Control charts

ISO 7870-3:2012 gives guidance on the uses of acceptance control charts and establishes general procedures for determining sample sizes, action limits and decision criteria. This 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. This chart is typically used when the process variable under study is normally distributed, however, it can be applied to a non-normal distribution. Examples are included to illustrate a variety of circumstances in which this technique has advantages and to provide details of the determination of the sample size, the action limits and the decision criteria.

Cartes de contrôle

General Information

Status
Replaced
Publication Date
21-Feb-2012
Withdrawal Date
21-Feb-2012
Current Stage
9599 - Withdrawal of International Standard
Completion Date
22-Feb-2012
Ref Project

RELATIONS

Effective Date
23-Apr-2020
Effective Date
28-Feb-2009

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INTERNATIONAL ISO
STANDARD 7870-3
First edition
2012-03-01
Control charts —
Part 3:
Acceptance control charts
Cartes de contrôle —
Partie 3: Cartes de contrôle pour acceptation
Reference number
ISO 7870-3:2012(E)
ISO 2012
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ISO 7870-3:2012(E)
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© ISO 2012

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ii © ISO 2012 – All rights reserved
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ISO 7870-3:2012(E)
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

8.2 Frequency of sampling ...................................................................................................................................... 8

9 Examples ............................................................................................................................................................... 9

9.1 Example 1 ............................................................................................................................................................. 9

9.2 Example 2 ............................................................................................................................................................10

10 Factors for acceptance control limits .......................................................................................................... 11

11 Modified acceptance control charts .............................................................................................................12

Annex A (normative) Nomographs for acceptance control chart design ..........................................................14

Bibliography .....................................................................................................................................................................20

© ISO 2012 – All rights reserved iii
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ISO 7870-3:2012(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.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

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.

ISO 7870-3 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee

SC 4, Applications of statistical methods in process management.
This first edition of ISO 7870-3 cancels and replaces ISO 7966:1993.

ISO 7870 consists of the following parts, under the general title Control charts:

— Part 1: General guidelines
— Part 2: Shewhart control charts
— Part 3: Acceptance control charts
— Part 4: Cumulative sum charts

Additional parts on specialized control charts and on the application of statistical process control (SPC)

charts are planned.
iv © ISO 2012 – All rights reserved
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ISO 7870-3:2012(E)
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.
© ISO 2012 – All rights reserved v
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INTERNATIONAL STANDARD ISO 7870-3:2012(E)
Control charts —
Part 3:
Acceptance control charts
1 Scope

This part of ISO 7870 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 part of ISO 7870 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 standards, in whole or in part, are normatively referenced in this document and are indispensable

for its application. For dated references, only the edition cited applies. For undated references, the latest edition

of the refferenced 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 document, the terms and definitions given in ISO 3534-1 and ISO 3534-2 apply.

3.1
acceptable process

process which is represented by a Shewhart control chart with a central line within the acceptable process zone

NOTE 1 Ideally, the average value X of such a control chart would be at the target value.

NOTE 2 The acceptable process zone is shown in Figure 1. Information on the Stewhart control chart can be found

in ISO 7870-2.
© ISO 2012 – All rights reserved 1
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ISO 7870-3:2012(E)

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 reason for this is to avoid misinterpretation of compound letters as an

indication of multiplication.
4.1 Symbols
A acceptance control limits
A acceptable process level
lower specification limit
subgroup sample size
p acceptable proportion nonconforming items
p rejectable proportion nonconforming items
P probability of acceptance
R rejectable process level or non-acceptable process zone
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

z variable that has a normal distribution with zero mean and unit standard deviation

z′ normal deviate that is exceeded by 100p′ % of the deviate in a specified direction (similarly for z , z ,

α β
etc.)
α risk of not accepting a process centred at the APL
β risk of not rejecting a process centred at the RPL
2 © ISO 2012 – All rights reserved
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ISO 7870-3:2012(E)
µ process mean

σ within-subgroup standard deviation corresponding to the inherent process variability

standard deviation of the subgroup average corresponding to the inherent process variability:

σσ= / n
4.2 Abbreviated terms
ACL acceptance control limits
APL acceptable process level
L lower specification limit (used as a subscript)
OC operating characteristic
RPL rejectable process level or non-acceptable process zone
U upper specification limit (used as a subscript)
5 Description of acceptance control chart practice

In the pursuit of an acceptable product or service, there often is room for some latitude in the ability to centre

a process around its target level. The contribution to overall variation of such location factors is additional to

the inherent random variability of individual elements around a given process level. In most cases, some shifts

in process level must be expected and can be tolerated. These shifts usually result from an assignable cause

that cannot be eliminated because of engineering or economic considerations. They often enter the system at

infrequent or irregular intervals, but can rarely be treated as random components of variance.

There are several seemingly different approaches to treating these location factors contributing variation beyond

that of inherent variability. At one extreme is the approach in which all variability that results in deviations from

the target value must be minimized. Supporters of such an approach seek to improve the capability to maintain a

process within tighter tolerance limits so that there is greater potential for process or product quality improvement.

At the other extreme is the approach that if a high level of process capability has been achieved, it is not only

uneconomic and wasteful of resources, but it can also be counterproductive to try to improve the capability

of the process. This often is the result of the introduction of pressures which encourage “tampering” with

the process (over-control) by people qualified to work on control aspects but not product or process quality

improvement programmes.

The acceptance control chart is a useful tool for covering this wide range of approaches in a logical and

simple manner. It distinguishes between the inherent variability components randomly occurring throughout

the process and the additional location factors which contribute at less frequent intervals.

When shifts appear, the process may then stabilize at a new level until the next such event occurs. Between

such disturbances, the process runs in control with respect to inherent variability.

An illustration of this situation is a process using large uniform batches of raw material. The within-batch

variability could be considered to be the inherent variability. When a new batch of material is introduced, its

deviation from the target may differ from that of the previous batch. The between-batch variation component

enters the system at discrete intervals.

An example of this within- and between-batch variation might very well occur in a situation where a blanking

die is blanking a machine part. The purpose of the chart is to determine when the die has worn to a point where

it must be repaired or reworked. The rate of wear is dependent upon the hardness of the successive batches

of material and is therefore not readily predictable. It will be seen that the use of an acceptance control chart

makes it possible to judge the appropriate time to service the blanking die.
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ISO 7870-3:2012(E)

The acceptance control chart is based on the Shewhart control chart (i.e. X – R chart or X – s chart) but is

set up so that the process mean can shift outside of control limits of the Shewhart control chart if the

specifications are sufficiently wide, or be confined to narrower limits if the inherent variability of the process is

comparatively large or a large fraction of the total tolerance spread.

What is required is protection against a process that has shifted so far from the target value that it will yield

some predetermined undesirable percentage of items falling outside the specification limits, or exhibits an

excessive degree of process level shift.

When a chart of the average value of data sets from a process is plotted, in sequence of the production, one

notices a continual variation in average values. In a central zone (acceptable process, Figure 1), there is a

product that is indisputably acceptable. Data in the outer zones (Figure 1) represent a process that is producing

product that is indisputably not acceptable.

Between the inner and the outer zones are zones where the product is acceptable but there is an indication

that the process should be watched and, as the outer zone is approached, corrective action may be taken.

These criteria are the basic concepts for the acceptance control chart. The description in this part of ISO 7870

is designed to provide practices for the establishment of appropriate action lines for one- and two-sided

specification situations.

Since it is impossible to have a single dividing line that can sharply distinguish a good from an unsatisfactory

quality level, one must define a process level that represents a process that should be accepted almost always

(1 −

α). This is called the acceptable process level (APL), and it marks the outer boundary of the acceptable

process zone located about the target value (see Figure 1).

Any process centred closer to the target value than the APL will have a risk smaller than α of not being

accepted. So the closer the process is to the target, the smaller the likelihood that a satisfactory process will

not be accepted.

It is also necessary to define the process level that represents processes that should almost never be accepted

(1 − β). This undesirable process level is labelled the rejectable process level (RPL). Any process located

further away from the target value than the RPL will have a risk of acceptance smaller than β.

The process levels lying between the APL and RPL would yield a product of borderline quality. That is, process

levels falling between the APL and RPL would represent quality which is not so good that it would be a waste

of time, or represent over-control, if the process were adjusted, and not so bad that the product could not be

used if no shift in level were made. This region is often called the “indifference zone”. The width of this zone is

a function of the requirements for a particular process and the risks one is willing to take in connection with it.

The narrower the zone, i.e. the closer the APL and RPL are to each other, the larger the sample size will have

to be. This approach will permit a realistic appraisal of the effectiveness of any acceptance control system, and

will provide a descriptive method for showing just what any given control system is intended to do.

As with any acceptance sampling system, the four elements required for the definition of an acceptance

control chart are:
a) an acceptable process level (APL) associated with a one-sided α-risk;
b) a rejectable process level (RPL) associated with a one-sided β-risk;
c) an action criterion or acceptance control limit (ACL);
d) the sample size (n).

NOTE Generally, the defined risks are one-sided in this part of ISO 7870. In the case of two-sided specifications, the risks

are either a 5 % risk to go above an upper limit or a 5 % risk to go below a lower limit. This results in a 5 % (not 10 %) total risk.

Simplicity of operation is of critical importance to the use of a procedure such as an acceptance control chart.

Only the acceptance control limits and the sampling instructions (such as sample size, frequency, or method

of selection) need to be known to the operator who uses the chart, although training him to understand the

derivation is not difficult and can be helpful. It is thus no more complicated to use than the Shewhart chart.

The supervisor, quality expert, or trained operator will derive these limits without much effort from the above

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ISO 7870-3:2012(E)

considerations and will obtain a more meaningful insight into the process acceptance procedure, and a better

understanding of the control implications.
6 Acceptance control of a process
6.1 Plotting the chart

The sample average value of the quality characteristic is plotted on acceptance control charts in the following

way. A point is plotted on the chart for each sample with an identification number (numerical order, time order,

etc.) on the horizontal scale, and the corresponding sample average on the vertical scale.

6.2 Interpreting the chart
When the plotted point falls above the upper acceptance c
...

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