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ASTM E2093-00

(Guide)

Standard Guide for Optimizing, Controlling and Reporting Test Method Uncertainties from Multiple Workstations in the Same Laboratory Organization

Standard Guide for Optimizing, Controlling and Reporting Test Method Uncertainties from Multiple Workstations in the Same Laboratory Organization

SCOPE
1.1 This guide describes a protocol for optimizing, controlling, and reporting test method uncertainties from multiple workstations in the same laboratory organization. It does not apply when different test methods, dissimilar instruments, or different parts of the same laboratory organization function independently to validate or verify the accuracy of a specific analytical measurement.
1.2 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
09-May-2000
ICS
03.120.30 - Application of statistical methods
Technical Committee
E01 - Analytical Chemistry for Metals, Ores, and Related Materials
Drafting Committee
E01.22 - Laboratory Quality
Current Stage
Ref Project

Relations

Replaced By
ASTM E2093-05 - Standard Guide for Optimizing, Controlling and Reporting Test Method Uncertainties from Multiple Workstations in the Same Laboratory Organization
Effective Date
01-May-2005

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ASTM E2093-00 - Standard Guide for Optimizing, Controlling and Reporting Test Method Uncertainties from Multiple Workstations in the Same Laboratory OrganizationASTM E2093-00 - Standard Guide for Optimizing, Controlling and Reporting Test Method Uncertainties from Multiple Workstations in the Same Laboratory Organization
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ASTM E2093-00 - Standard Guide for Optimizing, Controlling and Reporting Test Method Uncertainties from Multiple Workstations in the Same Laboratory Organization
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.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:E2093–00
Standard Guide for
Optimizing, Controlling and Reporting Test Method
Uncertainties from Multiple Workstations in the Same
Laboratory Organization
This standard is issued under the fixed designation E 2093; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope Calibration and Testing Laboratories
ISO 9000 Quality Management and Quality System Ele-
1.1 This guide describes a protocol for optimizing, control-
ments
ling, and reporting test method uncertainties from multiple
workstations in the same laboratory organization. It does not
3. Terminology
apply when different test methods, dissimilar instruments, or
3.1 Definitions—For definitions of terms used in this guide,
different parts of the same laboratory organization function
refer to Terminology E 135.
independently to validate or verify the accuracy of a specific
3.2 Definitions of Terms Specific to This Standard:
analytical measurement.
3.2.1 data quality objectives, n—a model used by the
1.2 This standard does not purport to address all of the
laboratory organization to specify the maximum error associ-
safety concerns, if any, associated with its use. It is the
ated with a report value, at a specified confidence level.
responsibility of the user of this standard to establish appro-
3.2.2 laboratory organization, n—a business entity that
priate safety and health practices and determine the applica-
provides similar types of measurements from more than one
bility of regulatory limitations prior to use.
workstation located in one or more laboratories, all of which
2. Referenced Documents operate under a unified quality system.
3.2.3 maximum deviation, n—the maximum error associ-
2.1 ASTM Standards:
ated with a report value, at a specified confidence level, for a
E 135 Terminology Relating to Analytical Chemistry for
given concentration of a given element, determined by a
Metals, Ores, and Related Materials
specific method, throughout a laboratory organization.
E 350 Test Methods for ChemicalAnalysis of Carbon Steel,
3.2.4 workstation, n—a combination of people and equip-
Low-Alloy Steel, Silicon Electrical Steel, Ingot Iron, and
ment that executes a specific test method using a single
Wrought Iron
specifiedmeasuringdevicetoquantifyoneormoreparameters,
E 415 Test Method for Optical Emission Vacuum Spectro-
with each report value having an established estimated uncer-
metric Analysis of Carbon and Low-Alloy Steel
tainty that complies with the data quality objectives of the
E 1329 Practice for Verification and the Use of Control
laboratory organization.
Charts in Spectrochemical Analysis
E 1601 Practice for Conducting an Interlaboratory Study to
4. Significance and Use
Evaluate the Performance of an Analytical Method
4.1 Many competent analytical laboratories comply with
E 2027 Practice for Conducting Proficiency Tests in the
accepted quality system requirements such as ISO 9000,
Chemical Analysis of Metals, Ores, and Related Materials
QS9000, and ISO 17025. When using standard test methods,
2.2 ISO Standards:
their test results on the same sample should agree with those
ISO 17025 General Requirements for the Competence of
from other similar laboratories within the reproducibility
estimates (R2) published in the standard. Reproducibility
estimates are generated as part of the interlaboratory studies
(ILS), of the type described in Practice E 1601, during the
This guide is under the jurisdiction of ASTM Committee E01 on Analytical
Chemistry for Metals, Ores and Related Materials and is the direct responsibility of
Subcommittee E01.22 on Statistics and Quality Control .
Current edition approved May 10, 2000. Published July 2000. Available from American National Standards Institute, 11 W. 42nd St., 13th
For referenced ASTM standards, visit the ASTM website, www.astm.org, or Floor, New York, NY 10036.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Quality Systems Requirements, Chrysler Corporation, Ford Motor Company,
Standards volume information, refer to the standard’s Document Summary page on and General Motors Corporation—available from AIAG, 26200 Lahser Rd.,
the ASTM website. Southfield, MI 48034.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E2093–00
standardization process. Competent laboratories participate in 5.2 Identify the workstations to be included in the protocol
proficiency tests, such as those carried out according to and harmonize their experimental procedures, calibrations, and
Practice E 2027, to confirm that that they perform consistently control strategies so that all performance data from all work-
over time. In both ILS and proficiency testing protocols, it is stations are directly statistically comparable.
generally assumed that only one work station is used to
5.3 Tabulate performance data for each workstation and
generate the data.
ensure that each workstation complies with the laboratory
4.2 Many laboratories have workloads, or logistical require-
organization’s data quality objectives.
ments, or both, that dictate the use of multiple work stations.
5.4 Document items covered in 5.1-5.3.
Some have multiple stations in the same area (central labora-
5.5 Establish and document a laboratory organization-wide
toryformat).Others’stationsarescatteredthroughoutafacility
proficiency test policy that provides traceability to all work-
(at-line laboratory format). Often, analysis reports do not
stations.
identify the workstation used for the testing, even if worksta-
5.6 Operate each workstation independently as described in
tions differ in their testing uncertainties. Problems can arise if
its associated documentation. If any changes are made to any
clientsmistakenlyattributevariationinreportvaluestoprocess
workstation or its performance levels, document the changes
rather then workstation variability. These problems can be
and ensure compliance with the laboratory organization’s data
minimized if the laboratory organization sets, complies with,
quality objectives.
and reports a unified set of data quality objectives throughout.
4.3 This guide describes a protocol for efficiently optimiz-
6. Procedure
ing and controlling variability in test results from different
workstations used to perform the same test. It harmonizes
6.1 Identify the test method and establish the data quality
calibration and control protocols, thereby providing the same
objectives to be met throughout the laboratory organization.
level of measurement traceability and control to all worksta-
6.1.1 Multi-element test methods can be handled concur-
tions. It streamlines documentation and training requirements,
rently, provided that all elements are measured using common
thereby facilitating flexibility in personnel assignments. Fi-
technology, and that the parameters that influence data quality
nally, it offers an opportunity to claim traceability of profi-
are tabulated and evaluated for each element individually. An
ciency test measurements to all included workstations, regard-
example is Test Method E 415 that covers the analysis of plain
less on which workstation the proficiency test sample was
carbon and low alloy steel by optical emission vacuum
tested. The potential benefits of utilizing this protocol increase
spectrometry. Workstations can be under manual or robotic
with the number of workstations included in the laboratory
control, as long as the estimated uncertainties are within the
organization.
specifieddataqualityobjectives.Avoidhandlingmulti-element
4.4 This guide can be used to identify and quantify benefits
test methods concurrently that use different measurement
derived from corrective actions relating to under-performing
technologies. Their procedures and error evaluations are too
workstations. It also provides means to track improved perfor-
diverse to be incorporated into one easy-to-manage package.
mance after improvements have been made.
An example of test methods that should not be combined into
4.5 It is assumed that all who use this guide comply with
one program is Test Methods E 350 because those methods
ISO 17025, especially including the use of documented proce-
cover many different measurement technologies.
dures, the application of statistical control of measurement
6.1.2 Set the data quality objectives for the application of
processes, and participation in proficiency testing.
the method throughout the laboratory organization, using
4.6 The general principles of this protocol can be adapted to
customer requirements and available performance data. At the
other types of measurements, such as mechanical testing and
conclusion of this effort, the laboratory organization will know
on-lineprocesscontrolmeasurements,suchastemperatureand
the maximum deviation allowed in any report value, at any
thickness gaging. In these areas, users may need to establish
concentrationlevel,usingthemethodofchoice.Anexampleof
their own models for defining data quality objectives and
a possible method for establishing data quality objectives is
proficiency testing may not be available or applicable.
given in Annex A1.
4.7 It is especially important that users of this guide take
6.2 Identify the workstations to be included in the protocol
responsibility for ensuring the accuracy of the measurements
and harmonize their experimental procedures, calibrations, and
madebytheworkstationstobeoperatedunderthisprotocol.In
control strategies so that all performance data from all work-
addition to the checks mentioned in 6.2.3, laboratories are
stations are directly statistically comparable.
encouraged to use other techniques, including, but not limited
6.2.1 Foreachworkstation,listthepersonnelandequipment
to, analyzing some materials by independent methods, either
that significantly influence data quality. Each component of
within the same laboratory or in collaboration with other
each workstation does not have to be identical, such as from
equally competent laboratories. The risks associated with
the same manufacturer or model number; however, each
generating large volumes of data from carefully synchronized,
workstation must perform the functions described in the test
but incorrectly calibrated multiple workstations are obvious
method.
and must be avoided.
6.2.2 Harmonize the experimental procedures associated
5. Summary
with each workstation to ensure that all stations are capable of
5.1 Identify the test method and establish the data quality generating statistically comparable data that can be expected to
objectives to be met throughout the laboratory organization. fall within the maximum allowable limits for the laboratory
E2093–00
organization. Ideally, all workstations within the laboratory
TABLE 1 Continued
organization will have essentially the same experimental pro-
Assumed
cedures.
ERM True Conc. WS Av. UCL LCL Std. Dev.
6.2.3 Harmonize calibration protocols so that the same
2 0.02475 0.02940 0.02010 0.00155
calibrants are used to cover the same calibration ranges for the 3 0.02467 0.02884 0.02050 0.00139
same elements on all instruments. Avoid the use of different
Si 638 0.01688 1 0.01565 0.01718 0.01412 0.00051
calibrants on different instruments that may lead to calibration
2 0.01755 0.01863 0.01647 0.00036
3 0.01743 0.01830 0.01656 0.00029
biases and uncertainties that are larger than necessary. Make
sure that all interferences and matrix effects are addressed.
648 0.23283 1 0.22900 0.23911 0.21889 0.00337
Verify the calibrations with certified reference materials not
2 0.23240 0.24404 0.22076 0.00388
3 0.23710 0.24619 0.22801 0.00303
used in the calibration, when possible. Record the findings for
each workstation.
Cu 638 0.26588 1 0.26685 0.27555 0.25815 0.00290
6.2.4 Use the same SPC materials and data collection
2 0.26569 0.27295 0.25843 0.00242
3 0.26511 0.27276 0.25746 0.00255
practices on all work stations (see Note 1). Carry SPC
materials through all procedural steps that contribute to the
648 0.10700 1 0.10654 0.11089 0.10219 0.00145
measurement uncertainty. Develop control charts in accor-
2 0.10753 0.11086 0.10420 0.00111
3 0.10694 0.13784 0.07604 0.01030
dance with E 1329, or equivalent practice.
NOTE 1—Generally, it is recommended that SPC concentrations be set Ni 638 0.69005 1 0.70014 0.72516 0.67512 0.00834
1 1
2 0.68252 0.69440 0.67064 0.00396
about ⁄3 from the top and ⁄3 from the bottom of each calibration range. It
3 0.68750 0.71309 0.66191 0.00853
isalsorecommendedthatsinglepoint,movingrangechartsbeusedsothat
calculatedstandarddeviationsreflectthenormalvariationinreportvalues.
648 0.25063 1 0.25174 0.25906 0.24442 0.00244
2 0.24891 0.25350 0.24432 0.00153
6.2.5 Collect at least 20 SPC data points from each work
3 0.25123 0.25927 0.24319 0.00268
station to ensure that the workstations are under control and
Cr 638 0.03746 1 0.03760 0.03886 0.03634 0.00042
that the control limits are representative.
2 0.03745 0.03832 0.03658 0.00029
6.3 Tabulate performance data for each workstation and
3 0.03732 0.03813 0.03651 0.00027
ensure that each workstation complies with the laboratory
648 0.23728 1 0.23190 0.23637 0.22743 0.00149
organization’s data quality objectives.
2 0.24012 0.24414 0.23610 0.00134
6.3.1 Tabulate the SPC data by parameter (element), Refer-
3 0.23982 0.24300 0.23664 0.00106
ence material, assumed true concentration, workstation, aver-
Sn 638 0.00278 1 0.00255 0.00507 0.00003 0.00084
age, upper control limit, lower control limit, and standard
2 0.00257 0.00296 0.00218 0.00013
deviation, as illustrated in Table 1 (see Notes 2 and 3).
3 0.00322 0.00490 0.00154 0.00056
648 0.01424 1 0.01402 0.01600 0.01204 0.00066
TABLE 1 Sample SPC Control Parameter Tabulation
2 0.01412 0.01502 0.01322 0.00030
3 0.01458 0.01668 0.01248 0.00070
Assumed
ERM True Conc. WS Av. UCL LCL Std. Dev.
Mo 638 0.06346 1 0.06253 0.06604 0.05902 0.00117
C 638 0.06014 1 0.05996 0.06764 0.05228 0.00256 2 0.06398 0.06533 0.06263 0.00045
2 0.06040 0.06364 0.05716 0.00108 3 0.06387 0.06621 0.06153 0.00078
3 0.06005 0.06308 0.05702 0.00101
648 0.08652 1 0.08539 0.08995 0.08083 0.00152
648 0.25665 1 0.25212 0.27069 0.23355 0.00619 2 0.08722 0.08941 0.08503 0.00073
2 0.25923 0.27402 0.24444 0.00493 3 0.08696 0.09011 0.08381 0.00105
3 0.25861 0.27283 0.24439 0.00474
V 638 0.02107 1 0.02076 0.02184 0.01968 0.00036
Mn 638 0.29832 1 0.29620 0.30304 0.28936 0.00228 2 0.02114 0.02219 0.02009 0.00035
2 0.29967 0.30567 0.29367 0.00200 3 0.02132 0.02231 0.02033 0.00
...

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4.1 The methodology was originally developed (1-4)6 for use in drug content uniformity and dissolution but has general application to any multistage test with multiple acceptance criteria. Practice E2709 summarizes the statistical aspects of this methodology. This practice applies the general methodology of Practice E2709 specifically to the UDU test.  
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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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4.2 The methodology in this practice defines an acceptance region for a set of test results from the sampled population such that, at a prescribed confidence level, the probability that a sample from the population will pass the acceptance procedure is greater than or equal to a prespecified lower bound.  
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4.2.2 This information can be used for process demonstration, validation of test methods, and qualification of instruments, processes, and materials.  
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4.2.4 If the results are to be applied to future test results from the same process, then it is assumed that the process is stable and predictable. If this is not the case then there can be no guarantee that the probability estimates would be valid predictions of future process performance.  
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4.4 Mathematical derivations would be required that are specific to the individual criteria of each test.
SCOPE
1.1 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.  
1.2 For a prescribed lower probability bound, the methodology can also generate an acceptance limit table, which defines a set of test method outcomes (for example, sample averages and standard deviations) that would pass the acceptance procedure at a prescribed confidence level.  
1.3 This approach may be used for demonstrating compliance with in-process, validation, or lot-release specifications.  
1.4 The system of units for this practice is not specified.  
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 of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM E141-10(2023)(Practice)
Standard Practice for Acceptance of Evidence Based on the Results of Probability Sampling

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.  
4.6 When the audit subsample shows that there was reasonable conformity with prescribed procedures and when the known instances of departures from the survey plan can be shown to have no appreciable effect on the est...
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.  
1.2 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. The methods may not give least uncertainty at least cost, they should however furnish a reasonable estimate with calculable uncertainty.  
1.3 This practice is primarily intended for one-of-a-kind studies. Repetitive surveys allow estimates of sampling uncertainties to be pooled; the emphasis of this practice is on estimation of sampling uncertainty from the sample itself. The parameter of interest for this practice is effectively a constant. Thus, the principal inference is a simple point estimate to be used as if it were the unknown constant, rather than, for example, a forecast or prediction interval or distribution...

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ASTM E2862-23(Practice)
Standard Practice for Probability of Detection Analysis for Hit/Miss Data

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).  
5.1.2 Discontinuity size is the predictor variable and can be accurately quantified.  
5.1.3 A relationship between discontinuity size and POD exists and is best described by a generalized linear model with the appropriate link function for binary outcomes.  
5.2 This practice does not limit the use of a generalized linear model with more than one predictor variable or other types of statistical models if justified as more appropriate for the hit/miss data.  
5.3 If the initial response from a nondestructive evaluation inspection system is measurable and can be classified as a continuous variable (for example, data collected from an Eddy Current inspection system), then Practice E3023 may be more appropriate.  
5.4 Prior to performing the analysis it is assumed that the discontinuity of interest is clearly defined; the number and distribution of induced discontinuity sizes in the POD specimen set is known and well-documented; discontinuities in the POD specimen set are unobstructed; and the POD examination administration procedure (including data collection method) is well-designed, well-defined, under control, and unbiased. The analysis results are only valid if convergence is achieved and the model adequately represents the data.  
5.5 The POD analysis method described herein is consistent with the analysis method for binary data described in MIL-HDBK-1823A, and is included in several widely utilized POD software packages to perform a POD analysis on hit/miss data. It is also found in statistical software packages that have generalized line...
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.  
1.3 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.  
1.4 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 E1994-09(2023)(Practice)
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 E2334-09(2023)(Practice)
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.
SIGNIFICANCE AND USE
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.  
1.4 This ...

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ASTM E1970-23(Practice)
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.  
1.2 The method describes the commonly encountered statistical tools of the mean, standard derivation, relative standard deviation, pooled standard deviation, pooled relative standard deviation, the best fit to a (linear regression of a) straight line (or plane), and propagation of uncertainties for all calculations encountered in thermal analysis methods (see Practice E2586).  
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.  
1.4 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.  
1.5 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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