letters as an indication of multiplication.
4.1 Symbols
A acceptance control limits
CL
A acceptable process level
PL
L lower specification limit
n subgroup sample size
p acceptable proportion nonconforming items
p rejectable proportion nonconforming items
P probability of acceptance
a
2 © ISO 2020 – All rights reserved
R rejectable process level or non-acceptable process zone
PL
T target value, i.e. the optimum value of the characteristic
U upper specification limit
average value of the variable X plotted on a control chart
X
z variable that has a normal dis
...
INTERNATIONAL ISO
STANDARD 7870-3
Second edition
2020-05
Control charts —
Part 3:
Acceptance control charts
Cartes de contrôle —
Partie 3: Cartes de contrôle pour acceptation
Reference number
©
ISO 2020
© 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 © ISO 2020 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 2
4.1 Symbols . 2
4.2 Abbreviated terms . 3
5 Description of acceptance control chart practice . 3
6 Acceptance control of a process . 5
6.1 Plotting the chart . 5
6.2 Interpreting the chart . 5
7 Specifications . 5
8 Calculation procedures . 6
8.1 Selection of pairs of elements . 6
8.1.1 Defining elements APL and RPL . 6
8.1.2 Defining elements APL, α, β and n . 9
8.2 Frequency of sampling . 9
9 Examples .10
9.1 Example 1 (see also Figures A.3 and A.4) .10
9.2 Example 2 (see also Figure A.5) .12
10 Factors for acceptance control limits .13
11 Modified acceptance control charts .14
Annex A (normative) Nomographs for acceptance control chart design .15
Bibliography .21
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.
This second edition cancels and replaces the first edition (ISO 7870-3:2012), of which it constitutes a
minor revision with the following changes:
— typo corrections in 9.1, example 1;
— editorial updates.
A list of all parts in the ISO 7870 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
An acceptance control chart combines consideration of control implications with elements of acceptance
sampling. It is an appropriate tool for helping to make decisions with respect to process acceptance.
The bases for the decisions may be defined in terms of
a) whether or not a designated percentage of units of a product or service derived from that process
will satisfy specification requirements;
b) whether or not a process has shifted beyond some allowable zone of process level locations.
A difference from most acceptance sampling approaches is the emphasis on process acceptability rather
than on product disposition decisions.
A difference from usual control chart approaches is that the concept of process acceptance is introduced
in the process control. The process usually does not need to be in control about a single standard
process level; as long as the within-subgroup variability remains in control and is much smaller than
the tolerance spread, it can (for the purpose of acceptance) run at any level or levels within a zone of
process levels which would be acceptable in terms of tolerance requirements. Thus, it is assumed that
some assignable causes will create shifts in the process levels which are small enough in relation to
requirements that it would be uneconomical to attempt to control them too tightly for the purpose of
mere acceptance.
The use of an acceptance control chart does not, however, rule out the possibility of identifying and
removing assignable causes for the purpose of continuing process improvement.
A check on the inherent stability of the process is required. Therefore, variables are monitored using
Shewhart-type range or sample standard deviation control charts to confirm that the variability
inherent within rational subgroups remains in a steady state. Supplementary examinations of the
distribution of the encountered process levels form an additional source of control information. A
preliminary Shewhart control chart study should be conducted to verify the validity of using an
acceptance control chart.
INTERNATIONAL STANDARD ISO 7870-3:2020(E)
Control charts —
Part 3:
Acceptance control charts
1 Scope
This document gives guidance on the uses of acceptance control charts and establishes general
procedures for determining sample sizes, action limits and decision criteria. An acceptance control
chart should be used only when:
a) the within subgroup variation is in-control and the variation is estimated efficiently;
b) a high level of process capability has been achieved.
An acceptance control chart is typically used when the process variable under study is normally
distributed; however, it can be applied to a non-normal distribution. The examples provided in this
document illustrate a variety of circumstances in which this technique has advantages; these examples
provide details of the determination of the sample size, the action limits and the decision criteria.
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 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2 and the
following apply.
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/
3.1
acceptable process
process which is represented by a Shewhart control chart with a central line within the acceptable
process zone
Note 1 to entry: Ideally, the average value X of such a control chart would be at the target value.
Note 2 to entry: The acceptable process zone is shown in Figure 1. Information on the Stewhart control chart can
be found in ISO 7870-2.
Key
1 rejectable processes
2 indifference zone
3 acceptable processes
4 target level
upper RPL line
R
PL
U
upper APL line
A
PL
U
lower APL line
A
PL
L
lower RPL line
R
PL
L
Figure 1 — Two-sided specification limits: Upper and lower APL and RPL lines in relation to
processes of acceptable, rejectable, and indifference (borderline) quality
4 Symbols and abbreviated terms
NOTE The ISO/IEC Directives makes it necessary to depart from common SPC usage in respect to the
differentiation between abbreviated terms and symbols. An abbreviated term and its symbol can differ in
appearance in two ways: by font and by layout. To distinguish between abbreviated terms and symbols,
abbreviated terms are given in Arial upright and symbols in Times New Roman or Greek italics, as applicable.
Whereas abbreviated terms can contain multiple letters, symbols consist only of a single letter. For example, the
conventional abbreviation of acceptable process limit, APL, is valid but its symbol in equations becomes A . The
PL
reason for this is to avoid misinterpretation of compound letters as an indication of multiplication.
4.1 Symbols
A acceptance control limits
CL
A acceptable process level
PL
L lower specification limit
n subgroup sample size
p acceptable proportion nonconforming items
p rejectable proportion nonconforming items
P probability of acceptance
a
2 © ISO 2020 – All rights reserved
R rejectable process level or non-acceptable process zone
PL
T target value, i.e. the optimum value of the characteristic
U upper specification limit
average value of the variable X plotted on a control chart
X
z variable that has a normal dis
...
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