SIST-TP ISO/TR 8550-1:2010
Guidance on the selection and usage of acceptance sampling systems for inspection of discrete items in lots -- Part 1: Acceptance sampling
Guidance on the selection and usage of acceptance sampling systems for inspection of discrete items in lots -- Part 1: Acceptance sampling
ISO TR 8550-1:2007 gives general guidance on the selection of an acceptance sampling system, scheme or plan. It does this principally in the context of standards that either already exist or are presently under development.
The guidance is confined to acceptance sampling of products that are supplied in lots and that can be classified as consisting of discrete items (i.e. discrete articles of product). It is assumed that each item in a lot can be identified and segregated from the other items in the lot and has an equal chance of being included in the sample. Each item of product is countable and has specific characteristics that are measurable or classifiable as being conforming or nonconforming (to a given product specification).
Standards on acceptance sampling are typically generic, as a result of which they can be applied to a wide variety of inspection situations. These include, but are not limited to, the following: end items, such as complete products or sub-assemblies; components and raw materials; services; materials in process; supplies in storage; maintenance operations; data or records; and administrative procedures.
Although ISO TR 8550-1:2007 is written principally in terms of manufacture and production, this should be interpreted liberally, as it is applicable to the selection of sampling systems, schemes and plans for all types of products and processes as defined in ISO 9000.
Lignes directrices pour la sélection d'un système, d'un programme ou d'un plan d'échantillonnage pour acceptation pour le contrôle d'unités discrètes en lots -- Partie 1: Lignes directrices générales pour l'échantillonnage pour acceptation
Napotek za izbiro in uporabo sistemov prevzemnega vzorčenja za kontrolo diskretnih primerkov v partijah (lotih) - 1. del: Prevzemno vzorčenje
Ta del ISO/TR 8660 podaja splošen napotek za izbiro sistema prevzemnega vzorčenja ali načrta. Podaja ga predvsem glede na standarde, ki bodisi že obstajajo bodisi se trenutno razvijajo. (Za bolj podrobne informacije glede določenih sistemov prevzemnega vzorčenja, glej ISO/TR 8550-2 za vzorčenje po opisnih spremenljivkah ali ISO/TR 8550-3 za vzorčenje po spremenljivkah). Napotek v tem delu ISO/TR 8550 je omejen na prevzemno vzorčenje produktov, ki se dobavljajo v partijah, in ki se lahko klasificirajo kot sestavljeni iz diskretnih primerkov (tj. diskretni predmeti produkta). Predpostavlja se, da se lahko vsak primerek iz partije prepozna in loči od drugih primerkov iz partije ter ima enako možnost vključitve v vzorec. Vsak primerek produkta je števen in ima določene karakteristike, ki se lahko merijo in razvrstijo kot skladne ali neskladne (s podano produktno specifikacijo).
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-julij-2010
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GLVNUHWQLKSULPHUNRYYSDUWLMDK ORWLK GHO 3UHY]HPQRY]RUþHQMH
Guidance on the selection and usage of acceptance sampling systems for inspection of
discrete items in lots -- Part 1: Acceptance sampling
Lignes directrices pour la sélection d'un système, d'un programme ou d'un plan
d'échantillonnage pour acceptation pour le contrôle d'unités discrètes en lots -- Partie 1:
Lignes directrices générales pour l'échantillonnage pour acceptation
Ta slovenski standard je istoveten z: ISO/TR 8550-1:2007
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
TECHNICAL ISO/TR
REPORT 8550-1
First edition
2007-06-01
Guidance on the selection and usage of
acceptance sampling systems for
inspection of discrete items in lots —
Part 1:
Acceptance sampling
Lignes directrices pour la sélection d'un système, d'un programme ou
d'un plan d'échantillonnage pour acceptation pour le contrôle d'unités
discrètes en lots —
Partie 1: Lignes directrices générales pour l'échantillonnage pour
acceptation
Reference number
©
ISO 2007
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ii © ISO 2007 – All rights reserved
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Abuses and uses of acceptance sampling . 2
5 Acceptance sampling plans, schemes and systems. 5
6 Practical and economic advantages of using standard sampling plans. 5
7 Attributes versus variables. 7
8 Further considerations influencing a selection. 8
9 Making a comparison of the methods for sampling inspection . 23
10 Other methods sometimes adopted in practice . 29
11 Relevance of market and production conditions . 31
12 The final selection — Realism . 32
Annex A (informative) Example of a simple model for profit maximization under destructive
inspection by attributes . 33
Bibliography . 37
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.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
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/TR 8550-1 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This first edition of ISO/TR 8550-1, together with ISO/TR 8550-2 and ISO/TR 8550-3, cancels and replaces
ISO/TR 8550:1994.
ISO/TR 8550 consists of the following parts, under the general title Guidance on the selection and usage of
acceptance sampling systems for inspection of discrete items in lots:
⎯ Part 1: Acceptance sampling
⎯ Part 3: Sampling by variables
The following part is under preparation:
⎯ Part 2: Sampling by attributes
iv © ISO 2007 – All rights reserved
Introduction
This part of ISO/TR 8550 gives guidance on the selection of an appropriate acceptance sampling scheme for
the inspection of discrete items submitted in lots from the schemes described in various national and
international standards.
There are many situations where products (materials, parts, components, assemblies and systems) are
transferred from one organization to another, where the organizations may be different companies or parts of
a single company or even different shops within a plant. In these situations both the supplier and the customer
may use acceptance sampling procedures to satisfy themselves that the product is of acceptable quality.
Suppliers will be seeking to maintain a reputation for good quality and to reduce the likelihood of claims under
warranty, but without incurring unnecessary production and supply costs. On the other hand, customers will
require adequate evidence, at minimum cost to themselves, that the product they receive conforms to
specifications. Compared with, say, 100 % inspection, suitable sampling methods will often be beneficial in
achieving these aims. Sometimes acceptance sampling methods are the only practical procedure, especially
when the tests for conformance are destructive.
Several types of sampling systems, schemes and plans are available for these purposes. They are presented
in a number of ISO Standards that explain how they are to be used. However, it is often difficult to decide on
the most appropriate procedure for use in a particular situation. The purpose of this part of ISO/TR 8550 is to
assist in that decision.
The choice of sampling system, scheme or plan depends on a number of conditions and on the prevailing
circumstances. In any supply situation, the first essential is that the supplier and the customer understand,
and have agreed upon, the requirements and the basis for release and acceptance of the product, including
any acceptance sampling methods to be used.
Lots that are non-acceptable cause difficulties for both supplier and customer. The supplier incurs additional
costs in rework, scrap, increased inspection, damage to reputation and possibly loss of sales. Delays in
delivery and re-inspection costs are a burden to the customer. For these reasons, it is usually considered
essential for the supplier to provide lots that have a very high probability of being accepted, i.e. 95 % or more.
The supplier has to ensure that quality control of the production or delivery process provides lots of a quality
sufficient to meet this objective. A basic principle of some acceptance sampling inspection schemes is to
promote the production of lots of acceptable quality. The primary purpose of these schemes is not to
discriminate between acceptable and non-acceptable lots, i.e. to sort, but to keep production under control to
yield an acceptable process average quality. Although all acceptance sampling plans are discriminatory to
some degree, the process average quality (expressed in terms of percent nonconforming or number of
nonconformities) should not be greater than half the acceptance quality limit in order to ensure a very high
probability of acceptance.
The primary purpose of the ISO/TR 8550 series is to give guidance on the selection of an acceptance
sampling system, scheme or plan. It does this principally by reviewing the available systems specified by
various standards and showing ways in which these can be compared in order to assess their suitability for an
intended application. The guide also indicates how prior knowledge of the manufacturing or service delivery
process and quality performance might influence the choice of sampling system, scheme or plan, and likewise
how the particular needs of the customer affect selection. Some specific circumstances encountered in
practice are described and the method of choosing a plan is explained. Some checklists or pointers and tables
are provided to assist users in selecting an appropriate system, scheme or plan for their purposes. Charts are
included to illustrate the procedures to be followed in the selection process.
This publication does not purport to include all the necessary provisions of a contract. Users are responsible
for its correct application.
TECHNICAL REPORT ISO/TR 8550-1:2007(E)
Guidance on the selection and usage of acceptance sampling
systems for inspection of discrete items in lots —
Part 1:
Acceptance sampling
1 Scope
This part of ISO/TR 8550 gives general guidance on the selection of an acceptance sampling system, scheme
or plan. It does this principally in the context of standards that either already exist or are presently under
development. (For more detailed information about specific acceptance sampling systems, see
ISO/TR 8550-2 for sampling by attributes or ISO/TR 8550-3 for sampling by variables.)
The guidance in this part of ISO/TR 8550 is confined to acceptance sampling of products that are supplied in
lots and that can be classified as consisting of discrete items (i.e. discrete articles of product). It is assumed
that each item in a lot can be identified and segregated from the other items in the lot and has an equal
chance of being included in the sample. Each item of product is countable and has specific characteristics that
are measurable or classifiable as being conforming or nonconforming (to a given product specification).
Standards on acceptance sampling are typically generic, as a result of which they can be applied to a wide
variety of inspection situations. These include, but are not limited to, the following:
a) end items, such as complete products or sub-assemblies;
b) components and raw materials;
c) services;
d) materials in process;
e) supplies in storage;
f) maintenance operations;
g) data or records;
h) administrative procedures.
Although this part of ISO/TR 8550 is written principally in terms of manufacture and production, this should be
interpreted liberally, as it is applicable to the selection of sampling systems, schemes and plans for all types of
products and processes as defined in ISO 9000.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition listed applies. For undated references, the latest edition of the referenced
document (including any amendment) 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
ISO 9000, Quality management systems — Fundamentals and vocabulary
3 Terms and definitions
For the purposes of this part of ISO/TR 8550, the terms and definitions given in ISO 3534-1, ISO 3534-2 and
ISO 9000 apply.
4 Abuses and uses of acceptance sampling
4.1 Abuses of acceptance sampling
Acceptance sampling has become unpopular since the early 1980s. Some of the reasons for this (although
certainly not all) are well founded, so it is important to be able to distinguish those situations where
acceptance sampling should not be used from those where it may be appropriate.
The chief arguments used against the use of acceptance sampling are as follows.
a) When quality is generally very high, the sample sizes needed to detect a slip in quality are
uneconomically large.
b) Quality cannot be inspected into a product.
c) It is far better to establish a robust design and to implement comprehensive process controls than to try to
find and eliminate nonconforming items after manufacture.
d) Most acceptance sampling standards are indexed in terms of acceptable quality level (AQL). Once an
AQL has been established and quality has been brought sufficiently below the AQL to achieve high
probabilities of lot acceptance, there is no incentive for the producer to try continuously to improve quality.
e) Quoting an AQL is tantamount to granting a licence to produce defects.
f) The only acceptable quality level is zero defects.
These arguments are examined in turn in the following subclauses.
4.2 Example 1
[18]
The following simplified example, devised by Baillie , demonstrates how the optimum sampling plan can
vary according to the quality level against which it is desired to guard. A certain item is produced in lots of size
10 000, with a unit production cost of £10,00. The selling price per item is £a in accepted lots and at a
discounted price of £0,50 in lots non-accepted by the acceptance procedure. Testing is destructive, and the
cost of testing each item is £1,00. The downstream cost (e.g. warranty cost plus loss of goodwill) of a
nonconforming item in an accepted lot is £10 000, but zero in non-accepted lots sold at a discount. Historical
data indicate that the process fraction nonconforming is p for 99 % of lots, but that it unaccountably and
randomly slips to 100p for 1 % of the lots. A single sampling plan by attributes is to be used, i.e. a random
sample of size n is to be selected from each lot, and the lot is to be considered acceptable if the sample
contains no more than Ac nonconforming items. What is the optimal sampling plan, i.e. the plan that
maximizes the profit per item sold?
Mathematical details are provided in Annex A for information. Table 1 shows the optimal sampling plan for a
range of values of the process quality level p. The results are instructive.
2 © ISO 2007 – All rights reserved
Table 1 — Optimal sampling plans for Example 1
Optimal plan
Selling price
Usual quality Quality level Average profit
level, in fraction after slippage, in per item sold
per item, a
Acceptance
nonconforming fraction nonconforming Sample size n (£)
(£)
number, Ac
0,001 00 0,100 104 2 20,25 0,022
0,000 50 0,050 139 1 15,40 0,091
0,000 30 0,030 197 1 13,60 0,211
0,000 20 0,020 249 1 12,75 0,280
0,000 10 0,010 141 0 12,00 0,378
0,000 09 0,009 137 0 11,95 0,436
0,000 08 0,008 129 0 11,90 0,499
0,000 07 0,007 113 0 11.85 0,570
0,000 06 0,006 86 0 11,75 0,603
0,000 05 0,005 34 0 11,70 0,710
0,000 04 0,004 Accept without sampling 11,60 0,804
0,000 03 0,003 Accept without sampling 11,50 0,903
0,000 02 0,002 Accept without sampling 11,35 0,952
0,000 01 0,001 Accept without sampling 11,20 1,001
Not surprisingly, it is found that improvements in the quality level allow the selling price to be decreased while
at the same time increasing the profit per item sold. At first, improvements in quality levels necessitate larger
sample sizes in order to be able to provide the necessary discrimination between the two quality levels. As
quality levels improve, the optimal acceptance number Ac reduces and there comes a point when the sample
size that is required also begins to reduce until, eventually, it becomes uneconomical to sample at all. This
final state is called “indirect inspection” as the inspection has effectively been transferred from the producer to
the consumer; nonconforming items are so rare that it is more economical not to sample and inspect but to
reimburse consumers on the infrequent occasions that they invoke the warranty. Thus 4.1a) is seen to be
misleading for, when quality levels reach a sufficiently high level, acceptance sampling simply becomes an
unnecessary overhead rather than requiring uneconomically large sample sizes.
4.3 Inspecting quality into a product
Inspection makes little difference to the outgoing quality if the incoming quality is more or less constant unless
the sample size is a large proportion of the lot size, in which case the inspection process is a large overhead.
Either way, it is not a particularly sensible approach to improving quality levels.
4.4 Design and control
The advantages of establishing a robust design and a comprehensive process control system are many. The
robust design places the least possible demands on the manufacturing process and the process control
system tends to prevent process parameters from straying too far from their target values, so process
variation and waste is kept low and output quality is kept high. Moreover, the design and the control system of
the production process can be reviewed and improved in the light of experience to provide continual quality
improvement.
4.5 AQLs
The initials AQL used to stand for Acceptable Quality Level, although in reality the AQL is simply an index to a
sampling plan. Standards tried to make this clear by explaining that the level was acceptable for the purposes
of acceptance sampling (rather than in an absolute sense). Indeed, lot quality levels typically have to be better
than half the AQL to have a very high chance of being accepted.
During the late 20th century, many companies came to realize that the only way to survive in a global
marketplace was to strive endlessly for improved levels of quality. The notion that any level of quality other
than zero defects (see 4.7) was acceptable began to be scorned. In order to clarify the situation, the meaning
of the initials AQL was changed in international standards to Acceptance Quality Limit, which more accurately
describes its function. Unfortunately, the damage was already done, for many organizations no longer
entertain the use of standards indexed by AQL.
The argument that AQLs provide no incentive for the producer to continuously improve quality once it has
been improved to a level that is better than the AQL is not a strong one; in many medium or long-term
agreements between supplier and customer, a progressive reduction in the AQL could easily be agreed upon
and written into the contract. Moreover, a producer intent on staying in business is already striving for better
levels of quality in order to maintain or improve his place in the national or global market.
4.6 A licence to produce defects?
It is untrue that an AQL provides a licence for the producer to provide defects. Most AQL-indexed standards
expressly caution that the designation of an AQL does not imply that the supplier has the right knowingly to
supply any nonconforming items of product.
4.7 The zero defects philosophy
[19]
Crosby introduced the idea that quality can be free, i.e. the extra resources used to improve quality would
often be more than compensated for by the reduction in rework or scrap or loss of goodwill. Unfortunately, the
corresponding idea that the producer should strive for a perfect process that produces no nonconforming
items inevitably often became misconstrued to stipulate that acceptance sampling plans should always have
an acceptance number of zero, i.e. that the plans should lead to lot non-acceptance if one or more
nonconforming items are found in the sample. Example 1 shows this not to be an inevitable corollary. An
acceptance number of zero is seen to be optimal only over a certain range of quality levels; at lower quality
levels, acceptance numbers of 1 or more are optimal, while at higher quality levels, it is best not to sample at
all.
4.8 The use of acceptance sampling
For many mature production processes, quality levels will have become so close to perfection that it is a
needless waste of resources to implement acceptance sampling procedures. The design will have been
refined such that there are no difficulties in the production process due to any of the process parameters being
difficult to achieve or maintain, and safeguards will have been built into the process control system wherever
necessary.
It can be seen from Table 1 that acceptance sampling became redundant at a quality level somewhere in the
range 0,000 1 to 0,000 2 nonconforming. One of the variables in Example 1 was the 1 % of lots that slip to the
worse quality level. If this percentage could be substantially reduced, then acceptance sampling would
become redundant at quality levels in the good lots worse than 0,000 2 nonconforming. Thus a two-pronged
attack on internal variation and on external, “special causes” of variation in the production process, together
with repeated reviews of the product design, ultimately lead to acceptance sampling becoming unnecessary
for many products.
However, what about the early stages while the process and its controls are being refined? Example 1
demonstrates that appropriate use of acceptance sampling can play a key part in maximizing profitability
during this interim period.
Some processes never run long enough to become mature. This is particularly true for some defence
industries. There is not much point in continuing to build an offensive weapon of a given specification once an
effective defence to it has been devised and is widely available. Specifications are therefore frequently
modified, which can make it difficult to achieve a robust design or efficient process controls. Sometimes the
4 © ISO 2007 – All rights reserved
materials used in the production of armaments are so new that they have properties and limitations that are
not completely understood. Sometimes it is in the assembly of individually sound components into complex
items where it might be necessary to use acceptance sampling to maintain quality; it will be too late once the
items are being used in anger. Sometimes what might seem to be very high levels of nonconformity may be
acceptable. For example, an over-the-shoulder anti-tank weapon system would be more than acceptable even
if it had only a 50 % chance of destroying a tank costing one thousand times as much, although this translates
into 50 % nonconforming. Acceptance sampling may be applied periodically to munitions held in storage over
many years, to check that they have not degraded to an intolerable level. In the computer industry, a process
yield as low as 50 % when etching the latest and fastest computer chips may be considered acceptable.
Acceptance sampling might even be used as a tool by which to verify statistical process control results.
In summary, acceptance sampling has a legitimate part to play in the quality assurance of many products.
5 Acceptance sampling plans, schemes and systems
An acceptance sampling plan is a set of rules by which a lot is to be inspected and its acceptability determined.
The plan stipulates the number of items (units) in the sample, to be drawn randomly from a lot for inspection
against the product specification. The lot is then sentenced as “acceptable” or “non-acceptable” according to
how the inspection results compare with the criteria of the acceptance sampling plan.
Sometimes, when a long series of lots is being inspected, a sampling procedure might call for a shift from one
sampling plan to another, depending on the current and previous sample results. Sampling procedures that
call for switching from one sampling plan to another, and possibly back again, are called sampling schemes.
A sampling scheme might also call for discontinuation of inspection if product quality appears to remain poor.
The customer may then shift to another supplier, if available, or initiate 100 % screening until the supplier can
improve the production process sufficiently to produce acceptable product.
In the case of destructive testing, the customer may cease to accept product until the supplier has
demonstrated to his satisfaction that the production problems that were giving rise to the previous low quality
have been overcome.
A collection of sampling plans and related sampling schemes constitute a sampling system. The system is
generally indexed in some way, e.g. by lot size, inspection level and acceptance quality limit (e.g. ISO 2859-1).
The standards reviewed in ISO/TR 8550-2 and ISO/TR 8550-3 present plans for single, double, multiple or
sequential sampling. Procedures for skip-lot sampling for inspection by attributes are given in ISO 2859-3.
A comparison of the various sampling methods and the principles on which they are based assists in
assessing their suitability for a particular application and enables an appropriate selection to be made.
6 Practical and economic advantages of using standard sampling plans
To those concerned with the writing of specifications, it is of benefit that statistically sound sampling
procedures be provided. Because there are economies of scale for larger lots, most sampling schemes
presented in the standards reviewed in ISO/TR 8550-2 and ISO/TR 8550-3 relate sample size to lot size.
Apart from providing control over the methods of selection of the sample, these standards should normally be
invoked because they specify requirements that control the treatment of nonconformities found during
inspection and the treatment of lots resubmitted after initial non-acceptance. Furthermore, most of these
sampling systems contain built-in switching rules (e.g. from ‘normal’ to ‘tightened’ or to ‘reduced’ inspection) to
adjust the sampling plan in the event of deterioration or improvement in quality. Use of these basic reference
standards can save much time often wasted in subjective discussion, and reduce the large areas of discretion
often contained in non-standard sampling schemes that have only limited value, particularly for international
trade.
Sampling involves risk and, quite naturally, all parties concerned attempt to minimize their share. Theoretically,
these risks are functions of the sampling plan and the quality level agreed upon, without relation to the
industry or the product. In practice, these risks are reduced by controlling the production process and
improving the level of quality.
These risks cannot be eliminated, but they can be precisely calculated and economically assessed by the use
of modern statistical techniques. Consequently, it is of benefit to all parties that statistically sound acceptance
criteria be specified in product/process specifications and that, wherever possible, the generally applicable
basic reference standards on sampling, such as the ISO 2859 and ISO 3951 series, be utilized.
In general, when arriving at the optimum performance of an acceptance sampling plan or scheme, the costs of
preventing nonconformities should be balanced against the probabilities of failure in service. Subject to
various assumptions being made with regard to the sample size to lot size ratio (n/N) and to the appropriate
distribution theory, it is a relatively straightforward matter to formulate sampling plans from statistical theory.
Note that, while existing standards on sampling by variables are only applicable to product characteristics that
have normal distributions, standards on sampling by attributes are not dependent on the distributional shape
of the product characteristics.
Development of generic acceptance sampling standards is a more difficult matter. There are undeniable
advantages in having relatively few standard schemes, as this leads to greater uniformity of action and
simplifies the administrative procedures across organizational and national boundaries. However, for these to
be adopted for general use by industry worldwide, sampling standards have to be practical and flexible
enough to take account of the many and varied situations met in practice. The established AQL-indexed
procedures given in the ISO 2859 and ISO 3951 series, and in corresponding international standards, have
served industry well in the past, and are continuing to be developed to fulfil current and future needs.
The motivation for acceptance sampling is primarily economic: inspection of a sample from a lot is the (usually
small) price paid to achieve desirable quality in the accepted lots. This quality is achieved by two pressures:
1) the purely statistical pressure of different probabilities of acceptance of good and bad quality lots;
2) when sequences of lots are purchased, the commercial pressure of frequent non-acceptance of lots
and the switch to tightened inspection or discontinuation of inspection when quality is poor.
The problem associated with acceptance sampling inspection relates to defining unambiguously the criteria
used to judge discrete individual items supplied in quantity, the criterion for acceptance of the lot, the quality
level expected from the manufacturing process, the discrimination afforded by the sampling plans and the
rules to be followed when a lot is not accepted. Above all, however, it is necessary to design the sampling
scheme so that it can be invoked easily in a purchasing contract. The sampling plans in the sets of related
standards discussed in ISO/TR 8550-2 and ISO/TR 8550-3 enable this to be done efficiently.
The parties should agree on the following:
a) the specification to which the discrete items of product are to conform; this is necessary because, in all
dealings between the parties, there has to be agreement on what constitutes a conforming item and what
constitutes a nonconforming item;
b) whether the acceptance of the product is to be determined by the acceptance of individual items or
collectively by the acceptance of inspection lots of items (acceptance of individual items precludes
sampling).
When the acceptance is to be on a lot basis, the agreement between supplier and recipient needs to include
— the criteria for item conformance,
— the criteria for lot acceptance,
— the criteria for non-acceptance of the lot, and
— the acceptance sampling system, scheme or plan to be used.
The latter should be based on risk factors that are mutually acceptable to both producer and customer.
6 © ISO 2007 – All rights reserved
Having agreed on the acceptance sampling system, scheme or plan to use, the supplier knows, for various
quality levels, the probability that his supply lots will be accepted. Likewise, the customer understands the
protection provided by the sampling system, scheme or plan against acceptance of poor quality product.
Current standards present plans for single, double, multiple, sequential and skip-lot sampling. A comparison of
the various sampling methods and the principles on which they are based will assist in assessing their
suitability for a particular application and enable an appropriate selection to be made.
7 Attributes versus variables
Acceptance sampling standards generally describe procedures for inspection by attributes or for inspection by
variables; a key decision to make is which of these to use.
If certain assumptions are true, the variables method has the advantage of generally requiring a smaller
sample size than the attributes method to attain a given degree of protection against incorrect decisions. In
addition, it provides more information on whether quality is being adversely affected by process mean,
process variability, or both.
The attributes method has the advantage that it is more robust in the sense that it is not subject to
assumptions of distributional shape, and that it is simpler to use. The larger sample sizes and consequential
increased costs associated with using attribute sampling methods might be justifiable for these reasons.
Furthermore, an attribute scheme might be understood and accepted more readily by inspection personnel.
To avoid the assumption of normality and the attendant inability or difficulty in checking for this with “short
runs” or lots of an “isolated” nature, sampling by attributes is recommended even to the extent of converting
measurements to attributes.
When the quality characteristics are known to be normally distributed, at least to a good approximation,
sampling by variables has a substantial advantage when inspection is expensive, e.g. when testing is
destructive. Often, a simple mathematical transformation, such as taking the logarithm or square root, will
convert a set of measurements from a non-normal to a normal, or near-normal, distribution.
Table 2 gives a comparison of the sample sizes for inspection by attributes and by variables for certain lot size
ranges when using single sampling plans at inspection level II (see 8.6.1) under normal inspection. Similar
advantages exist when comparing inspection by variables and by attributes in double and sequential sampling.
Table 2 — Comparison of sample sizes in inspection by attributes and by variables
Single sample sizes under normal inspection
Inspection by variables (ISO 3951-1)
Inspection
Lot sizes
by attributes
Unknown process Known process standard
(ISO 2859-1)
standard deviation deviation
16 to 25 5 4 3
91 to 150 20 13 8
281 to 500 50 25 12
1 201 to 3 200 125 50 18
35 001 to 150 000 500 125 32
8 Further considerations influencing a selection
8.1 Long and short production runs
Most acceptance sampling standards are intended for use primarily on a continuing series of lots of sufficient
duration to allow the switching rules to be applied. This implies a “long” production run.
The principal exception is ISO 2859-2, which comprises limiting quality (LQ) plans that can be used when the
switching rules of ISO 2859-1 are not applicable. These are primarily intended for use with single lots or lots of
an “isolated nature”. By implication, this embraces a “short” series of inspection lots - or a “short” production
run.
ISO 2859-5 and ISO 3951-5 provide sequential plans that match other standards in their respective series,
and in many cases are thus similarly applicable to long or short runs.
In order for a production run to qualify as “long”, one criterion is clearly that the switching rules have a
reasonable chance of coming into effect if “the quality is unsatisfactory”. It is equally clear that this alone
raises a number of supplementary issues (as indicated by the quotation marks) depending on the
requirements and circumstances prevailing in each case considered. It is impossible to stipulate simply and
precisely what constitutes a short run (number of lots) in the context of sampling inspection.
In the absence of any other guide or evidence on which to base a judgement, anything up to 10 consecutive
inspection lots should be considered as a “short run”, and the plans in ISO 2859-2 should be used. However,
lots should not be subdivided arbitrarily in order to create a “long run”. It is generally preferable to have large
homogeneous lots because they allow a smaller sample size to lot size ratio, and provide better
representation by the sample, sharper discrimination and more economical inspection.
In a long production run, there is continuity and stability, so production settles down to a long-term stable
process average. Nevertheless, the quality of individual lots varies about this process average. On the other
hand, at the start of production, after a significant break or change in production, or for a short production run,
the lot quality might well be somewhat different and more variable, even markedly so. The practical factor to
consider is whether there is evidence that a stable process average has been established and still exists.
8.2 Nonconformity and nonconforming item
8.2.1 Failure to conform
8.2.1.1 General
Any failure to conform to a specified product characteristic, dimension, attribute or performance requirement
represents nonconformity. A nonconforming item might have one or more nonconformities.
The failure of a ballpoint pen to write, for example, is a nonconformity; the pen is nonconforming. However,
the same pen might have failed to conform in a number of other ways, e.g. colour, dimensions, etc. A pen that
exhibited several nonconformities would still be counted as one nonconforming item.
The qualification “nonconformity” does not necessarily imply that the unit of product cannot be used for the
purpose intended. For example, a brick with one of its dimensions outside the prescribed tolerance interval,
though nonconforming, can still be used for building.
The distinction between nonconformity and nonconforming item is of no importance if the items have no more
than one nonconformity, but becomes essential when multiple nonconformities can occur.
The quality of a given quantity of product may be expressed either as “percent nonconforming” or as the
“number of nonconformities per hundred items”, but these are only interchangeable when items can have no
more than one nonconformity.
Under sampling by attributes, sampling plans are available for either percent nonconforming or the number of
nonconformities per hundred items.
8 © ISO 2007 – All rights reserved
8.2.1.2 Example 2
In counting pinholes in metal foil, the number of pinholes per square metre might be of interest. Here we
would count all the pinholes in each square metre (item) examined and then express the quality in pinholes
per 100 m .
8.2.1.3 Example 3
Suppose that a lot consists of 500 articles. Of these, 480 conform and are acceptable, 15 have one
nonconformity each, four have two nonconformities each, and one has three nonconformities.
The lot percent nonconforming is given by the formula:
number of nonconforming items
Percent nonconforming =×100
total number of items
=×100
=4;
that is, the lot is 4 % nonconforming.
The number of nonconformities per hundred items in the lot is given by the formula:
number of nonconformities
Nonconformities per 100 items =×100
total number of items
=×100
= 5,2 ;
that is, the lot has 5,2 nonconformities per hundred items.
8.2.1.4 Comments on Examples 2 and 3
Hence, under sampling by attributes, whether percent nonconforming or nonconformities per hundred items is
to be used is a matter for individual consideration in each particular case. The important thing is that it has to
be considered, specified, and agreed upon beforehand, not left until a sample has been inspected and then
considered.
Under sampling by variables, sampling plans are only available for percent nonconforming, so there is no
choice to be made. However, different quality characteristics might belong to different classes (see 8.2.3), in
which case they are treated separately.
8.2.1.5 Factors to be taken into account
Factors to be taken into account in deciding whether to use percent nonconforming or nonconformities per
hundred items under sampling by attributes are as follows.
a) Under inspection for percent nonconforming it is assumed that, if an item contains one or more
nonconformities, the item is nonconforming and is not acceptable.
It also presupposes that the number of different ways in which an item can be nonconforming is limited
and known, e.g. there are only 5 ways in which each particular item could be nonconforming [see also
item b)].
b) Under inspection for nonconformities, every nonconformity found is counted. Three nonconformities found
in one item count as three, and are given the same weight as three items each having one nonconformity.
A special case arises when a nonconformity can occur an unknown and almost unlimited number of times
in items, e.g. surface blemishes or pinholes can occur in any number and it is not known how many times
they do not occur, so percent nonconforming for this feature is meaningless. In such cases,
nonconformities per hundred items should be used (see Example 2).
NOTE Percent nonconforming under sampling inspection by attributes implies a binomial distribution; for
nonconformities per hundred items, a Poisson distribut
...
TECHNICAL ISO/TR
REPORT 8550-1
First edition
2007-06-01
Guidance on the selection and usage of
acceptance sampling systems for
inspection of discrete items in lots —
Part 1:
Acceptance sampling
Lignes directrices pour la sélection d'un système, d'un programme ou
d'un plan d'échantillonnage pour acceptation pour le contrôle d'unités
discrètes en lots —
Partie 1: Lignes directrices générales pour l'échantillonnage pour
acceptation
Reference number
©
ISO 2007
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ii © ISO 2007 – All rights reserved
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Abuses and uses of acceptance sampling . 2
5 Acceptance sampling plans, schemes and systems. 5
6 Practical and economic advantages of using standard sampling plans. 5
7 Attributes versus variables. 7
8 Further considerations influencing a selection. 8
9 Making a comparison of the methods for sampling inspection . 23
10 Other methods sometimes adopted in practice . 29
11 Relevance of market and production conditions . 31
12 The final selection — Realism . 32
Annex A (informative) Example of a simple model for profit maximization under destructive
inspection by attributes . 33
Bibliography . 37
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.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
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/TR 8550-1 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 5, Acceptance sampling.
This first edition of ISO/TR 8550-1, together with ISO/TR 8550-2 and ISO/TR 8550-3, cancels and replaces
ISO/TR 8550:1994.
ISO/TR 8550 consists of the following parts, under the general title Guidance on the selection and usage of
acceptance sampling systems for inspection of discrete items in lots:
⎯ Part 1: Acceptance sampling
⎯ Part 3: Sampling by variables
The following part is under preparation:
⎯ Part 2: Sampling by attributes
iv © ISO 2007 – All rights reserved
Introduction
This part of ISO/TR 8550 gives guidance on the selection of an appropriate acceptance sampling scheme for
the inspection of discrete items submitted in lots from the schemes described in various national and
international standards.
There are many situations where products (materials, parts, components, assemblies and systems) are
transferred from one organization to another, where the organizations may be different companies or parts of
a single company or even different shops within a plant. In these situations both the supplier and the customer
may use acceptance sampling procedures to satisfy themselves that the product is of acceptable quality.
Suppliers will be seeking to maintain a reputation for good quality and to reduce the likelihood of claims under
warranty, but without incurring unnecessary production and supply costs. On the other hand, customers will
require adequate evidence, at minimum cost to themselves, that the product they receive conforms to
specifications. Compared with, say, 100 % inspection, suitable sampling methods will often be beneficial in
achieving these aims. Sometimes acceptance sampling methods are the only practical procedure, especially
when the tests for conformance are destructive.
Several types of sampling systems, schemes and plans are available for these purposes. They are presented
in a number of ISO Standards that explain how they are to be used. However, it is often difficult to decide on
the most appropriate procedure for use in a particular situation. The purpose of this part of ISO/TR 8550 is to
assist in that decision.
The choice of sampling system, scheme or plan depends on a number of conditions and on the prevailing
circumstances. In any supply situation, the first essential is that the supplier and the customer understand,
and have agreed upon, the requirements and the basis for release and acceptance of the product, including
any acceptance sampling methods to be used.
Lots that are non-acceptable cause difficulties for both supplier and customer. The supplier incurs additional
costs in rework, scrap, increased inspection, damage to reputation and possibly loss of sales. Delays in
delivery and re-inspection costs are a burden to the customer. For these reasons, it is usually considered
essential for the supplier to provide lots that have a very high probability of being accepted, i.e. 95 % or more.
The supplier has to ensure that quality control of the production or delivery process provides lots of a quality
sufficient to meet this objective. A basic principle of some acceptance sampling inspection schemes is to
promote the production of lots of acceptable quality. The primary purpose of these schemes is not to
discriminate between acceptable and non-acceptable lots, i.e. to sort, but to keep production under control to
yield an acceptable process average quality. Although all acceptance sampling plans are discriminatory to
some degree, the process average quality (expressed in terms of percent nonconforming or number of
nonconformities) should not be greater than half the acceptance quality limit in order to ensure a very high
probability of acceptance.
The primary purpose of the ISO/TR 8550 series is to give guidance on the selection of an acceptance
sampling system, scheme or plan. It does this principally by reviewing the available systems specified by
various standards and showing ways in which these can be compared in order to assess their suitability for an
intended application. The guide also indicates how prior knowledge of the manufacturing or service delivery
process and quality performance might influence the choice of sampling system, scheme or plan, and likewise
how the particular needs of the customer affect selection. Some specific circumstances encountered in
practice are described and the method of choosing a plan is explained. Some checklists or pointers and tables
are provided to assist users in selecting an appropriate system, scheme or plan for their purposes. Charts are
included to illustrate the procedures to be followed in the selection process.
This publication does not purport to include all the necessary provisions of a contract. Users are responsible
for its correct application.
TECHNICAL REPORT ISO/TR 8550-1:2007(E)
Guidance on the selection and usage of acceptance sampling
systems for inspection of discrete items in lots —
Part 1:
Acceptance sampling
1 Scope
This part of ISO/TR 8550 gives general guidance on the selection of an acceptance sampling system, scheme
or plan. It does this principally in the context of standards that either already exist or are presently under
development. (For more detailed information about specific acceptance sampling systems, see
ISO/TR 8550-2 for sampling by attributes or ISO/TR 8550-3 for sampling by variables.)
The guidance in this part of ISO/TR 8550 is confined to acceptance sampling of products that are supplied in
lots and that can be classified as consisting of discrete items (i.e. discrete articles of product). It is assumed
that each item in a lot can be identified and segregated from the other items in the lot and has an equal
chance of being included in the sample. Each item of product is countable and has specific characteristics that
are measurable or classifiable as being conforming or nonconforming (to a given product specification).
Standards on acceptance sampling are typically generic, as a result of which they can be applied to a wide
variety of inspection situations. These include, but are not limited to, the following:
a) end items, such as complete products or sub-assemblies;
b) components and raw materials;
c) services;
d) materials in process;
e) supplies in storage;
f) maintenance operations;
g) data or records;
h) administrative procedures.
Although this part of ISO/TR 8550 is written principally in terms of manufacture and production, this should be
interpreted liberally, as it is applicable to the selection of sampling systems, schemes and plans for all types of
products and processes as defined in ISO 9000.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition listed applies. For undated references, the latest edition of the referenced
document (including any amendment) 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
ISO 9000, Quality management systems — Fundamentals and vocabulary
3 Terms and definitions
For the purposes of this part of ISO/TR 8550, the terms and definitions given in ISO 3534-1, ISO 3534-2 and
ISO 9000 apply.
4 Abuses and uses of acceptance sampling
4.1 Abuses of acceptance sampling
Acceptance sampling has become unpopular since the early 1980s. Some of the reasons for this (although
certainly not all) are well founded, so it is important to be able to distinguish those situations where
acceptance sampling should not be used from those where it may be appropriate.
The chief arguments used against the use of acceptance sampling are as follows.
a) When quality is generally very high, the sample sizes needed to detect a slip in quality are
uneconomically large.
b) Quality cannot be inspected into a product.
c) It is far better to establish a robust design and to implement comprehensive process controls than to try to
find and eliminate nonconforming items after manufacture.
d) Most acceptance sampling standards are indexed in terms of acceptable quality level (AQL). Once an
AQL has been established and quality has been brought sufficiently below the AQL to achieve high
probabilities of lot acceptance, there is no incentive for the producer to try continuously to improve quality.
e) Quoting an AQL is tantamount to granting a licence to produce defects.
f) The only acceptable quality level is zero defects.
These arguments are examined in turn in the following subclauses.
4.2 Example 1
[18]
The following simplified example, devised by Baillie , demonstrates how the optimum sampling plan can
vary according to the quality level against which it is desired to guard. A certain item is produced in lots of size
10 000, with a unit production cost of £10,00. The selling price per item is £a in accepted lots and at a
discounted price of £0,50 in lots non-accepted by the acceptance procedure. Testing is destructive, and the
cost of testing each item is £1,00. The downstream cost (e.g. warranty cost plus loss of goodwill) of a
nonconforming item in an accepted lot is £10 000, but zero in non-accepted lots sold at a discount. Historical
data indicate that the process fraction nonconforming is p for 99 % of lots, but that it unaccountably and
randomly slips to 100p for 1 % of the lots. A single sampling plan by attributes is to be used, i.e. a random
sample of size n is to be selected from each lot, and the lot is to be considered acceptable if the sample
contains no more than Ac nonconforming items. What is the optimal sampling plan, i.e. the plan that
maximizes the profit per item sold?
Mathematical details are provided in Annex A for information. Table 1 shows the optimal sampling plan for a
range of values of the process quality level p. The results are instructive.
2 © ISO 2007 – All rights reserved
Table 1 — Optimal sampling plans for Example 1
Optimal plan
Selling price
Usual quality Quality level Average profit
level, in fraction after slippage, in per item sold
per item, a
Acceptance
nonconforming fraction nonconforming Sample size n (£)
(£)
number, Ac
0,001 00 0,100 104 2 20,25 0,022
0,000 50 0,050 139 1 15,40 0,091
0,000 30 0,030 197 1 13,60 0,211
0,000 20 0,020 249 1 12,75 0,280
0,000 10 0,010 141 0 12,00 0,378
0,000 09 0,009 137 0 11,95 0,436
0,000 08 0,008 129 0 11,90 0,499
0,000 07 0,007 113 0 11.85 0,570
0,000 06 0,006 86 0 11,75 0,603
0,000 05 0,005 34 0 11,70 0,710
0,000 04 0,004 Accept without sampling 11,60 0,804
0,000 03 0,003 Accept without sampling 11,50 0,903
0,000 02 0,002 Accept without sampling 11,35 0,952
0,000 01 0,001 Accept without sampling 11,20 1,001
Not surprisingly, it is found that improvements in the quality level allow the selling price to be decreased while
at the same time increasing the profit per item sold. At first, improvements in quality levels necessitate larger
sample sizes in order to be able to provide the necessary discrimination between the two quality levels. As
quality levels improve, the optimal acceptance number Ac reduces and there comes a point when the sample
size that is required also begins to reduce until, eventually, it becomes uneconomical to sample at all. This
final state is called “indirect inspection” as the inspection has effectively been transferred from the producer to
the consumer; nonconforming items are so rare that it is more economical not to sample and inspect but to
reimburse consumers on the infrequent occasions that they invoke the warranty. Thus 4.1a) is seen to be
misleading for, when quality levels reach a sufficiently high level, acceptance sampling simply becomes an
unnecessary overhead rather than requiring uneconomically large sample sizes.
4.3 Inspecting quality into a product
Inspection makes little difference to the outgoing quality if the incoming quality is more or less constant unless
the sample size is a large proportion of the lot size, in which case the inspection process is a large overhead.
Either way, it is not a particularly sensible approach to improving quality levels.
4.4 Design and control
The advantages of establishing a robust design and a comprehensive process control system are many. The
robust design places the least possible demands on the manufacturing process and the process control
system tends to prevent process parameters from straying too far from their target values, so process
variation and waste is kept low and output quality is kept high. Moreover, the design and the control system of
the production process can be reviewed and improved in the light of experience to provide continual quality
improvement.
4.5 AQLs
The initials AQL used to stand for Acceptable Quality Level, although in reality the AQL is simply an index to a
sampling plan. Standards tried to make this clear by explaining that the level was acceptable for the purposes
of acceptance sampling (rather than in an absolute sense). Indeed, lot quality levels typically have to be better
than half the AQL to have a very high chance of being accepted.
During the late 20th century, many companies came to realize that the only way to survive in a global
marketplace was to strive endlessly for improved levels of quality. The notion that any level of quality other
than zero defects (see 4.7) was acceptable began to be scorned. In order to clarify the situation, the meaning
of the initials AQL was changed in international standards to Acceptance Quality Limit, which more accurately
describes its function. Unfortunately, the damage was already done, for many organizations no longer
entertain the use of standards indexed by AQL.
The argument that AQLs provide no incentive for the producer to continuously improve quality once it has
been improved to a level that is better than the AQL is not a strong one; in many medium or long-term
agreements between supplier and customer, a progressive reduction in the AQL could easily be agreed upon
and written into the contract. Moreover, a producer intent on staying in business is already striving for better
levels of quality in order to maintain or improve his place in the national or global market.
4.6 A licence to produce defects?
It is untrue that an AQL provides a licence for the producer to provide defects. Most AQL-indexed standards
expressly caution that the designation of an AQL does not imply that the supplier has the right knowingly to
supply any nonconforming items of product.
4.7 The zero defects philosophy
[19]
Crosby introduced the idea that quality can be free, i.e. the extra resources used to improve quality would
often be more than compensated for by the reduction in rework or scrap or loss of goodwill. Unfortunately, the
corresponding idea that the producer should strive for a perfect process that produces no nonconforming
items inevitably often became misconstrued to stipulate that acceptance sampling plans should always have
an acceptance number of zero, i.e. that the plans should lead to lot non-acceptance if one or more
nonconforming items are found in the sample. Example 1 shows this not to be an inevitable corollary. An
acceptance number of zero is seen to be optimal only over a certain range of quality levels; at lower quality
levels, acceptance numbers of 1 or more are optimal, while at higher quality levels, it is best not to sample at
all.
4.8 The use of acceptance sampling
For many mature production processes, quality levels will have become so close to perfection that it is a
needless waste of resources to implement acceptance sampling procedures. The design will have been
refined such that there are no difficulties in the production process due to any of the process parameters being
difficult to achieve or maintain, and safeguards will have been built into the process control system wherever
necessary.
It can be seen from Table 1 that acceptance sampling became redundant at a quality level somewhere in the
range 0,000 1 to 0,000 2 nonconforming. One of the variables in Example 1 was the 1 % of lots that slip to the
worse quality level. If this percentage could be substantially reduced, then acceptance sampling would
become redundant at quality levels in the good lots worse than 0,000 2 nonconforming. Thus a two-pronged
attack on internal variation and on external, “special causes” of variation in the production process, together
with repeated reviews of the product design, ultimately lead to acceptance sampling becoming unnecessary
for many products.
However, what about the early stages while the process and its controls are being refined? Example 1
demonstrates that appropriate use of acceptance sampling can play a key part in maximizing profitability
during this interim period.
Some processes never run long enough to become mature. This is particularly true for some defence
industries. There is not much point in continuing to build an offensive weapon of a given specification once an
effective defence to it has been devised and is widely available. Specifications are therefore frequently
modified, which can make it difficult to achieve a robust design or efficient process controls. Sometimes the
4 © ISO 2007 – All rights reserved
materials used in the production of armaments are so new that they have properties and limitations that are
not completely understood. Sometimes it is in the assembly of individually sound components into complex
items where it might be necessary to use acceptance sampling to maintain quality; it will be too late once the
items are being used in anger. Sometimes what might seem to be very high levels of nonconformity may be
acceptable. For example, an over-the-shoulder anti-tank weapon system would be more than acceptable even
if it had only a 50 % chance of destroying a tank costing one thousand times as much, although this translates
into 50 % nonconforming. Acceptance sampling may be applied periodically to munitions held in storage over
many years, to check that they have not degraded to an intolerable level. In the computer industry, a process
yield as low as 50 % when etching the latest and fastest computer chips may be considered acceptable.
Acceptance sampling might even be used as a tool by which to verify statistical process control results.
In summary, acceptance sampling has a legitimate part to play in the quality assurance of many products.
5 Acceptance sampling plans, schemes and systems
An acceptance sampling plan is a set of rules by which a lot is to be inspected and its acceptability determined.
The plan stipulates the number of items (units) in the sample, to be drawn randomly from a lot for inspection
against the product specification. The lot is then sentenced as “acceptable” or “non-acceptable” according to
how the inspection results compare with the criteria of the acceptance sampling plan.
Sometimes, when a long series of lots is being inspected, a sampling procedure might call for a shift from one
sampling plan to another, depending on the current and previous sample results. Sampling procedures that
call for switching from one sampling plan to another, and possibly back again, are called sampling schemes.
A sampling scheme might also call for discontinuation of inspection if product quality appears to remain poor.
The customer may then shift to another supplier, if available, or initiate 100 % screening until the supplier can
improve the production process sufficiently to produce acceptable product.
In the case of destructive testing, the customer may cease to accept product until the supplier has
demonstrated to his satisfaction that the production problems that were giving rise to the previous low quality
have been overcome.
A collection of sampling plans and related sampling schemes constitute a sampling system. The system is
generally indexed in some way, e.g. by lot size, inspection level and acceptance quality limit (e.g. ISO 2859-1).
The standards reviewed in ISO/TR 8550-2 and ISO/TR 8550-3 present plans for single, double, multiple or
sequential sampling. Procedures for skip-lot sampling for inspection by attributes are given in ISO 2859-3.
A comparison of the various sampling methods and the principles on which they are based assists in
assessing their suitability for a particular application and enables an appropriate selection to be made.
6 Practical and economic advantages of using standard sampling plans
To those concerned with the writing of specifications, it is of benefit that statistically sound sampling
procedures be provided. Because there are economies of scale for larger lots, most sampling schemes
presented in the standards reviewed in ISO/TR 8550-2 and ISO/TR 8550-3 relate sample size to lot size.
Apart from providing control over the methods of selection of the sample, these standards should normally be
invoked because they specify requirements that control the treatment of nonconformities found during
inspection and the treatment of lots resubmitted after initial non-acceptance. Furthermore, most of these
sampling systems contain built-in switching rules (e.g. from ‘normal’ to ‘tightened’ or to ‘reduced’ inspection) to
adjust the sampling plan in the event of deterioration or improvement in quality. Use of these basic reference
standards can save much time often wasted in subjective discussion, and reduce the large areas of discretion
often contained in non-standard sampling schemes that have only limited value, particularly for international
trade.
Sampling involves risk and, quite naturally, all parties concerned attempt to minimize their share. Theoretically,
these risks are functions of the sampling plan and the quality level agreed upon, without relation to the
industry or the product. In practice, these risks are reduced by controlling the production process and
improving the level of quality.
These risks cannot be eliminated, but they can be precisely calculated and economically assessed by the use
of modern statistical techniques. Consequently, it is of benefit to all parties that statistically sound acceptance
criteria be specified in product/process specifications and that, wherever possible, the generally applicable
basic reference standards on sampling, such as the ISO 2859 and ISO 3951 series, be utilized.
In general, when arriving at the optimum performance of an acceptance sampling plan or scheme, the costs of
preventing nonconformities should be balanced against the probabilities of failure in service. Subject to
various assumptions being made with regard to the sample size to lot size ratio (n/N) and to the appropriate
distribution theory, it is a relatively straightforward matter to formulate sampling plans from statistical theory.
Note that, while existing standards on sampling by variables are only applicable to product characteristics that
have normal distributions, standards on sampling by attributes are not dependent on the distributional shape
of the product characteristics.
Development of generic acceptance sampling standards is a more difficult matter. There are undeniable
advantages in having relatively few standard schemes, as this leads to greater uniformity of action and
simplifies the administrative procedures across organizational and national boundaries. However, for these to
be adopted for general use by industry worldwide, sampling standards have to be practical and flexible
enough to take account of the many and varied situations met in practice. The established AQL-indexed
procedures given in the ISO 2859 and ISO 3951 series, and in corresponding international standards, have
served industry well in the past, and are continuing to be developed to fulfil current and future needs.
The motivation for acceptance sampling is primarily economic: inspection of a sample from a lot is the (usually
small) price paid to achieve desirable quality in the accepted lots. This quality is achieved by two pressures:
1) the purely statistical pressure of different probabilities of acceptance of good and bad quality lots;
2) when sequences of lots are purchased, the commercial pressure of frequent non-acceptance of lots
and the switch to tightened inspection or discontinuation of inspection when quality is poor.
The problem associated with acceptance sampling inspection relates to defining unambiguously the criteria
used to judge discrete individual items supplied in quantity, the criterion for acceptance of the lot, the quality
level expected from the manufacturing process, the discrimination afforded by the sampling plans and the
rules to be followed when a lot is not accepted. Above all, however, it is necessary to design the sampling
scheme so that it can be invoked easily in a purchasing contract. The sampling plans in the sets of related
standards discussed in ISO/TR 8550-2 and ISO/TR 8550-3 enable this to be done efficiently.
The parties should agree on the following:
a) the specification to which the discrete items of product are to conform; this is necessary because, in all
dealings between the parties, there has to be agreement on what constitutes a conforming item and what
constitutes a nonconforming item;
b) whether the acceptance of the product is to be determined by the acceptance of individual items or
collectively by the acceptance of inspection lots of items (acceptance of individual items precludes
sampling).
When the acceptance is to be on a lot basis, the agreement between supplier and recipient needs to include
— the criteria for item conformance,
— the criteria for lot acceptance,
— the criteria for non-acceptance of the lot, and
— the acceptance sampling system, scheme or plan to be used.
The latter should be based on risk factors that are mutually acceptable to both producer and customer.
6 © ISO 2007 – All rights reserved
Having agreed on the acceptance sampling system, scheme or plan to use, the supplier knows, for various
quality levels, the probability that his supply lots will be accepted. Likewise, the customer understands the
protection provided by the sampling system, scheme or plan against acceptance of poor quality product.
Current standards present plans for single, double, multiple, sequential and skip-lot sampling. A comparison of
the various sampling methods and the principles on which they are based will assist in assessing their
suitability for a particular application and enable an appropriate selection to be made.
7 Attributes versus variables
Acceptance sampling standards generally describe procedures for inspection by attributes or for inspection by
variables; a key decision to make is which of these to use.
If certain assumptions are true, the variables method has the advantage of generally requiring a smaller
sample size than the attributes method to attain a given degree of protection against incorrect decisions. In
addition, it provides more information on whether quality is being adversely affected by process mean,
process variability, or both.
The attributes method has the advantage that it is more robust in the sense that it is not subject to
assumptions of distributional shape, and that it is simpler to use. The larger sample sizes and consequential
increased costs associated with using attribute sampling methods might be justifiable for these reasons.
Furthermore, an attribute scheme might be understood and accepted more readily by inspection personnel.
To avoid the assumption of normality and the attendant inability or difficulty in checking for this with “short
runs” or lots of an “isolated” nature, sampling by attributes is recommended even to the extent of converting
measurements to attributes.
When the quality characteristics are known to be normally distributed, at least to a good approximation,
sampling by variables has a substantial advantage when inspection is expensive, e.g. when testing is
destructive. Often, a simple mathematical transformation, such as taking the logarithm or square root, will
convert a set of measurements from a non-normal to a normal, or near-normal, distribution.
Table 2 gives a comparison of the sample sizes for inspection by attributes and by variables for certain lot size
ranges when using single sampling plans at inspection level II (see 8.6.1) under normal inspection. Similar
advantages exist when comparing inspection by variables and by attributes in double and sequential sampling.
Table 2 — Comparison of sample sizes in inspection by attributes and by variables
Single sample sizes under normal inspection
Inspection by variables (ISO 3951-1)
Inspection
Lot sizes
by attributes
Unknown process Known process standard
(ISO 2859-1)
standard deviation deviation
16 to 25 5 4 3
91 to 150 20 13 8
281 to 500 50 25 12
1 201 to 3 200 125 50 18
35 001 to 150 000 500 125 32
8 Further considerations influencing a selection
8.1 Long and short production runs
Most acceptance sampling standards are intended for use primarily on a continuing series of lots of sufficient
duration to allow the switching rules to be applied. This implies a “long” production run.
The principal exception is ISO 2859-2, which comprises limiting quality (LQ) plans that can be used when the
switching rules of ISO 2859-1 are not applicable. These are primarily intended for use with single lots or lots of
an “isolated nature”. By implication, this embraces a “short” series of inspection lots - or a “short” production
run.
ISO 2859-5 and ISO 3951-5 provide sequential plans that match other standards in their respective series,
and in many cases are thus similarly applicable to long or short runs.
In order for a production run to qualify as “long”, one criterion is clearly that the switching rules have a
reasonable chance of coming into effect if “the quality is unsatisfactory”. It is equally clear that this alone
raises a number of supplementary issues (as indicated by the quotation marks) depending on the
requirements and circumstances prevailing in each case considered. It is impossible to stipulate simply and
precisely what constitutes a short run (number of lots) in the context of sampling inspection.
In the absence of any other guide or evidence on which to base a judgement, anything up to 10 consecutive
inspection lots should be considered as a “short run”, and the plans in ISO 2859-2 should be used. However,
lots should not be subdivided arbitrarily in order to create a “long run”. It is generally preferable to have large
homogeneous lots because they allow a smaller sample size to lot size ratio, and provide better
representation by the sample, sharper discrimination and more economical inspection.
In a long production run, there is continuity and stability, so production settles down to a long-term stable
process average. Nevertheless, the quality of individual lots varies about this process average. On the other
hand, at the start of production, after a significant break or change in production, or for a short production run,
the lot quality might well be somewhat different and more variable, even markedly so. The practical factor to
consider is whether there is evidence that a stable process average has been established and still exists.
8.2 Nonconformity and nonconforming item
8.2.1 Failure to conform
8.2.1.1 General
Any failure to conform to a specified product characteristic, dimension, attribute or performance requirement
represents nonconformity. A nonconforming item might have one or more nonconformities.
The failure of a ballpoint pen to write, for example, is a nonconformity; the pen is nonconforming. However,
the same pen might have failed to conform in a number of other ways, e.g. colour, dimensions, etc. A pen that
exhibited several nonconformities would still be counted as one nonconforming item.
The qualification “nonconformity” does not necessarily imply that the unit of product cannot be used for the
purpose intended. For example, a brick with one of its dimensions outside the prescribed tolerance interval,
though nonconforming, can still be used for building.
The distinction between nonconformity and nonconforming item is of no importance if the items have no more
than one nonconformity, but becomes essential when multiple nonconformities can occur.
The quality of a given quantity of product may be expressed either as “percent nonconforming” or as the
“number of nonconformities per hundred items”, but these are only interchangeable when items can have no
more than one nonconformity.
Under sampling by attributes, sampling plans are available for either percent nonconforming or the number of
nonconformities per hundred items.
8 © ISO 2007 – All rights reserved
8.2.1.2 Example 2
In counting pinholes in metal foil, the number of pinholes per square metre might be of interest. Here we
would count all the pinholes in each square metre (item) examined and then express the quality in pinholes
per 100 m .
8.2.1.3 Example 3
Suppose that a lot consists of 500 articles. Of these, 480 conform and are acceptable, 15 have one
nonconformity each, four have two nonconformities each, and one has three nonconformities.
The lot percent nonconforming is given by the formula:
number of nonconforming items
Percent nonconforming =×100
total number of items
=×100
=4;
that is, the lot is 4 % nonconforming.
The number of nonconformities per hundred items in the lot is given by the formula:
number of nonconformities
Nonconformities per 100 items =×100
total number of items
=×100
= 5,2 ;
that is, the lot has 5,2 nonconformities per hundred items.
8.2.1.4 Comments on Examples 2 and 3
Hence, under sampling by attributes, whether percent nonconforming or nonconformities per hundred items is
to be used is a matter for individual consideration in each particular case. The important thing is that it has to
be considered, specified, and agreed upon beforehand, not left until a sample has been inspected and then
considered.
Under sampling by variables, sampling plans are only available for percent nonconforming, so there is no
choice to be made. However, different quality characteristics might belong to different classes (see 8.2.3), in
which case they are treated separately.
8.2.1.5 Factors to be taken into account
Factors to be taken into account in deciding whether to use percent nonconforming or nonconformities per
hundred items under sampling by attributes are as follows.
a) Under inspection for percent nonconforming it is assumed that, if an item contains one or more
nonconformities, the item is nonconforming and is not acceptable.
It also presupposes that the number of different ways in which an item can be nonconforming is limited
and known, e.g. there are only 5 ways in which each particular item could be nonconforming [see also
item b)].
b) Under inspection for nonconformities, every nonconformity found is counted. Three nonconformities found
in one item count as three, and are given the same weight as three items each having one nonconformity.
A special case arises when a nonconformity can occur an unknown and almost unlimited number of times
in items, e.g. surface blemishes or pinholes can occur in any number and it is not known how many times
they do not occur, so percent nonconforming for this feature is meaningless. In such cases,
nonconformities per hundred items should be used (see Example 2).
NOTE Percent nonconforming under sampling inspection by attributes implies a binomial distribution; for
nonconformities per hundred items, a Poisson distribution is appropriate.
c) Two properties are dependent if nonconformities in an item arise, in part or wholly, through some
common cause, or if one property affects the other. Detailed knowledge of the production process is thus
needed to decide whether properties are independent. In statistical terms, if two characteristics, say
length and diameter, are independent, it means that if all the units produced were taken and sorted into
two groups according to whether the length was nonconforming or not, then the percent nonconforming
for diameter would be found to be essentially the same in each of these two groups; or, alternatively, if
they were sorted into two groups according to whether the diameter was nonconforming or not, then the
percent nonconforming for length would be essentially the same in the two groups. It can be shown
mathematically that these two procedures are equivalent.
If two nonconformities are not independent, then they are said to be related, or dependent. It should be
agreed that the occurrence of both in one item is to count as only one nonconformity, not as two.
Occasionally the correlation between two related nonconformities is low. Under these conditions, the two
may be considered independent. Inspection for percent nonconforming avoids this difficulty.
d) If the percentage of nonconformities in the lot is less than 2,5 %, then the probability distributions of
nonconforming items and nonconformities will be almost identical. In the range 2,5 % to 10 % some
differenc
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