ISTM - Statistical methods

This document specifies an acceptance sampling system for inspection by attributes indexed by limiting quality (LQ). The sampling system is used for lots in isolation (isolated sequences of lots, an isolated lot, a unique lot or a short series of lots), where switching rules, such as those of ISO 2859‑1, are not applicable. Inspection levels, as provided by ISO 2859‑1 to control the relative amount of inspection, are not provided in this document. In many industrial situations, in which switching rules might be used, they are not applied for a number of reasons, not all of which might be valid:
a) production is intermittent (not continuous);
b) production is from several different sources in varying quantities, i.e. "job lots";
c) lots are isolated;
d) lots are resubmitted after inspection.
The sampling plans in this document are indexed by a series of specified values of limiting quality (LQ), where the consumer's risk (the probability of acceptance at the LQ) is usually below 0,10 (10 %), except in some instances.
This document is intended both for inspection for nonconforming items and for inspection for nonconformities per 100 items.
It is intended to be used when the supplier and the consumer both regard the lot to be in isolation. That is, the lot is unique in that it is the only one of its type produced. It can also be used when there is a series of lots too short for switching rules to be applied.

This document presents key elements and the philosophy of the control chart approach, and identifies a wide variety of control charts (including those related to the Shewhart control chart, those stressing process acceptance or online process adjustment, and specialized control charts).
It presents an overview of the basic principles and concepts of control charts and illustrates the relationship among various control chart approaches to aid in the selection of the most appropriate part of ISO 7870 for given circumstances. It does not specify statistical control methods using control charts. These methods are specified in the relevant parts of ISO 7870.

1.1 This document
— amplifies the general principles for designing experiments for the numerical estimation of the precision of measurement methods by means of a collaborative interlaboratory experiment;
— provides a detailed practical description of the basic method for routine use in estimating the precision of measurement methods;
— provides guidance to all personnel concerned with designing, performing or analysing the results of the tests for estimating precision.
NOTE Modifications to this basic method for particular purposes are given in other parts of ISO 5725.
1.2 It is concerned exclusively with measurement methods which yield measurements on a continuous scale and give a single value as the test result, although this single value can be the outcome of a calculation from a set of observations.
1.3 It assumes that in the design and performance of the precision experiment, all the principles as laid down in ISO 5725-1 are observed. The basic method uses the same number of test results in each laboratory, with each laboratory analysing the same levels of test sample; i.e. a balanced uniform-level experiment. The basic method applies to procedures that have been standardized and are in regular use in a number of laboratories.
1.4 The statistical model of ISO 5725-1:1994, Clause 5, is accepted as a suitable basis for the interpretation and analysis of the test results, the distribution of which is approximately normal.
1.5 The basic method, as described in this document, (usually) estimates the precision of a measurement method:
a) when it is required to determine the repeatability and reproducibility standard deviations as defined in ISO 5725-1;
b) when the materials to be used are homogeneous, or when the effects of heterogeneity can be included in the precision values; and
c) when the use of a balanced uniform-level layout is acceptable.
1.6 The same approach can be used to make a preliminary estimate of precision for measurement methods which have not reached standardization or are not in routine use.

1.1 This document
— specifies basic methods for estimating the bias of a measurement method and the laboratory bias when a measurement method is applied;
— provides a practical approach of a basic method for routine use in estimating the bias of measurement methods and laboratory bias;
— provides a brief guidance to all personnel concerned with designing, performing or analysing the results of the measurements for estimating bias.
1.2 It is concerned exclusively with measurement methods which yield measurements on a continuous scale and give a single value as the measurement result, although the single value can be the outcome of a calculation from a set of observations.
1.3 This document applies when the measurement method has been standardized and all measurements are carried out according to that measurement method.
NOTE In ISO/IEC Guide 99:2007(VIM), "measurement procedure" (2.6) is an analogous term related to the term "measurement method" used in this document.
1.4 This document applies only if an accepted reference value can be established to substitute the true value by using the value, for example:
— of a suitable reference material;
— of a suitable measurement standard;
— referring to a suitable measurement method;
— of a suitable prepared known sample.
1.5 This document applies only to the cases where it is sufficient to estimate bias on one property at a time. It is not applicable if the bias in the measurement of one property is affected by the level of any other property (i.e. it does not consider interferences by any influencing quantity). Comparison of the trueness of two-measurement methods is considered in ISO 5725-6.

This International Standard specifies sequential sampling plans and procedures for inspection by
variables of discrete items.
The plans are indexed in terms of producer’s risk point and the consumer’s risk point. Therefore, they
are suitable not only for the purposes of acceptance sampling, but for the more general purpose of the
testing of simple statistical hypotheses for proportions.
The purpose of this International Standard is to provide procedures for the sequential assessment
of inspection results that may be used to induce the supplier to supply lots of a quality having a high
probability of acceptance. At the same time, the consumer is protected by a prescribed upper limit to
the probability of accepting a lot (or process) of poor quality.
This International Standard is primarily designed for use under the following conditions:
a) where the inspection procedure is to be applied to a continuing series of lots of discrete products
all supplied by one producer using one production process. In such a case, sampling of particular
lots is equivalent to the sampling of the process. If there are different producers or production
processes, this International Standard shall be applied to each one separately;
b) where only a single quality characteristic x of these products is taken into consideration, which
must be measurable on a continuous scale;
c) where the measurement error is negligible (i.e. with a standard deviation no more than 10 % of the
process standard deviation);
d) where production is stable (under statistical control) and the quality characteristic x has a known
standard deviation, and is distributed according to a normal distribution or a close approximation
to the normal distribution;
CAUTION — The procedures in this International Standard are not suitable for application to
lots that have been screened previously for nonconforming items.
e) where a contract or standard defines an upper specification limit U, a lower specification limit L, or
both; an item is qualified as conforming if and only if its measured quality characteristic, x, satisfies
the appropriate one of the following inequalities:
1) x ≤ U (i.e. the upper specification limit is not violated);
2) x ≥ L (i.e. the lower specification limit is not violated);
3) x U and x  L (i.e. neither the upper nor the lower specification limit is violated.)
Inequalities 1) and 2) are called cases with a “single specification limit”, and 3) is the case with “double
specification limits”.
In this International Standard, it is assumed that, where double specification limits apply, conformance
to both specification limits is either equally important to the integrity of the product or is considered
separately for both specification limits. In the first case, it is appropriate to control the combined
percentage of product outside the two specification limits. This is referred to as combined control. In
the second case, nonconformity beyond each of the limits is controlled separately, and this is referred
to as separate control.

This International Standard specifies, for quality levels expressed as nonconforming items per million
items, procedures for estimating the quality level of a single entity (e.g. a lot) and, when the production
process is in statistical control, for estimating the process quality level based on evidence from several
samples. Procedures are also specified for using this information when selecting a suitable sampling
plan so as to verify that the quality level of a given lot does not exceed a stated limiting quality level
(LQL). For the case where no prior sample data is available, guidance is given for presuming a process
quality level in selecting a plan.

This International Standard provides double sampling plans by attributes for the acceptance inspection of lots of discrete items. The plans are indexed by the producer's risk quality (PRQ) and the consumer's
risk quality (CRQ) where the nominal producer's and consumer's risks are respectively either (5 %,
5 %), (5 %, 10 %) or (10 %, 10 %). Plans are provided for inspection for percent nonconforming and for
inspection for nonconformities per 100 items. The lot is accepted if there are no nonconforming items
(nonconformities) in the first random sample, and rejected if it contains two or more nonconforming
items (nonconformities). If precisely one nonconforming item is found in the first sample, a second
random sample is drawn; the lot is then accepted if the second sample contains no nonconforming items
(nonconformities) and rejected otherwise.
The objective of this International Standard is to provide procedures that enable lot disposition to be
determined quickly and economically if quality is particularly good or bad. For intermediate quality,
a second sample is drawn in order to be able to discriminate more reliably between acceptable and
unacceptable lots. The two sample sizes are chosen to minimize the maximum expected sample size
with respect to incoming quality subject to the nominal risks not being exceeded.
Similarly, the plans may be used to test the hypothesis that a lot or process quality level is equal to the
PRQ (i.e. acceptable) against the alternative hypothesis that the quality level is equal to the CRQ (i.e.
unacceptable).
The plans are preferable to single sampling plans where the cost of inspection is high, where the delay
and uncertainty caused by the possible requirement for second samples is inconsequential and where a
relatively large ratio of the consumer's risk quality to the producer's risk quality can be tolerated.
The plans are suitable for isolated lots or for short series of lots, where the sum of the two sample sizes
is no larger than about 10 % of the size of the lot. The plans are also suitable for continuing series of lots
when lots that fail to satisfy the acceptance criteria are 100 % inspected and all nonconforming items
replaced by conforming items; however, for continuing series of lots, consideration should also be given
to using double sampling plans from ISO 2859-1.
The statistical theory underlying the plans, tables and figures is provided in Annex A.

This International Standard specifies sequential sampling plans and procedures for inspection by
attributes of discrete items.
The plans are indexed in terms of the producer's risk point and the consumer's risk point. Therefore,
they can be used not only for the purposes of acceptance sampling, but for a more general purpose of
the verification of simple statistical hypotheses for proportions.
The purpose of this International Standard is to provide procedures for sequential assessment of
inspection results that may be used to induce the supplier, through the economic and psychological
pressure of non-acceptance of lots of inferior quality, to supply lots of a quality having a high probability
of acceptance. At the same time, the consumer is protected by a prescribed upper limit to the probability
of accepting lots of poor quality.
This International Standard provides sampling plans that are applicable, but not limited, to inspection
in different fields, such as:
— end items,
— components and raw materials,
— operations,
— materials in process,
— supplies in storage,
— maintenance operations,
— data or records, and
— administrative procedures.
This International Standard contains sampling plans for inspection by attributes of discrete items.
The sampling plans may be used when the extent of nonconformity is expressed either in terms of
proportion (or percent) nonconforming items or in terms of nonconformities per item (per 100 items).
The sampling plans are based on the assumption that nonconformities occur randomly and with
statistical independence. There may be good reasons to suspect that one nonconformity in an item
could be caused by a condition also likely to cause others. If so, it would be better to consider the items
just as conforming or not, and ignore multiple nonconformities.
The sampling plans from this International Standard should primarily be used for the analysis of
samples taken from processes. For example, they may be used for the acceptance sampling of lots taken
from a process that is under statistical control. However, they may also be used for the acceptance
sampling of an isolated lot when its size is large, and the expected fraction nonconforming is small
(significantly smaller than 10 %).
In the case of the acceptance sampling of continuing series of lots, the system of sequential sampling
plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection published in ISO 2859-5 should
be applied.

This International Standard provides a general introduction to acceptance sampling by attributes and
provides a brief summary of the attribute sampling schemes and plans used in ISO 2859-1, ISO 2859-2,
ISO 2859-3, ISO 2859-4 and ISO 2859-5, which describe specific types of attribute sampling systems.
It also provides guidance on the selection of the appropriate inspection system for use in a particular
situation.

This document gives guidance for
— evaluation of measurement uncertainties using data obtained from studies conducted in accordance
with ISO 5725-2, and
— comparison of collaborative study results with measurement uncertainty (MU) obtained using
formal principles of uncertainty propagation (see Clause 14).
ISO 5725-3 provides additional models for studies of intermediate precision. However, while the same
general approach may be applied to the use of such extended models, uncertainty evaluation using
these models is not incorporated in this document.
This document is applicable to all measurement and test fields where an uncertainty associated with a
result has to be determined.
This document does not describe the application of repeatability data in the absence of
reproducibility data.
This document assumes that recognized, non-negligible systematic effects are corrected, either by
applying a numerical correction as part of the method of measurement, or by investigation and removal
of the cause of the effect.
The recommendations in this document are primarily for guidance. It is recognized that while the
recommendations presented do form a valid approach to the evaluation of uncertainty for many
purposes, it is also possible to adopt other suitable approaches.
In general, references to measurement results, methods and processes in this document are normally
understood to apply also to testing results, methods and processes.

This document describes a procedure for the determination of statistics for estimating the quality
capability or performance of product and process characteristics. The process results of these quality
characteristics are categorized into eight possible distribution types. Calculation formulae for the
statistical measures are placed with every distribution.
The statistical methods described in this document only relate to continuous quality characteristics.
They are applicable to processes in any industrial or economical sector.
NOTE This method is usually applied in case of a great number of serial process results, but it can also be
used for small series (a small number of process results).

This part of ISO 22514 describes process capability and performance measures that are commonly used.

This part of ISO 3534 defines applied statistics terms, and expresses them in a conceptual framework in accordance with ISO normative terminology practice. Term entries are arranged thematically. An alphabetical index is provided. Standardized symbols and abbreviations are defined. It has been recognized that the acceptance of applied statistics as a means to improving the effectiveness and efficiency of organizations has been hampered by the complexity and confusion introduced by conflicting designation and usage of terms, definitions, abbreviations and symbols. The two principal purposes of this part of ISO 3534 are, specifically, to establish a common vocabulary for use throughout ISO/TC 69 standards, together with the broader intent to enhance the preciseness, clarity and cohesiveness in the usage/application of applied statistics generally. The mathematical level has deliberately been kept to a low level in order for the content to be made readily comprehensible to the widest possible readership. ISO 3534-1 and ISO 3534-2 are intended to be compatible. However, ISO 3534-1, on terms used in probability and statistics, is foundational; so, by necessity, it is presented at a more sophisticated mathematical level than ISO 3534-2. As users of this part of ISO 3534 on applied statistics may occasionally consult ISO 3534-1 for certain terms, copious notes and examples in ISO 3534-1 follow selected terms providing colloquial explanations of formal terms.

This part of ISO 16269 describes procedures for establishing statistical tolerance intervals that include
at least a specified proportion of the population with a specified confidence level. Both one‑sided and
two‑sided statistical tolerance intervals are provided, a one‑sided interval having either an upper or a
lower limit while a two‑sided interval has both upper and lower limits. Two methods are provided, a
parametric method for the case where the characteristic being studied has a normal distribution and
a distribution‑free method for the case where nothing is known about the distribution except that it is
continuous. There is also a procedure for the establishment of two‑sided statistical tolerance intervals
for more than one normal sample with common unknown variance.

This part of ISO 22514 describes the fundamental principles of capability and performance of
manufacturing processes. It has been prepared to provide guidance about circumstances where a
capability study is demanded or necessary to determine if the output from a manufacturing process
or the production equipment (a production machine) is acceptable according to appropriate criteria.
Such circumstances are common in quality control when the purpose for the study is part of some
kind of production acceptance. These studies can also be used when diagnosis is required concerning a
production output or as part of a problem solving effort. The methods are very versatile and have been
applied for many situations.
This part of ISO 22514 is applicable to the following:
— organizations seeking confidence that their product characteristics requirements are fulfilled;
— organizations seeking confidence from their suppliers that their product specifications are and will
be satisfied;
— those internal or external to the organization who audit it for conformity with the product
requirements;
— those internal to the organization who deal with analysing and evaluating the existing production
situation to identify areas for process improvement.

This part of ISO 3951 is primarily designed for use under the following conditions: a) where the inspection procedure is to be applied to a continuing series of lots of discrete products all supplied by one producer using one production process; b) where only a single quality characteristic, x, of these products is taken into consideration, which must be measurable on a continuous scale; c) where production is stable (under statistical control) and the quality characteristic, x, is distributed according to a normal distribution or a close approximation to the normal distribution; d) where a contract or standard defines a lower specification limit, L, an upper specification limit, U, or both; an item is qualified as conforming if and only if its measured quality characteristic, x, satisfies the appropriate one of the following inequalities: 1) x ≥ L (i.e. the lower specification limit is not violated); 2) x ≤ U (i.e. the upper specification limit is not violated); 3) x ≥ L and x ≤ U (i.e. neither the lower nor the upper specification limit is violated). Inequalities 1) and 2) are called cases with a single specification limit and 3), a case with double specification limits. Where double specification limits apply, it is assumed in this part of ISO 3951 that conformance to both specification limits is equally important to the integrity of the product. In such cases, it is appropriate to apply a single AQL to the combined percentage of a product outside the two specification limits. This is referred to as combined control.

This part of ISO 3534 defines the terms used in the field of design of experiments and may be used in the drafting of other International Standards. More specifically, it defines terms used in the field of design of experiments for which the response variable is one-dimensional and continuous and for which the expectation of the response variable is linear in the parameters. The terms with regard to the statistical analysis are based on the assumption that the error term follows a normal distribution with constant variance.

This part of ISO 16269 provides detailed descriptions of sound statistical testing procedures and graphical data analysis methods for detecting outliers in data obtained from measurement processes. It recommends sound robust estimation and testing procedures to accommodate the presence of outliers. This part of ISO 16269 is primarily designed for the detection and accommodation of outlier(s) from univariate data. Some guidance is provided for multivariate and regression data.

This part of ISO 22514 provides methods for calculating performance and capability statistics for process or product quantities where it is necessary or beneficial to consider a family of singular quantities in relation to each other. The methods provided here mostly are designed to describe quantities that follow a bivariate normal distribution. This part of ISO 22514 does not offer an evaluation of the different provided methods with respect to different situations of possible application of each method. For the current state, the selection of one preferable method might be done following the users preferences. The purpose is to give definitions for different approaches of index calculation for performance and capability in the case of a multiple process or product quantity description.

This part of ISO 11462 provides a catalogue of tools and techniques to help an organization in planning, implementation and evaluation of an effective statistical process control (SPC) system. This catalogue gives tools and techniques that are essential for the successful realization of the SPC elements specified in ISO 11462-1.

This Technical Report describes a broad range of statistical methods applicable to the management, control and improvement of processes.

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). 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 on a continuous scale. Each characteristic has, at least to a good approximation, a normal distribution or a distribution that can be transformed so that it closely resembles a normal distribution.

This part of ISO 16269 specifies methods of determining prediction intervals for a single continuously distributed variable. These are ranges of values of the variable, derived from a random sample of size n, for which a prediction relating to a further randomly selected sample of size m from the same population may be made with a specified confidence. Three different types of population are considered, namely: a) normally distributed with unknown standard deviation; b) normally distributed with known standard deviation; c) continuous but of unknown form. For each of these three types of population, two methods are presented, one for one-sided prediction intervals and one for symmetric two-sided prediction intervals. In all cases, there is a choice from among six confidence levels. The methods presented for cases a) and b) may also be used for non-normally distributed populations that can be transformed to normality. For cases a) and b) the tables presented in this part of ISO 16269 are restricted to prediction intervals containing all the further m sampled values of the variable. For case c) the tables relate to prediction intervals that contain at least m - r of the next m values, where r takes values from 0 to 10 or 0 to m - 1, whichever range is smaller. For normally distributed populations a procedure is also provided for calculating prediction intervals for the mean of m further observations.

The guidance given 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). 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 specification). Standards on acceptance sampling by attributes are applicable 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, it is applicable to the selection of sampling systems, schemes and plans for all types of product and processes as defined in ISO 9000.

This part of ISO 2859 specifies sequential sampling schemes that supplement the ISO 2859-1 acceptance sampling system for inspection by attributes. The ISO 2859-1 acceptance sampling system is indexed in terms of the acceptance quality limit (AQL). Its purpose is to induce a supplier, through the economic and psychological pressure of lot non-acceptance, to maintain a process average at least as good as the specified acceptance quality limit, while at the same time providing an upper limit for the risk to the consumer of accepting the occasional poor lot. The sampling schemes defined in this part of ISO 2859 are applicable, but not limited, to the inspection of: - end items, - components and raw materials, - operations, - materials in process, - supplies in storage, -ç maintenance operations, -ç data or records, and -ç administrative procedures. These schemes are designed to be applied to a continuing series of lots, that is, a series long enough to permit the switching rules in 10.3 to be applied. These switching rules provide a) enhanced protection to the consumer (by means of tightened sampling inspection criteria or discontinuation of sampling inspection) should deterioration in quality occur, b) an incentive, at the discretion of the responsible authority, to reduce inspection costs (by means of reduced sampling inspection criteria) should consistently good quality be demonstrated over time. The individual sampling plans are not designed to be used outside of the schemes in which they are presented. Where lots are produced in isolation or in a series too short for this part of ISO 2859 to apply, the user is advised to consult ISO 2859-2 for appropriate sampling plans.

This part of ISO 10576 sets out guidelines: a) for drafting requirements that may be formulated as limiting values for a quantifiable characteristic; b) for checking conformity to such requirements when the test or measurement result is subject to uncertainty. This part of ISO 10576 is applicable whenever the uncertainty may be quantified according to the principles laid down in GUM. The term uncertainty is thus a descriptor for all elements of variation in the measurement result, including uncertainty due to sampling.

This part of ISO 22514 prescribes the steps to be taken in conducting short-term performance studies that are typically performed on machines where parts produced consecutively under repeatability conditions are considered. The number of observations to be analysed will vary according to the patterns the data produce, or if the runs (the rate at which items are produced) on the machine are low in quantity. The methods are not recommended where the sample size produced is less than 30 observations. Methods to be used for handling the data and carrying out the calculations are described. In addition, machine performance indices and the actions required at the conclusion of a machine performance study are described. The document is not applicable when tool wear patterns are expected to be present during the duration of the study, nor if autocorrelation between observations is present. The situation where a machine has captured the data, sometimes thousands of data points collected in a minute, is not considered suitable for the application of this part of ISO 22514.

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).

This International Standard defines procedures for random sampling and randomization. Several methods are provided, including approaches based on mechanical devices, tables of random numbers, and portable computer algorithms. This International Standard is applicable whenever a regulation, contract, or other standard requires random sampling or randomization to be used. The methods are applicable to such situations as a) acceptance sampling of discrete units presented for inspection in lots, b) sampling for survey purposes, c) auditing of quality management system results, and d) selecting experimental units, allocating treatments to them, and determining evaluation order in the conduct of designed experiments. Information is also included to facilitate auditing or other external review of random sampling or randomization results where this is required by quality management personnel or regulatory bodies. This International Standard does not provide guidance as to the appropriate random sampling or randomization procedures to be used for any particular experimental situation or give guidance with respect to possible sampling strategy selection or sample size determination. Other ISO standards (such as those listed in the Introduction) or authoritative references should be consulted for guidance in such areas.

This International Standard specifies methods for generating uniform and non-uniform random variates for Monte Carlo simulation purposes. Cryptographic random number generation methods are not included. This International Standard is applicable, inter alia, by - researchers, industrial engineers or experts in operations management, who use statistical simulation, - statisticians who need randomization related to SQC methods, statistical design of experiments or sample surveys, - applied mathematicians who plan complex optimization procedures that require the use of Monte Carlo methods, and - software engineers who implement algorithms for random variate generation.

Statistical process control (SPC) concerns the use of statistical techniques and/or statistical or stochastic control algorithms to achieve one or more of the following objectives: a) to increase knowledge about a process; b) to steer a process to behave in the desired way; c) to reduce variation of final-product parameters, or in other ways improve performance of a process.

Specifies procedures for establishing a point estimate and confidence intervals for the median of any continues probability of a population, based on a random sample of size n from the population. These procedures are distribution-free, i.e. they do not require knowledge of the family of distributions to which the population distribution belongs. Similar products can be applied to estimate quartiles and/or percentities.

This part of ISO 2859 establishes sampling plans and procedures that can be used to assess whether the quality level of an entity (lot, process, etc) conforms to a declared value. The sampling plans have been devised so as to obtain a risk of less than of contradicting a correct declared quality level. The risk is of failing to contradict an incorrect declared quality level which is related to the limiting quality ratio (see clause 4). Sampling plans are provided corresponding to three levels of discriminatory ability. In contrast to the procedures in the other parts of ISO 2859, the procedures in this part of ISO 2859 are not applicable to acceptance assessment of lots. Generally, the balancing of the risks of reaching incorrect conclusions in assessment procedures will differ from the balancing in the procedures for acceptance sampling. 5 % 10 %.

This part of ISO 3534 defines general statistical terms and terms used in probability which may be used in the drafting of other International Standards. In addition, it defines symbols for a limited number of these terms. The terms are classified as: a) general statistical terms (Clause 1); b) terms used in probability (Clause 2). Annex A gives a list of symbols and abbreviations recommended to be used for this part of ISO 3534. The entries in this part of ISO 3534 are arranged in association with concept diagrams provided as Annexes B and C.

This part of ISO 2859 specifies generic  skip-lot sampling procedures for  acceptance inspection by attributes. The  purpose of these procedures is to provide a  way of reducing the inspection effort on  products of high quality submitted by a  supplier who has a satisfactory quality  assurance system and effective quality  controls. The reduction in inspection effort  is achieved by determining at random, with  a specified probability, whether a lot  presented for inspection will be accepted  without inspection. This procedure extends  the principle of the random selection of  sample items already applied in ISO 2859-1  to the random selection of lots. The skip-lot  sampling procedures specified in this part of  ISO 2859 are applicable to, but not limited  to, inspection of a) end items, such as  complete products or sub-assemblies, b)  components and raw materials, and c)  materials in process.

The purpose is to outline the general principles to be understood when assessing accuracy (trueness and precision) of measurement methods and results, and in applications, and to establish practical estimations of the various measures by experiment. Is concerned exclusively with measurement methods which yield measurements on a continuous scale and give a single value as the test result. May be applied to a very wide range of materials, including liquids, powders and solid objects, manufactured or naturally occurring, provided that due consideration is given to any heterogeneity of the material.

The purpose is to give some indications of the way in which accuracy data can be used in various practical situations by: giving a standard method of calculating the repeatability limit, the reproducibility limit and other limits, providing a way of checking the acceptability of test results obtained under repeatability or reproducibility conditions, describing how to assess the stability of results within a laboratory over a period of time, describing how to assess whether a given laboratory is able to use a given standard measurement method in a satisfactory way, describing how to compare alternative measurement methods.

Specifies four intermediate measures due to changes in observation conditions (time, calibration, operator and equipment) within a laboratory. These intermediate measures can be established by an experiment within a specific laboratory or by an interlaboratory experiment. Furthermore, discusses the implications of the definitions of intermediate precision measures, presents guidance on the interpretation and application of the estimates of intermediate precision measures in practical situations, discusses the connections between trueness and measurement conditions.

Concerns the estimation of the mean of a normal population on the basis of a series of tests applied to a random sample of individuals drawn from this population when the variance of the population is unknown and calculation of the conficence interval for the population mean therefrom and from the standard deviation. Test method may be subject to systematic errors.

Follows on from ISO 2854 and puts forward notions of the type II risk, the probability of not rejecting the null hypothesis when it is false. Deals with comparison of a mean with a given value (variance known or unknown), of two means (variance known or unknown), of a variance with a given value, and of two variances, and gives sets of curves for these type II risk for a given alternative and given size of sample and to determine the size of sample to be selected for a given alternative and a given values of type II risk.

A method is specified for comparing the mean of a population of differences with zero or any other preassigned value. It may be applied to establish a difference between two treatments, where "treatment" should be understood in a wide sense, e.g. as a test method, measuring instrument or laboratory involved, and is applicable under the conditions that the series of differences can be considered as a series of independent random items and the distribution of the differences is normal or approximately normal. If the distribution deviates from the normal, it remains valid provided the sample size is sufficiently large (100 and more).

Comparison of a variance with a given value, estimation of a variance, comparison of two variances, estimation of the ratio of two variances, and the same procedures for a mean with known or unknown variance are dealt with. Techniques are valid for sample elements drawn at random and being independent, when the distribution of the observed variable is normal, for a sample size not too small (5 to 10 at least) approximately also when the distribution does not deviate very much from the normal. Techniques of verification of the hypothesis of normality are briefly dealt with in the examples.