ASTM E105-21

Standard Guide for Probability Sampling of Materials

ABSTRACT
This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material. The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of some chemical. A probability sampling plan will possess an objective procedure for the selection of the sample with the use of random numbers and a definite formula for the estimate and standard error of any estimate.
SIGNIFICANCE AND USE
4.1 The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.  
4.2 The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.  
4.3 The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile or shipment.  
4.4 Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly, as well. Proper sampling requires that any random numbers were generated properly, the units to be sampled from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not exceeding the required purposes.  
4.5 Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional data which may introduce experimental error.
SCOPE
1.1 This guide is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.  
1.2 A system of units is not specified in this 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.

General Information

• Status: Published
• Publication Date: 31-May-2021
• ICS: 91.100.01 - Construction materials in general
• Technical Committee: E11 - Quality and Statistics
• Drafting Committee: E11.10 - Sampling / Statistics

Relations

• Refers: ASTM E1402-13(2023) - Standard Guide for Sampling Design
• Effective Date: 01-Nov-2023
• Refers: ASTM E141-10(2023) - Standard Practice for Acceptance of Evidence Based on the Results of Probability Sampling
• Effective Date: 01-Nov-2023
• Refers: ASTM E456-13a(2022)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Apr-2022
• Refers: ASTM E1402-13(2018) - Standard Guide for Sampling Design
• Effective Date: 01-Nov-2018
• Refers: ASTM E141-10(2018) - Standard Practice for Acceptance of Evidence Based on the Results of Probability Sampling
• Effective Date: 01-Apr-2018
• Refers: ASTM E456-13A(2017)e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Oct-2017
• Refers: ASTM E456-13A(2017)e3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-Oct-2017
• Refers: ASTM E456-13a - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13ae3 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13ae2 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13ae1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Nov-2013
• Refers: ASTM E456-13 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 15-Aug-2013
• Refers: ASTM E1402-13 - Standard Guide for Sampling Design
• Effective Date: 01-Aug-2013
• Refers: ASTM E456-12e1 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-May-2012
• Refers: ASTM E456-12 - Standard Terminology Relating to Quality and Statistics
• Effective Date: 01-May-2012

Overview

ASTM E105-21: Standard Guide for Probability Sampling of Materials provides a comprehensive framework for developing sampling plans using probability-based methods. Published by ASTM International, this standard serves as a set of guiding principles for technical committees and professionals preparing a sampling plan for specific materials. The core purpose of probability sampling is to obtain samples objectively and randomly, enabling reliable statistical inference about the properties or quality of larger populations such as lots, shipments, or bulk materials. By adhering to the principles outlined in ASTM E105-21, users can calculate uncertainties, bias, and variance validly, reducing the risk of sampling errors and supporting rational actions in materials inspection and process control.

Key Topics

• Probability Sampling Principles: Outlines the importance of using random numbers and objective selection procedures to ensure each part of a lot, pile, or shipment has a nonzero chance of inclusion in the sample.
• Sampling Plan Requirements: Details the minimum standards necessary for a compliant probability sampling plan, including the description of the sampling units, selection methods, formulas for estimation, and error calculation.
• Random Selection Techniques: Explains proper use of random numbers and mechanical randomizers while emphasizing the limitations of nonrandom and judgment-based sampling.
• Handling Bulk Materials: Addresses specific considerations for sampling bulk materials, underlining challenges related to homogeneity, access, mixing, and environmental impacts.
• Bias and Variance Calculation: Provides for the calculation of bias, variance, and risks associated with the sampling process, supporting the integrity and precision of the estimated results.
• Practical Planning Guidance: Offers strategies for overcoming common obstacles in the preparation and implementation of sampling plans, including cost management and cooperation between statisticians and engineers.

Applications

ASTM E105-21 has wide-ranging applications across industries involved in materials testing, quality control, and process monitoring. Typical use cases include:

• Estimation of Material Properties: Supports estimating average characteristics, constituent percentages, or chemical contents of large lots or shipments through representative sampling.
• Quality Control: Forms the basis for acceptance sampling, helping identify items that meet or fail specific requirements and supporting consistent product quality.
• Regulatory Compliance: Ensures sampling practices conform to international standards and regulatory expectations regarding unbiased and statistically valid sampling.
• Process Optimization: Guides rational decision-making for production and process improvements based on reliable data.
• Bulk Material Handling: Provides methodologies for accurately sampling bulk materials, including industrial chemicals, powders, or granulates, especially where physical access or mixing is challenging.

By using ASTM E105-21, organizations can develop robust sampling plans that minimize bias, control error rates, and provide precise data for decision-making in material evaluation processes.

Related Standards

For comprehensive sampling practices and terminology, ASTM E105-21 references several related ASTM standards, including:

• ASTM E122 - Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process
• ASTM E300 - Practice for Sampling Industrial Chemicals
• ASTM E141 - Practice for Acceptance of Evidence Based on the Results of Probability Sampling
• ASTM E456 - Terminology Relating to Quality and Statistics
• ASTM E1402 - Guide for Sampling Design

Users may consult these documents for detailed methodologies, sample size calculations, acceptance criteria, and consistent terminology related to probability sampling in materials analysis and quality assurance.

Keywords: probability sampling, random sampling, materials sampling plan, ASTM E105-21, bulk material sampling, sampling bias, sample variance, industrial quality control, random number selection, stratified sampling, systematic sampling, acceptance sampling.

Standards Content (Sample)

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.
Designation: E105 − 21 An American National Standard
Standard Guide for
Probability Sampling of Materials
This standard is issued under the fixed designation E105; 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 positional, or other cues that are believed to be related to the
variable of interest, so that the selected items appear to match
1.1 This guide is primarily a statement of principles for the
the population.
guidance of ASTM technical committees and others in the
3.1.2 probability sampling plan, n—a procedure which pro-
preparation of a sampling plan for a specific material.
vides a result from a randomly selected set of sampling units
1.2 A system of units is not specified in this standard.
that will agree, within calculable limits of variation, with the
1.3 This standard does not purport to address all of the
population value.
safety concerns, if any, associated with its use. It is the
3.1.2.1 Discussion—Probabilitysamplingplansmakeuseof
responsibility of the user of this standard to establish appro-
the theory of probability to combine a suitable procedure for
priate safety, health, and environmental practices and deter-
selecting sample items with an appropriate procedure for
mine the applicability of regulatory limitations prior to use.
summarizing the test results so that inferences may be drawn
1.4 This international standard was developed in accor-
and risks calculated from the test results by the theory of
dance with internationally recognized principles on standard-
probability. For any given set of conditions, there will usually
ization established in the Decision on Principles for the
be several possible plans, all valid, but differing in speed,
Development of International Standards, Guides and Recom-
simplicity, and cost.
mendations issued by the World Trade Organization Technical
3.1.2.2 Discussion—FurtherdiscussionisprovidedinGuide
Barriers to Trade (TBT) Committee.
E1402 and Practice E141.
2. Referenced Documents
4. Significance and Use
2.1 ASTM Standards:
4.1 The purpose of the sample may be to estimate properties
E122 Practice for Calculating Sample Size to Estimate,With
of a larger population, such as a lot, pile or shipment, the
Specified Precision, the Average for a Characteristic of a
percentage of some constituent, the fraction of the items that
Lot or Process
fail to meet (or meet) a specified requirement, the average
E300 Practice for Sampling Industrial Chemicals
characteristic or quality of an item, the total weight of the
E141 Practice for Acceptance of Evidence Based on the
shipment, or the probable maximum or minimum content of,
Results of Probability Sampling
say, some chemical.
E456 Terminology Relating to Quality and Statistics
4.2 The purpose may be the rational disposition of a lot or
E1402 Guide for Sampling Design
shipment without the intermediate step of the formation of an
3. Terminology
estimate.
3.1 Definitions—Unless otherwise noted in this standard, all 4.3 The purpose may be to provide aid toward rational
terms relating to quality and statistics are defined in Terminol- actionconcerningtheproductionprocessthatgeneratedthelot,
ogy E456. pile or shipment.
3.1.1 judgment sampling, n—a procedure whereby enu-
4.4 Whatever the purpose of the sample, adhering to the
merators select a few items of the population, based on visual,
principles of probability sampling will allow the uncertainties,
such as bias and variance of estimates or the risks of the
This guide is under the jurisdiction of ASTM Committee E11 on Quality and
rational disposition or action, to be calculated objectively and
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
validly from the theory of combinatorial probabilities. This
Statistics.
assumes, of course, that the sampling operations themselves
Current edition approved June 1, 2021. Published June 2021. Originally
were carried out properly, as well. Proper sampling requires
approved in 1954. Last previous edition approved in 2016 as E105 – 16. DOI:
10.1520/E0105-21.
that any random numbers were generated properly, the units to
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
be sampled from were correctly identified, located, and drawn,
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
and the measurements were made with measurement error at a
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. level not exceeding the required purposes.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E105 − 21
4.5 Determination of bias and variance and of risks can be estimate of the overall average quality. Similarly, in acceptance
calculated when the selection was only partially determined by inspection, samples of equal size drawn from lots that vary
random numbers and a frame, but they then require supposi- widely in size serve primarily to provide consistent judgment
tions and assumptions which may be more or less mistaken or with respect to each lot, and secondarily to provide an estimate
require additional data which may introduce experimental of the process average. Where the estimate of the overall
error. average of a number of lots is the important objective, samples
proportional to the sizes of the subgroups will usually yield an
5. Characteristics of a Probability Sampling Plan
efficient estimate. For other possible criteria, sizes intermediate
5.1 A probability sampling plan will possess certain char-
between equal and proportional sampling from the subgroups
acteristics of importance, as follows:
will be appropriate.
5.1.1 It will possess an objective procedure for the selection
6.4 It is not easy to describe in a few words the many sorts
of the sample, with the use of random numbers.
of plans that will meet the requirements of 6.1.2 (see Guide
5.1.2 It will include a definite formula for the estimate, if
E1402). Nor is it easy to describe how these plans differ from
there is to be an estimate; also for the standard error of any
those that do not satisfy the requirement. Many standard
estimate. If the sample is used for decision without the
techniques, such as pure random unstratified sampling, random
intermediate step of an estimate, the decision process will
stratified sampling, and sampling with probabilities in propor-
follow definite rules. In acceptance sampling, for example,
tion to size, will satisfy the requirement; likewise every plan
these are often based on predetermined risks of taking the
will do so where the sample is made up of separate identifiable
undesired action when the true levels of the characteristic
subsamples that were selected independently and by the use of
concerned have predetermined values; for example, acceptable
random numbers.
and rejectable quality levels may be specified.
6.5 A probability sampling plan for any particular material
5.2 The minimum requirements that must be met in order to
must be workable, and if several alternative plans are possible,
obtain the characteristics mentioned in 5.1 appear in Section 6,
each of which will provide the desired level of precision, the
which also indicates the minimum requirements for the de-
plan adopted should be the one that involves the lowest cost.
scription of a satisfactory sampling plan.
6.6 Aprobability sampling plan must describe the sampling
6. Minimum Standards for a Probability Sampling Plan
units and how they are to be selected (with or without
stratification, equal probabilities, etc.).The sampling plan must
6.1 For a sampling plan to have the requirements mentioned
also describe:
in Section 5, it is necessary:
6.6.1 The formula for calculating an estimate (average
6.1.1 That every part of the pile, lot, or shipment have a
concentration, minimum concentration, range, total weight,
nonzero chance of selection,
etc.),
6.1.2 That these probabilities of selection be known, at least
6.6.2 A formula or procedure by which to calculate the
for the parts actually selected, and
standard error of any estimate from the results of the sample
6.1.3 That, either in measurement or in computation, each
itself, and
item be weighted in inverse proportion to its probability of
6.6.3 Sources of possible bias in the sampling procedure or
selection. This latter criterion should not be departed from; for
in the estimating formulas, together with data pertaining to the
example, equal weights should not be used when the probabili-
possible magnitudes of the biases and their effects on the uses
ties of selection are unequal, unless calculations show that
of the data.
biases introduced thereby will not impair the usefulness of the
results.
6.7 The development of a good sampling plan will usually
take place in steps, such as:
6.2 To meet the requirements of 6.1.1 and 6.1.2, the
6.7.1 A statement of the problem for which an estimate is
sampling plan must describe the sampling units and how they
necessary,
are to be selected. To meet requirements of 5.1.1, the sampling
6.7.2 Collection of information about relevant properties of
plan must specify that the selection will be made objectively at
the material to be sampled (averages, components of variance,
random. To achieve random selection, a table of random
etc.),
numbers or a sequence of random numbers generated by a
6.7.3 Consideration of a number of possible types of sam-
random number generator may be used. Random number
pling plans, with comparisons of overall costs, precisions, and
generation is commonly available in commercial software. For
difficulties,
a discussion of sample size related to specified precision, see
6.7.4 An evaluation of the possible plans, in terms of cost of
Practice E122.
sampling and testing, delay, supervisory time, inconvenience,
6.3 In meeting the requirements of 6.1.3, carefully state the
6.7.5 Selection of a plan from among the various possible
purposes served by sampling, lest a relatively unimportant aim
plans, and
overbalance a more important one. For example, estimates of
6.7.6 Reconsideration of all the preceding steps.
the overall average quality of a stock of items may be less
important than the rational disposition of subgroups of the
7. Selection of Sample
stock of inferior quality. In this case the method of using
subsamples of equal size drawn from each subgroup is more 7.1 Calculation of the margin of error or the risk in the use
efficient, although at some expense to the efficiency of the of the results of samples is possible only if the selection of the
E105 − 21
items for test is made at random. This is true whether the selection of the individual items of the sample, nor in making
procedure is stratified or unstratified. the inferences, nor in calc
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E105 − 16 E105 − 21 An American National Standard
Standard PracticeGuide for
Probability Sampling of Materials
This standard is issued under the fixed designation E105; 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
1.1 This practiceguide is primarily a statement of principles for the guidance of ASTM technical committees and others in the
preparation of a sampling plan for a specific material.
1.2 A system of units is not specified in this 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.
2. Referenced Documents
2.1 ASTM Standards:
E122 Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or
Process
E300 Practice for Sampling Industrial Chemicals
E141 Practice for Acceptance of Evidence Based on the Results of Probability Sampling
E456 Terminology Relating to Quality and Statistics
E1402 Guide for Sampling Design
3. Terminology
3.1 Definitions:Definitions
3.1.1 For general terminology, refer to Terminology E456 and Guide E1402.—Unless otherwise noted in this standard, all terms
relating to quality and statistics are defined in Terminology E456.
3.1.1 judgment sampling, n—a procedure whereby enumerators select a few items of the population, based on visual, positional,
or other cues that are believed to be related to the variable of interest, so that the selected items appear to match the population.
3.1.2 probability sampling plan, n—a sampling plan which makes use of the theory of probability to combine a suitable procedure
This practiceguide is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling /
Statistics.
Current edition approved April 1, 2016June 1, 2021. Published April 2016June 2021. Originally approved in 1954. Last previous edition approved in 20102016 as
E105 – 10.E105 – 16. DOI: 10.1520/E0105-16.10.1520/E0105-21.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E105 − 21
for selecting sample items with an appropriate procedure for summarizing the test results so that inferences may be drawn and risks
calculated from the test results by the theory of probability.procedure which provides a result from a randomly selected set of
sampling units that will agree, within calculable limits of variation, with the population value.
3.1.2.1 Discussion—
Probability sampling plans make use of the theory of probability to combine a suitable procedure for selecting sample items with
an appropriate procedure for summarizing the test results so that inferences may be drawn and risks calculated from the test results
by the theory of probability. For any given set of conditions, there will usually be several possible plans, all valid, but differing
in speed, simplicity, and cost. Further discussion is provided in Practice E141.
3.1.2.2 Discussion—
Further discussion is provided in Guide E1402 and Practice E141.
4. Significance and Use
4.1 The purpose of the sample may be to estimate properties of a larger population, such as a lot, pile or shipment, the percentage
of some constituent, the fraction of the items that fail to meet (or meet) a specified requirement, the average characteristic or quality
of an item, the total weight of the shipment, or the probable maximum or minimum content of, say, some chemical.
4.2 The purpose may be the rational disposition of a lot or shipment without the intermediate step of the formation of an estimate.
4.3 The purpose may be to provide aid toward rational action concerning the production process that generated the lot, pile or
shipment.
4.4 Whatever the purpose of the sample, adhering to the principles of probability sampling will allow the uncertainties, such as
bias and variance of estimates or the risks of the rational disposition or action, to be calculated objectively and validly from the
theory of combinatorial probabilities. This assumes, of course, that the sampling operations themselves were carried out properly,
as well. For example, Proper sampling requires that any random numbers required were generated properly, the units to be sampled
from were correctly identified, located, and drawn, and the measurements were made with measurement error at a level not
exceeding the required purposes.
4.5 Determination of bias and variance and of risks can be calculated when the selection was only partially determined by random
numbers and a frame, but they then require suppositions and assumptions which may be more or less mistaken or require additional
data which may introduce experimental error.
5. Characteristics of a Probability Sampling Plan
5.1 A probability sampling plan will possess certain characteristics of importance, as follows:
5.1.1 It will possess an objective procedure for the selection of the sample, with the use of random numbers.
5.1.2 It will include a definite formula for the estimate, if there is to be an estimate; also for the standard error of any estimate.
If the sample is used for decision without the intermediate step of an estimate, the decision process will follow definite rules. In
acceptance sampling, for example, these are often based on predetermined risks of taking the undesired action when the true levels
of the characteristic concerned have predetermined values; for example, acceptable and rejectable quality levels may be specified.
5.2 The minimum requirements that must be met in order to obtain the characteristics mentioned in 5.1 appear in Section 6, which
also indicates the minimum requirements for the description of a satisfactory sampling plan.
6. Minimum Standards for a Probability Sampling Plan
6.1 For a sampling plan to have the requirements mentioned in Section 5, it is necessary:
6.1.1 That every part of the pile, lot, or shipment have a nonzero chance of selection,
6.1.2 That these probabilities of selection be known, at least for the parts actually selected, and
6.1.3 That, either in measurement or in computation, each item be weighted in inverse proportion to its probability of selection.
E105 − 21
This latter criterion should not be departed from; for example, equal weights should not be used when the probabilities of selection
are unequal, unless calculations show that biases introduced thereby will not impair the usefulness of the results.
6.2 To meet the requirements of 6.1.1 and 6.1.2, the sampling plan must describe the sampling units and how they are to be
selected. To meet requirements of 5.1.1, the sampling plan must specify that the selection will be made objectively at random. To
achieve random selection, a table of random numbers or a sequence of random numbers generated by a random number generator
may be used. Random number generation is commonly available in commercial software. For a discussion of sample size related
to specified precision, see Practice E122.
6.3 In meeting the requirements of 6.1.3, carefully state the purposes served by sampling, lest a relatively unimportant aim
overbalance a more important one. For example, estimates of the overall average quality of a stock of items may be less important
than the rational disposition of subgroups of the stock of inferior quality. In this case the method of using subsamples of equal size
drawn from each subgroup is more efficient, although at some expense to the efficiency of the estimate of the overall average
quality. Similarly, in acceptance inspection, samples of equal size drawn from lots that vary widely in size serve primarily to
provide consistent judgment with respect to each lot, and secondarily to provide an estimate of the process average. Where the
estimate of the overall average of a number of lots is the important objective, samples proportional to the sizes of the subgroups
will usually yield an efficient estimate. For other possible criteria, sizes intermediate between equal and proportional sampling from
the subgroups will be appropriate.
6.4 It is not easy to describe in a few words the many sorts of plans that will meet the requirements of 6.1.2 (see Guide E1402).
Nor is it easy to describe how these plans differ from those that do not satisfy the requirement. Many standard techniques, such
as pure random unstratified sampling, random stratified sampling, and sampling with probabilities in proportion to size, will satisfy
the requirement; likewise every plan will do so where the sample is made up of separate identifiable subsamples that were selected
independently and by the use of random numbers.
6.5 A probability sampling plan for any particular material must be workable, and if several alternative plans are possible, each
of which will provide the desired level of precision, the plan adopted should be the one that involves the lowest cost.
6.6 A probability sampling plan must describe the sampling units and how they are to be selected (with or without stratification,
equal probabilities, etc.). The sampling plan must also describe:
6.6.1 The formula for calculating an estimate (average concentration, minimum concentration, range, total weight, etc.),
6.6.2 A formula or procedure by which to calculate the standard error of any estimate from the results of the sample itself, and
6.6.3 Sources of possible bias in the sampling procedure or in the estimating formulas, together with data pertaining to the possible
magnitudes of the biases and their effects on the uses of the data.
6.7 The development of a good sampling plan will usually take place in steps, such as:
6.7.1 A statement of the problem for which an estimate is necessary,
6.7.2 Collection of information about relevant properties of the material to be sampled (averages, components of variance, etc.),
6.7.3 Consideration of a number of possible types of sampling plans, with comparisons of overall costs, precisions, and difficulties,
6.7.4 An evaluation of the possible plans, in terms of cost of sampling and testing, delay, supervisory time, inconvenience,
6.7.5 Selection of a plan from among the various possible plans, and
6.7.6 Reconsideration of all the preceding steps.
7. Selection of Sample
7.1 Calculation of the margin of error or the risk in the use of the results of samples is possible
...