ASTM D5956-21
(Guide)Standard Guide for Sampling Strategies for Heterogeneous Wastes
Standard Guide for Sampling Strategies for Heterogeneous Wastes
SIGNIFICANCE AND USE
4.1 This guide is suitable for sampling heterogeneous wastes.
4.2 The focus of this guidance is on wastes; however, the approach described in this guide may be applicable to non-waste populations as well.
4.3 Sections 5 – 10 describe a guide for the sampling of heterogeneous waste according to project objectives. Appendix X1 describes an application of the guide to heterogeneous wastes. The user is strongly advised to read Annex A1 prior to reading and employing Sections 5 – 10 of this guide.
4.4 Annex A1 contains an introductory discussion of heterogeneity, stratification, and the relationship of samples and populations.
4.5 This guide is intended for those who manage, design, or implement sampling and analytical plans for the characterization of heterogeneous wastes.
SCOPE
1.1 This guide is a practical, nonmathematical discussion for heterogeneous waste sampling strategies. This guide is consistent with the particulate material sampling theory as well as inferential statistics, and may serve as an introduction to the statistical treatment of sampling issues.
1.2 This guide does not provide comprehensive sampling procedures, nor does it serve as a guide to any specification. It is the responsibility of the user to ensure appropriate procedures are used.
1.3 Units—The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard. All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026. Reporting of test results in units other than SI shall not be regarded as nonconformance with this standard.
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.
General Information
Relations
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: D5956 − 21
Standard Guide for
Sampling Strategies for Heterogeneous Wastes
This standard is issued under the fixed designation D5956; 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 3. Terminology
1.1 This guide is a practical, nonmathematical discussion 3.1 Definitions—For definitions of terms used in this
for heterogeneous waste sampling strategies. This guide is standard, see Terminology D5681.
consistentwiththeparticulatematerialsamplingtheoryaswell
3.2 Definitions of Terms Specific to This Standard:
as inferential statistics, and may serve as an introduction to the
3.2.1 component, n—aneasilyidentifieditemsuchasalarge
statistical treatment of sampling issues.
crystal, an agglomerate, rod, container, block, glove, piece of
1.2 This guide does not provide comprehensive sampling wood, or concrete.
procedures, nor does it serve as a guide to any specification. It
3.2.2 composite sample, n—a combination of two or more
is the responsibility of the user to ensure appropriate proce-
samples.
dures are used.
3.2.2.1 Discussion—When compositing samples to detect
1.3 Units—The values stated in SI units are to be regarded hot spots or whenever there may be a reason to determine
as standard. No other units of measurement are included in this which of the component samples that constitute the composite
standard. All observed and calculated values shall conform to are the source of the detected contaminant, it can be helpful to
the guidelines for significant digits and rounding established in composite only portions of the component samples. The
Practice D6026. Reporting of test results in units other than SI remainders of the component samples then can be archived for
shall not be regarded as nonconformance with this standard. future reference and analysis. This approach is particularly
helpful when sampling is expensive, hazardous, or difficult.
1.4 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
3.2.3 correlation, n—the mutual relation of two or more
responsibility of the user of this standard to establish appro- things.
priate safety, health, and environmental practices and deter-
3.2.4 item, n—a distinct part of a population (for example,
mine the applicability of regulatory limitations prior to use.
microscopic particles, macroscopic particles, and 20-ft long
1.5 This international standard was developed in accor-
steel beams).
dance with internationally recognized principles on standard-
3.2.4.1 Discussion—Theterm componentdefinesasubsetof
ization established in the Decision on Principles for the
items. Components are those items that are easily identified as
Development of International Standards, Guides and Recom-
being different from the remainder of items that constitute the
mendations issued by the World Trade Organization Technical
population.The identification of components may facilitate the
Barriers to Trade (TBT) Committee.
stratification and sampling of a highly stratified population
when the presence of the characteristic of interest is correlated
2. Referenced Documents
with a specific component.
2.1 ASTM Standards:
3.2.5 practical homogeneity, n—the condition of the popu-
D5681 Terminology for Waste and Waste Management
lation under which all items of the population are not identical.
D6026 Practice for Using Significant Digits and Data Re-
For the characteristic of interest, however, the differences
cords in Geotechnical Data
between individual physical samples are not measurable or
significant relative to project objectives.
3.2.5.1 Discussion—For practical purposes, the population
This guide is under the jurisdiction of ASTM Committee D34 on Waste
is homogeneous.
Management and is the direct responsibility of Subcommittee D34.01.01 on
Planning for Sampling.
3.2.6 random, n—lack of order or patterns in a population
Current edition approved Oct. 1, 2021. Published October 2021. Originally
whose items have an equal probability of occurring.
approved in 1996. Last previous edition approved in 2015 as D5956 – 15. DOI:
10.1520/D5956-21.
3.2.6.1 Discussion—The word random is used in two dif-
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
ferent contexts in this guide. In relation to sampling, random
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
means that all items of a population have an equal probability
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. of being sampled. In relation to the distribution of a population
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5956 − 21
characteristic, random means that the characteristic has an addressed or the resulting limitations well documented.Afield
equal probability of occurring in any and all items of the notebook is likely to describe difficulties in collecting large
population. items or the fact that the center of a waste pile could not be
accessed.
3.2.7 sample variance, n—a measure of the dispersion of a
set of results. Variance is the sum of the squares of the
5.4 Population size, heterogeneity, and item size have a
individual deviations from the sample mean divided by one
substantial impact on sampling. The cost and difficulty of
less than the number of results involved. It may be expressed
accurately sampling a population usually is correlated with the
2 2
as s 5 ~x 2x¯! /~n21!.
( knowledge of these population attributes and characteristics.
i
The least understood population attribute is heterogeneity of
4. Significance and Use
the characteristic of interest. If heterogeneity is not known
through process knowledge, then some level of preliminary
4.1 This guide is suitable for sampling heterogeneous
sampling or field analysis is often required prior to sampling
wastes.
design.
4.2 The focus of this guidance is on wastes; however, the
5.5 Sampling of any population may be difficult. However,
approach described in this guide may be applicable to non-
with all other variables being the same, nonrandom heteroge-
waste populations as well.
neous populations are usually more difficult to sample. The
4.3 Sections5–10 describe a guide for the sampling of
increased difficulty in sampling nonrandom heterogeneous
heterogeneouswasteaccordingtoprojectobjectives.Appendix
populations is due to the existence of unidentified or numerous
X1 describes an application of the guide to heterogeneous
strata, or both. If the existence of strata is not considered when
wastes. The user is strongly advised to read AnnexA1 prior to
sampling a nonrandom heterogeneous population, the resulting
reading and employing Sections5–10 of this guide.
data will average the measured characteristics of the individual
4.4 Annex A1 contains an introductory discussion of
strata over the entire population. If the different strata are
heterogeneity, stratification, and the relationship of samples
relatively similar in composition, then the mean characteristic
and populations.
of the population may be a good predictor for portions of the
population and will often allow the project-specific objectives
4.5 This guide is intended for those who manage, design, or
to be achieved. As the difference in composition between
implement sampling and analytical plans for the characteriza-
different strata increases, average population characteristics
tion of heterogeneous wastes.
become less useful in predicting composition or properties of
individual portions of the population. In this latter case, when
5. Sampling Difficulties
possible, it is advantageous to sample the individual strata
5.1 There are numerous difficulties that can complicate
separately and, if an overall average of a population charac-
efforts to sample a population. These difficulties can be
teristic is needed, it can be calculated mathematically using the
classified into four general categories:
weighted averages of the sampling stratum means (1).
5.1.1 Population access problems making it difficult to
sample all or portions of the population;
6. Stratification
5.1.2 Sample collection difficulties due to physical proper-
6.1 Strata can be thought of as different portions of a
ties of the population (for example, unwieldy large items or
population which may be separated in time or space, with each
high viscosity);
portion having internally similar concentrations or properties,
5.1.3 Planning difficulties caused by insufficient knowledge
which are different from adjacent portions of the population
regarding population size, heterogeneity of the contaminant of
(that is, concentrations/properties are correlated with space,
interest, item size, or a combination thereof; and
time, component, or source). Fig. 1 is a graphical depiction of
5.1.4 Budget problems that prevent implementation of a
different types of strata.
workable, but too costly, sampling design.
6.1.1 A landfill may display spatially separated strata since
5.2 The difficulties included in the first three categories are
old cells may contain different wastes than new cells (stratifi-
a function of the physical properties of the population being
cation over space).
sampled. The last sampling difficulty category is a function of
6.1.2 A waste pipe may discharge temporally separated
budget restraints that dictate a less costly sampling approach
strata if night-shift production varies from the day shift
thatoftenresultsinareducednumberofsamplesandareduced
(stratification over time).
certainty in the estimates of population characteristics. Budget
6.1.3 Lead-acid batteries will constitute a strata separate
restraints can make it difficult to balance costs with the levels
from commingled soil if lead is the characteristic of interest
of confidence needed in decision-making. These difficulties
(stratification by component).
may be resolved by changing the objectives or sampling/
6.1.4 Drums from an inorganic process may constitute a
analytical plans since population attributes or physical proper-
different strata from those co-disposed drums generated by an
ties of the population can seldom be altered. Documents on
organic process (a subtype of stratification by component
DQOs discuss a process for balancing budgets with needed
referred to as stratification by source).
levels of confidence.
5.3 Population access and sample collection difficulties
The boldface numbers in parentheses refer to the list of references at the end of
often are obvious and, therefore, more likely either to be this standard.
D5956 − 21
FIG. 1 Types of Stratified Heterogeneous Wastes
with the constituent of interest having different concentrations in each
6.2 Different strata often are generated by different pro-
strata.
cessesorasignificantvariantofthesameprocess.Thedifferent
origins of the strata usually result in a different concentration 6.4 Certainpopulationsdonotdisplayanyobvioustemporal
distribution and mean concentration. or spatial stratification, yet the distribution of the target
characteristic is excessively erratic. For these populations, it
6.3 Highly stratified populations, a type of nonrandom
may be helpful to consider stratification of the population by
heterogeneous populations, have so many strata that they
component. Stratification by component is applied to popula-
become difficult to sample and characterize. Classifying a
tions that contain easily identifiable items, such as large
population according to its level of stratification is a relative
crystals or agglomerates, rods, blocks, gloves, pieces of wood,
issue pertaining to the persons planning and performing the
or concrete. Separating a population into sampling strata
sampling, their experience, available equipment, and budgets.
according to components is useful when a specific kind of
Highly stratified populations are such that it is not practical or
component is distributed within the population and when a
effective to employ conventional sampling approaches to
characteristic of interest is correlated with the component.
generate a representative database, nor would the mean con-
Stratification by source (for example, organic process waste
centrationofahighlystratifiedpopulationbeausefulpredictor
drums versus inorganic process waste drums) is a type of
(that is, the level of uncertainty is too great) for an individual
component stratification. Stratification by component is an
subset that may be subjected to evaluation, handling, storage,
important mechanism for understanding the properties of
treatment, or disposal.
component-heterogeneous populations and for designing ap-
NOTE 1—An example of a highly stratified population is a landfill, a
propriate sampling and analytical efforts.
candidate for remediation, that is contaminated with the pure and very
6.4.1 Componentstrataarenotnecessarilyseparatedintime
viscous Aroclor 1260 and with solutions containing varying concentra-
or space but are usually intermixed and the properties or
tions ofAroclor 1260. (Aroclor 1260 is viscous and can exist as globules
composition of the individual components are the basis of
of the pure Aroclor.) The detected concentration of Aroclors in analytical
subsamples would reflect a highly stratified population if some samples
stratification. For example, automobile batteries that are mixed
contained globules of pure 1260, while other samples contained soils that
in an unrelated waste would be a component that could
came in contact with solvents containing varying concentrations of 1260.
constituteanindividualstrataifleadwasatargetcharacteristic.
Highly nonrandom heterogeneous populations have numerous strata, each
If one were to sequester the batteries, they would have a
of which contains different distributions of contaminants or item sizes, or
both, such that an average value for the population would not be useful in consistent distribution that was different from the rest of the
predicting the composition or properties of individual portions of the
waste.
waste (that is, statistically speaking, the variance and standard error of the
6.4.2 There is usually no purpose in stratifying by compo-
mean will be large).
nent if different components have similar concentrations of the
A second and more visually obvious example of a highly stratified
target characteristic
...
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: D5956 − 15 D5956 − 21
Standard Guide for
Sampling Strategies for Heterogeneous Wastes
This standard is issued under the fixed designation D5956; 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 guide is a practical, nonmathematical discussion for heterogeneous waste sampling strategies. This guide is consistent
with the particulate material sampling theory,theory as well as inferential statistics, and may serve as an introduction to the
statistical treatment of sampling issues.
1.2 This guide does not provide comprehensive sampling procedures, nor does it serve as a guide to any specification. It is the
responsibility of the user to ensure appropriate procedures are used.
1.3 Units—The values stated in SI units are to be regarded as standard. No other units of measurement are included in this
standard. All observed and calculated values shall conform to the guidelines for significant digits and rounding established in
Practice D6026. Reporting of test results in units other than SI shall not be regarded as nonconformance with this standard.
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 safety, health, and healthenvironmental 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.
2. Referenced Documents
2.1 ASTM Standards:
D5681 Terminology for Waste and Waste Management
D6026 Practice for Using Significant Digits and Data Records in Geotechnical Data
3. Terminology
3.1 Definitions—For definitions of terms used in this standard, see Terminology D5681.
3.2 Definitions of Terms Specific to This Standard:
2.1.1 attribute, n—a quality of samples or a population.
This guide is under the jurisdiction of ASTM Committee D34 on Waste Management and is the direct responsibility of Subcommittee D34.01.01 on Planning for
Sampling.
Current edition approved May 1, 2015Oct. 1, 2021. Published May 2015October 2021. Originally approved in 1996. Last previous edition approved in 20062015 as
D5956 – 96 (2006)D5956 – 15., which was withdrawn in January 2015 and reinstated in May 2015. DOI: 10.1520/D5956-15. DOI: 10.1520/D5956-21.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. 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
D5956 − 21
2.1.1.1 Discussion—
Homogeneity, heterogeneity, and practical homogeneity are population attributes. Representativeness and intersample variance are
sample attributes.
2.1.2 characteristic, n—a property of items, a sample or population that can be measured, counted, or otherwise observed.
2.1.2.1 Discussion—
A characteristic of interest may be the cadmium concentration or ignitability of a population.
3.2.1 component, n—an easily identified item such as a large crystal, an agglomerate, rod, container, block, glove, piece of wood,
or concrete.
3.2.2 composite sample, n—a combination of two or more samples.
3.2.2.1 Discussion—
When compositing samples to detect hot spots or whenever there may be a reason to determine which of the component samples
that constitute the composite are the source of the detected contaminant, it can be helpful to composite only portions of the
component samples. The remainders of the component samples then can be archived for future reference and analysis. This
approach is particularly helpful when sampling is expensive, hazardous, or difficult.
3.2.3 correlation, n—the mutual relation of two or more things.
2.1.6 database, n—a comprehensive collection of related data organized for quick access.
2.1.6.1 Discussion—
Database as used in this guide refers to a collection of data generated by the collection and analysis of more than one physical
sample.
2.1.7 data quality objectives (DQO), n—DQOs are qualitative and quantitative statements derived from the DQO process
describing the decision rules and the uncertainties of the decision(s) within the context of the problem(s).
2.1.8 data quality objective process, n—a quality management tool based on the scientific method and developed by the U.S.
Environmental Protection Agency to facilitate the planning of environmental data collection activities.
2.1.8.1 Discussion—
The DQO process enables planners to focus their planning efforts by specifying the use of the data (the decision), the decision
criteria (action level) and the decision maker’s acceptable decision error rates. The products of the DQO process are the DQOs.
2.1.9 heterogeneity, n—the condition of the population under which items of the population are not identical with respect to the
characteristic of interest.
2.1.10 homogeneity, n—the condition of the population under which all items of the population are identical with respect to the
characteristic of interest.
2.1.10.1 Discussion—
Homogeneity is a word that has more than one meaning. In statistics, a population may be considered homogeneous when it has
one distribution (for example, if the concentration of lead varies between the different items that constitute a population and the
varying concentrations can be described by a single distribution and mean value, then the population would be considered
homogeneous). A population containing different strata would not have a single distribution throughout, and in statistics, may be
considered to be heterogeneous. The terms homogeneity and heterogeneity as used in this guide, however, reflect the understanding
more common to chemists, geologists, and engineers. The terms are used as described in the previous definitions and refer to the
similarity or dissimilarity of items that constitute the population. According to this guide, a population that has dissimilar items
would be considered heterogeneous regardless of the type of distribution.
3.2.4 item, n—a distinct part of a population (for example, microscopic particles, macroscopic particles, and 20-ft long steel
beams).
3.2.4.1 Discussion—
The term component defines a subset of items. Components are those items that are easily identified as being different from the
remainder of items that constitute the population. The identification of components may facilitate the stratification and sampling
of a highly stratified population when the presence of the characteristic of interest is correlated with a specific component.
D5956 − 21
2.1.12 population, n—the totality of items or units under consideration.
3.2.5 practical homogeneity, n—the condition of the population under which all items of the population are not identical. For the
characteristic of interest, however, the differences between individual physical samples are not measurable or significant relative
to project objectives.
3.2.5.1 Discussion—
For practical purposes, the population is homogeneous.
3.2.6 random, n—lack of order or patterns in a population whose items have an equal probability of occurring.
3.2.6.1 Discussion—
The word random is used in two different contexts in this guide. In relation to sampling, random means that all items of a
population have an equal probability of being sampled. In relation to the distribution of a population characteristic, random means
that the characteristic has an equal probability of occurring in any and all items of the population.
2.1.15 representative sample, n—a sample collected in such a manner that it reflects one or more characteristics of interest (as
defined by the project objectives) of a population from which it was collected.
2.1.15.1 Discussion—
A representative sample can be (1) a single sample, (2) a set of samples, or (3) one or more composite samples.
2.1.16 sample, n—a portion of material that is taken for testing or for record purposes.
2.1.16.1 Discussion—
Sample is a term with numerous meanings. The scientist collecting physical samples (for example, from a landfill, drum, or waste
pipe) or analyzing samples, considers a sample to be that unit of the population collected and placed in a container. In statistics,
a sample is considered to be a subset of the population, and this subset may consist of one or more physical samples. To minimize
confusion the term physical sample is a reference to the sample held in a sample container or that portion of the population that
is subjected to in situ measurements. One or more physical samples, discrete samples, or aliquots are combined to form a composite
sample. The term sample size has more than one meaning and may mean different things to the scientist and the statistician. To
avoid confusion, terms such as sample mass or sample volume and number of samples are used instead of sample size.
3.2.7 sample variance, n—a measure of the dispersion of a set of results. Variance is the sum of the squares of the individual
deviations from the sample mean divided by one less than the number of results involved. It may be expressed as s 5 x
~
(
i
2x¯ / n21 .
! ~ !
2.1.18 sampling, n—obtaining a portion of the material concerned.
2.1.19 stratum, n—a subgroup of a population separated in space or time, or both, from the remainder of the population, being
internally consistent with respect to a target constituent or property of interest, and different from adjacent portions of the
population.
2.1.19.1 Discussion—
A landfill may display spatially separated strata since old cells may contain different wastes than new cells. A waste pipe may
discharge temporally separated strata if night-shift production varies from the day shift. Also, a waste may have a contaminant of
interest associated with a particular component in the population, such as lead exclusively associated with a certain particle size.
2.1.19.2 Discussion—
Highly stratified populations consist of such a large number of strata that it is not practical or effective to employ conventional
sampling approaches, nor would the mean concentration of a highly stratified population be a useful predictor (that is, the level
of uncertainty is too great) for an individual subset that may be subjected to evaluation, handling, storage, treatment, or disposal.
Highly stratified is a relative term used to identify certain types of nonrandom heterogeneous populations. Classifying a population
according to its level of stratification is relative to the persons planning and performing the sampling, their experience, available
equipment, budgets, and sampling objectives. Under one set of circumstances a population could be considered highly stratified,
while under a different context the same population may be considered stratified.
2.1.19.3 Discussion—
The terms stratum and strata are used in two different contexts in this guide. In relation to the population of interest, stratum refers
to the actual subgroup of the population (for example, a single truck load of lead-acid batteries dumped in the northeast corner of
a landfill cell). In relation to sampling, stratum or strata refers to the subgroups or divisions of the population as assigned by the
sampling team. When assigning sampling strata, the sampling team should maximize the correlation between the boundaries of the
D5956 − 21
assigned sampling strata and the actual strata that exist within the population. To minimize confusion in this guide, those strata
assigned by the sampling team will be referred to as sampling strata.
4. Significance and Use
4.1 This guide is suitable for sampling heterogeneous wastes.
4.2 The focus of this guidance is on wastes; however, the approach described in this guide may be applicable to non-waste
populations,populations as well.
4.3 Sections 45 – 910 describe a guide for the sampling of heterogeneous waste according to project objectives. Appendix X1
describes an application of the guide to heterogeneous wastes. The user is strongly advised to read Annex A1 prior to reading and
employing Sections 45 – 910 of this guide.
4.4 Annex A1 contains an introductory discussion of heterogeneity, stratification, and the relationship of samples and populations.
4.5 This guide is intended for those who manage, design, or implement sampling and analytical plans for the characterization of
heterogeneous wastes.
5. Sampling Difficulties
5.1 There are numerous difficulties that can complicate efforts to sample a population. These difficulties can be classified into four
general categories:
5.1.1 Population access problems making it difficult to sample all or portions of the population;
5.1.2 Sample collection difficulties due to physical properties of the population (for example, unwieldy large items or high
viscosity);
5.1.3 Planning difficulties caused by insufficient knowledge regarding population size, heterogeneity of the contaminant of
interest, or item size, or a combination thereof; and,and
5.1.4 Budget problems that prevent implementation of a workable, but too costly, sampling design.
5.2 The difficulties included in the first three categories are a function of the physical properties of the population being sampled.
The last sampling difficulty category is a function of budget restraints that dictate a less-costly less costly sampling approach that
often results in a reduced number of samples and a reduced certainty in the estimates of population characteristics. Budget
restraints can make it difficult to balance costs with the levels of confidence needed in decision making. decision-making. These
difficulties may be resolved by changing the objectives or sampling/analytical plans since population attributes or physical
properties of the population can seldom be altered. Documents on DQOs discuss a process for balancing budgets with
...
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