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ASTM D7915-14

(Practice)

Standard Practice for Application of Generalized Extreme Studentized Deviate (GESD) Technique to Simultaneously Identify Multiple Outliers in a Data Set

Standard Practice for Application of Generalized Extreme Studentized Deviate (GESD) Technique to Simultaneously Identify Multiple Outliers in a Data Set

SIGNIFICANCE AND USE
3.1 The GESD procedure can be used to simultaneously identify up to a pre-determined number of outliers (r) in a data set, without having to pre-examine the data set and make a priori decisions as to the location and number of potential outliers.  
3.2 The GESD procedure is robust to masking. Masking describes the phenomenon where the existence of multiple outliers can prevent an outlier identification procedure from declaring any of the observations in a data set to be outliers.  
3.3 The GESD procedure is automation-friendly, and hence can easily be programmed as automated computer algorithms.
SCOPE
1.1 This practice provides a step by step procedure for the application of the Generalized Extreme Studentized Deviate (GESD) Many-Outlier Procedure to simultaneously identify multiple outliers in a data set. (See Bibliography.)  
1.2 This practice is applicable to a data set comprising observations that is represented on a continuous numerical scale.  
1.3 This practice is applicable to a data set comprising a minimum of six observations.  
1.4 This practice is applicable to a data set where the normal (Gaussian) model is reasonably adequate for the distributional representation of the observations in the data set.  
1.5 The probability of false identification of outliers associated with the decision criteria set by this practice is 0.01.  
1.6 It is recommended that the execution of this practice be conducted under the guidance of personnel familiar with the statistical principles and assumptions associated with the GESD technique.  
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

Status
Historical
Publication Date
30-Apr-2014
ICS
03.120.30 - Application of statistical methods
Technical Committee
D02 - Petroleum Products, Liquid Fuels, and Lubricants
Drafting Committee
D02.94 - Coordinating Subcommittee on Quality Assurance and Statistics
Current Stage
Ref Project

Relations

Referred By
ASTM D7372-21 - Standard Guide for Analysis and Interpretation of Proficiency Test Program Results
Effective Date
01-May-2014
Referred By
ASTM D6617-21 - Standard Practice for Laboratory Bias Detection Using Single Test Result from Standard Material
Effective Date
01-May-2014
Referred By
ASTM E3264-21 - Standard Guide for Homogeneity of Samples and Reference Materials Used for Inter- and Intra-Laboratory Studies
Effective Date
01-May-2014
Referred By
ASTM D7042-21a - Standard Test Method for Dynamic Viscosity and Density of Liquids by Stabinger Viscometer (and the Calculation of Kinematic Viscosity)
Effective Date
01-May-2014
Referred By
ASTM D6300-23 - Standard Practice for Determination of Precision and Bias Data for Use in Test Methods for Petroleum Products, Liquid Fuels, and Lubricants
Effective Date
01-May-2014
Referred By
ASTM D8098-23 - Standard Test Method for Permanent Gases in C<inf>2</inf> and C<inf>3</inf> Hydrocarbon Products by Gas Chromatography and Pulse Discharge Helium Ionization Detector
Effective Date
01-May-2014
Referred By
ASTM D6299-23e1 - Standard Practice for Applying Statistical Quality Assurance and Control Charting Techniques to Evaluate Analytical Measurement System Performance
Effective Date
01-May-2014
Referred By
ASTM D8321-22 - Standard Practice for Development and Validation of Multivariate Analyses for Use in Predicting Properties of Petroleum Products, Liquid Fuels, and Lubricants based on Spectroscopic Measurements
Effective Date
01-May-2014
Referred By
ASTM D6122-22 - Standard Practice for Validation of the Performance of Multivariate Online, At-Line, Field and Laboratory Infrared Spectrophotometer, and Raman Spectrometer Based Analyzer Systems
Effective Date
01-May-2014

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ASTM D7915-14 - Standard Practice for Application of Generalized Extreme Studentized Deviate &#40;GESD&#41; Technique to Simultaneously Identify Multiple Outliers in a Data SetASTM D7915-14 - Standard Practice for Application of Generalized Extreme Studentized Deviate &#40;GESD&#41; Technique to Simultaneously Identify Multiple Outliers in a Data Set
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ASTM D7915-14 - Standard Practice for Application of Generalized Extreme Studentized Deviate &#40;GESD&#41; Technique to Simultaneously Identify Multiple Outliers in a Data Set
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D7915 − 14 An American National Standard
Standard Practice for
Application of Generalized Extreme Studentized Deviate
(GESD) Technique to Simultaneously Identify Multiple
1
Outliers in a Data Set
This standard is issued under the fixed designation D7915; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope set, without having to pre-examine the data set and make a
priori decisions as to the location and number of potential
1.1 This practice provides a step by step procedure for the
outliers.
application of the Generalized Extreme Studentized Deviate
(GESD) Many-Outlier Procedure to simultaneously identify 3.2 The GESD procedure is robust to masking. Masking
multiple outliers in a data set. (See Bibliography.) describes the phenomenon where the existence of multiple
outliers can prevent an outlier identification procedure from
1.2 This practice is applicable to a data set comprising
declaring any of the observations in a data set to be outliers.
observations that is represented on a continuous numerical
scale. 3.3 The GESD procedure is automation-friendly, and hence
can easily be programmed as automated computer algorithms.
1.3 This practice is applicable to a data set comprising a
minimum of six observations.
4. Procedure
1.4 Thispracticeisapplicabletoadatasetwherethenormal
4.1 Specifythemaximumnumberofoutliers(r)inadataset
(Gaussian) model is reasonably adequate for the distributional
to be identified.
representation of the observations in the data set.
4.1.1 The recommended maximum number of outliers (r)
by this practice is two (2) for data sets with six to twelve
1.5 The probability of false identification of outliers asso-
observations.
ciated with the decision criteria set by this practice is 0.01.
4.1.2 For data sets with more than twelve observations, the
1.6 It is recommended that the execution of this practice be
recommended maximum number of outliers (r) is the lesser of
conducted under the guidance of personnel familiar with the
ten or 20 %.
statistical principles and assumptions associated with the
4.1.3 The recommended values for r in 4.1.1 and 4.1.2 are
GESD technique.
not intended to be mandatory. Users can specify other values
1.7 This standard does not purport to address all of the
based on their specific needs.
safety concerns, if any, associated with its use. It is the
4.2 Compute test statistic T for each observation in the
responsibility of the user of this standard to establish appro-
initial starting data set (DTS ) as follows:
0
priate safety and health practices and determine the applica-
T 5 |x 2 x¯|⁄s (1)
bility of regulatory limitations prior to use.
where:
2. Terminology
x = an observation in the data set,
2.1 Definitions of Terms Specific to This Standard:
x¯ = average calculated using all observations in the data set,
2.1.1 outlier, n—anobservation(orasubsetofobservations)
and
which appears to be inconsistent with the remainder of the data
s = sample standard deviation calculated using all observa-
set.
tions in the data set.
3. Significance and Use
4.3 Remove the observation in the data set with the largest
absolute magnitude of the test statistic T and form a reduced
3.1 The GESD procedure can be used to simultaneously
data set (DTS), where i = number of observations removed
i
identify up to a pre-determined number of outliers (r) in a data
from the initial data set.
1 4.4 Re-calculate T for all observations in the reduced data
This practice is under the jurisdiction of ASTM Committee D02 on Petroleum
Products, Liquid Fuels, and Lubricants and is the direct responsibility of Subcom-
set from 4.3.
mittee D02.94 on Coordinating Subcommittee on Quality Assurance and Statistics.
4.5 Repeat steps 4.3 to 4.4 until r number of observations
Current edition approved May 1, 2014. Published June 2014. DOI: 10.1520/
D7915-14. have been removed from the initial data set. That is, until
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
D7915 − 14
calculationofall T’sforallobservationsinthereduceddataset 5. Worked Example
DTS has been completed.
r
5.1 Listed below is a data set comprising 30 observations:
4.6 Compare the maximum T computed in each data set
35.0 36.6 34.7 36.2 37.0 25.3 37.2 41.3 26.0 24.6
33.5 35.5 35.4 39.9 39.2 36.6 37.2 33.2 34.0 35.7
(DTS toDTS )toacriticalvalueλ associatedthedataset
0 r critical
39.2 42.1 35.7 40.2 36.6 41.1 41.1 39.1 40.6 41.3
DTS, where λ is chosen based on a false identification
i
5.1.1 The total number of
...

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Standard Practice for Application of Generalized Extreme Studentized Deviate (GESD) Technique to Simultaneously Identify Multiple Outliers in a Data Set

SIGNIFICANCE AND USE
3.1 The GESD procedure can be used to simultaneously identify up to a pre-determined number of outliers (r) in a data set, without having to pre-examine the data set and make a priori decisions as to the location and number of potential outliers.  
3.2 The GESD procedure is robust to masking. Masking describes the phenomenon where the existence of multiple outliers can prevent an outlier identification procedure from declaring any of the observations in a data set to be outliers.  
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1.1 This practice provides a step by step procedure for the application of the Generalized Extreme Studentized Deviate (GESD) Many-Outlier Procedure to simultaneously identify multiple outliers in a data set. (See Bibliography.)  
1.2 This practice is applicable to a data set comprising observations that is represented on a continuous numerical scale.  
1.3 This practice is applicable to a data set comprising a minimum of six observations.  
1.4 This practice is applicable to a data set where the normal (Gaussian) model is reasonably adequate for the distributional representation of the observations in the data set.  
1.5 The probability of false identification of outliers associated with the decision criteria set by this practice is 0.01.  
1.6 It is recommended that the execution of this practice be conducted under the guidance of personnel familiar with the statistical principles and assumptions associated with the GESD technique.  
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ABSTRACT
This practice presents rules for accepting or rejecting evidence based on a sample. Statistical evidence for this practice is in the form of an estimate of a proportion, an average, a total, or other numerical characteristic of a finite population or lot. This practice is an estimate of the result which would have been obtained by investigating the entire lot or population under the same rules and with the same care as was used for the sample. One purpose of this practice is to describe straightforward sample selection and data calculation procedures so that courts, commissions, etc. will be able to verify whether such procedures have been applied.
SIGNIFICANCE AND USE
4.1 This practice is designed to permit users of sample survey data to judge the trustworthiness of results from such surveys. Practice E105 provides a statement of principles for guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. Guide E1402 describes the principal types of sampling designs. Practice E122 aids in deciding on the required sample size.  
4.2 Section 5 gives extended definitions of the concepts basic to survey sampling and the user should verify that such concepts were indeed used and understood by those who conducted the survey. What was the frame? How large (exactly) was the quantity N? How was the parameter θ estimated and its standard error calculated? If replicate subsamples were not used, why not? Adequate answers should be given for all questions. There are many acceptable answers to the last question.  
4.3 If the sample design was relatively simple, such as simple random or stratified, then fully valid estimates of sampling variance are easily available. If a more complex design was used then methods such as discussed in Ref (1)3 or in Guide E1402 may be acceptable. Use of replicate subsamples is the most straightforward way to estimate sampling variances when the survey design is complex.  
4.4 Once the survey procedures that were used satisfy Section 5, see if any increase in sample size is needed. The calculations for making it objectively are described in Section 6.  
4.5 Refer to Section 7 to guide in the interpretation of the uncertainty in the reported value of the parameter estimate, θ^, that is, the value of its standard error, se(θ^). The quantity se(θ^) should be reviewed to verify that the risks it entails are commensurate with the size of the sample.  
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SCOPE
1.1 This practice presents rules for accepting or rejecting evidence based on a sample. Statistical evidence for this practice is in the form of an estimate of a proportion, an average, a total, or other numerical characteristic of a finite population or lot. It is an estimate of the result which would have been obtained by investigating the entire lot or population under the same rules and with the same care as was used for the sample.  
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ASTM E3080-23(Practice)
Standard Practice for Regression Analysis with a Single Predictor Variable

ABSTRACT
This practice covers regression analysis of a set of data to define the statistical relationship between two numerical variables for use in predicting one variable from the other. This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.
SIGNIFICANCE AND USE
4.1 Regression analysis is a procedure that uses data to study the statistical relationships between two or more variables (1, 2).3 This practice is restricted in scope to consider only a single numerical response variable and a single numerical predictor variable. The objective is to obtain a regression model for use in predicting the value of the response variable Y for given values of the predictor variable X.  
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4.3 The information in this practice is arranged as follows.  
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SCOPE
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1.3 The resulting regression model can be useful for developing process knowledge through description of the variable relationship, in making predictions of future values, in relating the precision of a test method to the value of the characteristic being measured, and in developing control methods for the process generating values of the variables.  
1.4 The system of units for this practice is not specified. Dimensional quantities in the practice are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development ...

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Standard Practice for Demonstrating Capability to Comply with an Acceptance Procedure

ABSTRACT
This practice provides a general methodology for evaluating single-stage or multiple-stage acceptance procedures which involve a quality characteristic measured on a numerical scale. This methodology computes, at a prescribed confidence level, a lower bound on the probability of passing an acceptance procedure, using estimates of the parameters of the distribution of test results from a sampled population.
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4.1 This practice considers inspection procedures that may involve multiple-stage sampling, where at each stage one can decide to accept or to continue sampling, and the decision to reject is deferred until the last stage.  
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SCOPE
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SIGNIFICANCE AND USE
5.1 The POD analysis method described herein is based on a well-known and well established statistical regression method. It shall be used to quantify the demonstrated POD for a specific set of examination parameters and known range of discontinuity sizes under the following conditions.  
5.1.1 The initial response from a nondestructive evaluation inspection system is ultimately binary in nature (that is, hit or miss).  
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SCOPE
1.1 This practice covers the procedure for performing a statistical analysis on nondestructive testing hit/miss data to determine the demonstrated probability of detection (POD) for a specific set of examination parameters. Topics covered include the standard hit/miss POD curve formulation, validation techniques, and correct interpretation of results.  
1.2 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
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Standard Practice for Setting an Upper Confidence Bound for a Fraction or Number of Non-Conforming items, or a Rate of Occurrence for Non-Conformities, Using Attribute Data, When There is a Zero Response in the Sample

ABSTRACT
This practice presents methodology for the setting of an upper confidence bound regarding an unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered. In Case 1, the sample is selected from a process or a very large population of interest. In Case 2, a sample of n items is selected at random from a finite lot of N items. In Case 3, there is a process, but the output is a continuum, such as area (for example, a roll of paper or other material, a field of crop), volume (for example, a volume of liquid or gas), or time (for example, hours, days, quarterly, etc.) The sample size is defined as that portion of the �continuum� sampled, and the defined attribute may occur any number of times over the sampled portion.
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4.1 In Case 1, the sample is selected from a process or a very large population of interest. The population is essentially unlimited, and each item either has or has not the defined attribute. The population (process) has an unknown fraction of items p (long run average process non-conforming) having the attribute. The sample is a group of n discrete items selected at random from the process or population under consideration, and the attribute is not exhibited in the sample. The objective is to determine an upper confidence bound, pu, for the unknown fraction p whereby one can claim that p ≤ pu with some confidence coefficient (probability) C. The binomial distribution is the sampling distribution in this case.  
4.2 In Case 2, a sample of n items is selected at random from a finite lot of N items. Like Case 1, each item either has or has not the defined attribute, and the population has an unknown number, D, of items having the attribute. The sample does not exhibit the attribute. The objective is to determine an upper confidence bound, Du, for the unknown number D, whereby one can claim that D ≤ Du with some confidence coefficient (probability) C. The hypergeometric distribution is the sampling distribution in this case.  
4.3 In Case 3, there is a process, but the output is a continuum, such as area (for example, a roll of paper or other material, a field of crop), volume (for example, a volume of liquid or gas), or time (for example, hours, days, quarterly, etc.) The sample size is defined as that portion of the “continuum” sampled, and the defined attribute may occur any number of times over the sampled portion. There is an unknown average rate of occurrence, λ, for the defined attribute over the sampled interval of the continuum that is of interest. The sample does not exhibit the attribute. For a roll of paper, this might be blemishes per 100 ft2; for a volume of liquid, microbes per cubic litre; for a field of crop, spores per acre; for a time interval, ca...
SCOPE
1.1 This practice presents methodology for the setting of an upper confidence bound regarding a unknown fraction or quantity non-conforming, or a rate of occurrence for nonconformities, in cases where the method of attributes is used and there is a zero response in a sample. Three cases are considered.  
1.1.1 The sample is selected from a process or a very large population of discrete items, and the number of non-conforming items in the sample is zero.  
1.1.2 A sample of items is selected at random from a finite lot of discrete items, and the number of non-conforming items in the sample is zero.  
1.1.3 The sample is a portion of a continuum (time, space, volume, area, etc.) and the number of non-conformities in the sample is zero.  
1.2 Allowance is made for misclassification error in this practice, but only when misclassification rates are well understood or known and can be approximated numerically.  
1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.  
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Standard Practice for Statistical Treatment of Thermoanalytical Data

SIGNIFICANCE AND USE
5.1 The standard deviation, or one of its derivatives, such as relative standard deviation or pooled standard deviation, derived from this practice, provides an estimate of precision in a measured value. Such results are ordinarily expressed as the mean value ± the standard deviation, that is, X ± s.  
5.2 If the measured values are, in the statistical sense, “normally” distributed about their mean, then the meaning of the standard deviation is that there is a 67 % chance, that is 2 in 3, that a given value will lie within the range of ± one standard deviation of the mean value. Similarly, there is a 95 % chance, that is 19 in 20, that a given value will lie within the range of ± two standard deviations of the mean. The two standard deviation range is sometimes used as a test for outlying measurements.  
5.3 The calculation of precision in the slope and intercept of a line, derived from experimental data, commonly is required in the determination of kinetic parameters, vapor pressure or enthalpy of vaporization. This practice describes how to obtain these and other statistically derived values associated with measurements by thermal analysis.
SCOPE
1.1 This practice details the statistical data treatment used in some thermal analysis methods.  
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1.3 Some thermal analysis methods derive the analytical value from the slope or intercept of a linear regression straight line (or plane) assigned to three or more sets of data pairs. Such methods may require an estimation of the precision in the determined slope or intercept. The determination of this precision is not a common statistical tool. This practice details the process for obtaining such information about precision.  
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Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans

ABSTRACT
This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product. Two general types of tables are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection.
SIGNIFICANCE AND USE
4.1 Two general types of tables (Note 1) are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL. The broad conditions under which the different types have been found best adapted are indicated below.  
4.1.1 For each of the types, tables are provided both for single sampling and for double sampling. Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection. Because each line in the tables covers a range of lot sizes, the AOQL values in the LTPD tables and the LTPD values in the AOQL tables are often conservative.
Note 1: Tables in Annex A1 – Annex A4 and parts of the text are reproduced by permission of John R. Wiley and Sons. More extensive tables and discussion of the methods will be found in that text.  
4.2 The sampling tables based on lot quality protection (LTPD) (the tables in Annex A1 and Annex A2) are perhaps best adapted to conditions where interest centers on each lot separately, for example, where the individual lot tends to retain its identity either from a shipment or a service standpoint. These tables have been found particularly useful in inspections made by the ultimate consumer or a purchasing agent for lots or shipments purchased more or less intermittently.  
4.3 The sampling tables based on average quality protection (AOQL) (the tables in Annex A3 and Annex A4) are especially adapted for use where interest centers on the average quality of product after inspection rather than on the quality of each individual lot and where inspection is, therefore, intended to serve, if necessary, as a partial screen for defective pieces. The latter point of view has been found particularly helpful, for example, in consumer inspections of continuing purchases of large quantities of a product and in manufacturing process inspections of parts where the inspection lots tend to lose their identity by merger in a common storeroom from which quantities are withdraw...
SCOPE
1.1 This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of average outgoing quality limit, AOQL, and lot tolerance percent defective, LTPD, sampling plans for determining acceptable of lots of product.  
1.2 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM D7915-22(Practice)
Standard Practice for Application of Generalized Extreme Studentized Deviate (GESD) Technique to Simultaneously Identify Multiple Outliers in a Data Set

SIGNIFICANCE AND USE
3.1 The GESD procedure can be used to simultaneously identify up to a pre-determined number of outliers (r) in a data set, without having to pre-examine the data set and make a priori decisions as to the location and number of potential outliers.  
3.2 The GESD procedure is robust to masking. Masking describes the phenomenon where the existence of multiple outliers can prevent an outlier identification procedure from declaring any of the observations in a data set to be outliers.  
3.3 The GESD procedure is automation-friendly, and hence can easily be programmed as automated computer algorithms.
SCOPE
1.1 This practice provides a step by step procedure for the application of the Generalized Extreme Studentized Deviate (GESD) Many-Outlier Procedure to simultaneously identify multiple outliers in a data set. (See Bibliography.)  
1.2 This practice is applicable to a data set comprising observations that is represented on a continuous numerical scale.  
1.3 This practice is applicable to a data set comprising a minimum of six observations.  
1.4 This practice is applicable to a data set where the normal (Gaussian) model is reasonably adequate for the distributional representation of the observations in the data set.  
1.5 The probability of false identification of outliers associated with the decision criteria set by this practice is 0.01.  
1.6 It is recommended that the execution of this practice be conducted under the guidance of personnel familiar with the statistical principles and assumptions associated with the GESD technique.  
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM E122-17(2022)(Practice)
Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process

ABSTRACT
This practice covers simple methods for calculating how many units to include in a random sample in order to estimate with a specified precision, a measure of quality for all the units of a lot of material or produced by a process. It also treats the common situation where the sampling units can be considered to exhibit a single source of variability; it does not treat multi-level sources of variability.
SIGNIFICANCE AND USE
4.1 This practice is intended for use in determining the sample size required to estimate, with specified precision, a measure of quality of a lot or process. The practice applies when quality is expressed as either the lot average for a given property, or as the lot fraction not conforming to prescribed standards. The level of a characteristic may often be taken as an indication of the quality of a material. If so, an estimate of the average value of that characteristic or of the fraction of the observed values that do not conform to a specification for that characteristic becomes a measure of quality with respect to that characteristic. This practice is intended for use in determining the sample size required to estimate, with specified precision, such a measure of the quality of a lot or process either as an average value or as a fraction not conforming to a specified value.
SCOPE
1.1 This practice covers simple methods for calculating how many units to include in a random sample in order to estimate with a specified precision, a measure of quality for all the units of a lot of material, or produced by a process. This practice will clearly indicate the sample size required to estimate the average value of some property or the fraction of nonconforming items produced by a production process during the time interval covered by the random sample. If the process is not in a state of statistical control, the result will not have predictive value for immediate (future) production. The practice treats the common situation where the sampling units can be considered to exhibit a single (overall) source of variability; it does not treat multi-level sources of variability.  
1.2 The system of units for this standard is not specified. Dimensional quantities in the standard are presented only as illustrations of calculation methods. The examples are not binding on products or test methods treated.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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