r/EPA
United States
Environmental Protection
Agency
Office of Pesticides
and Toxic Substances
Washington, DC 20460
EPA 560/5 85 030b
December 198f.
Toxic Substances
Statistical Support Document
for Asbestos in Buildings:
Simplified Sampling Scheme
for Friable Surfacing
Materials
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December, 1985
Statistical Support Document
for
Asbestos in Buildings
Simplified Sampling Scheme for
Friable Surfacing Materials
Exposure Evaluation Division
Office of Toxic Substance
Office of Pesticides and Toxic Substances
U.S. Environmental Protection Agency
Washington, DC 20460
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS v
SECTION 1 —INTRODUCTION 1
SECTION 2—DEFINING HOMOGENEOUS
SAMPLING AREAS 2
SECTION 3—LOCATING SAMPLING POSITIONS
WITHIN HOMOGENEOUS AREAS 2
SECTION 4—DETERMINING THE NUMBER OF SAMPLES
FOR A HOMOGENEOUS SAMPLING AREA ... 3
SECTION 5—CONCLUSIONS 7
REFERENCES 9
LIST OF FIGURES
Figure 1. Probability of Finding Asbestos when it is Present as
a Function of Q (Where Q is the Probability that
Asbestos is in the Sample when the Surfacing Material
in the Homogeneous Sampling Area Contains at Least
1% Asbestos) for Sample Sizes of 3, 5, 7, and 9 ...
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Acknowledgements
This document was written by Bertram Price of National Economic
Research Associates, Inc., and Jean Chesson and Ted Berner of
Battelle Columbus Division, based on discussions with a working group
from EPA's Office of Toxic Substances. The group consisted of Joan
Blake, Joseph Breen, Joseph Carra, Elizabeth Dutrow and Cindy Stroup
of the Exposure Evaluation Division and David Mayer and Stephen
Schanamann of the Asbestos Action Program. We thank the individuals
who reviewed an earlier draft and provided comments, many of which
are incorporated in the final version. Karen J. Krasner of Battelle man-
aged the production of text and graphics.
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1. INTRODUCTION
This report provides the statistical basis for the recommended
sampling protocol found in "Asbestos in Buildings: Simplified Sam-
pling Scheme for Friable Surfacing Materials" (USEPA, 1985; referred
to as the primary document). Obtaining samples of friable surfacing
materials is one of the first steps in testing a building for the presence
of asbestos. Sampling of sprayed- or troweled-on surfacing materials,
followed by analysis by Polarized Light Microscopy (PLM) to determine
if asbestos is present, is required for schools by "Friable Asbestos-
Containing Materials in Schools; Identification and Notification Rule"
(40 CFR Part 763). Sampling and analysis programs are also conducted
in other buildings to provide information for the development of risk
management programs and the planning of abatement projects where
necessary.
The sampling protocol, which encompasses the overall plan for
sampling and analysis, must assure that the data obtained are represen-
tative of the actual situation and that sufficient information is collected
to determine whether or not asbestos is present. The data will be
representative if all areas that could contain asbestos have been iden-
tified and if the samples are obtained from these areas in an unbiased
manner. The sampling protocol must specify the following:
• boundaries of homogeneous sampling areas (i.e., areas contain-
ing surfacing materials that are uniform in texture and appearance,
were installed at one time, and are unlikely to consist of more than
one type or formulation of mix);
• sampling locations within each homogeneous area; and
• the minimum number of samples required for each homogeneous
area.
The boundaries of homogeneous sampling areas are determined
through two activities: (1) by reviewing building documents, including
construction plans and repair and renovation records; and (2) by a
thorough visual inspection to find material not mentioned in records and
to note changes in the appearance of materials. The sampling locations
are centers of rectangles* dividing homogeneous areas into nine equally-
sized subareas (see Section 6 of the primary document). A minimum
of nine samples is recommended, except when the homogeneous
sampling area is very small (e.g., a closet). Previous guidance recom-
mended either three, five or seven samples for areas less than 1000
*Other shapes may be used to divide an irregular homogeneous area into equally-sized
subareas.
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square feet, between 1000 and 5000 square feet, and greater than 5000
square feet, respectively. In many situations these smaller numbers of
samples will suffice. However, a larger number of samples provides a
greater amount of information, reducing the likelihood of error. In each
instance the building owner should assess the tradeoff between poten-
tial errors in determining if asbestos is present and costs associated
with additional sampling and analysis.
The remainder of this report discusses each of the three re-
quirements listed above and their recommended solutions. Information
is provided that may be used to evaluate sampling schemes that go
beyond those formulated here.
2. DEFINING HOMOGENEOUS SAMPLING AREAS
Locating all surfacing materials that may contain asbestos and
establishing boundaries for homogeneous sampling areas are the most
crucial steps in the assessment process. Errors of omission at this stage
of the process dominate all other types of potential errors. If an area
with sprayed- or troweled-on material is overlooked in the initial inspec-
tion, it is a potential source of asbestos that will never be tested. De-
tailed guidance for conducting a thorough review of records and inspec-
tion of materials is found in the primary sampling document. All subse-
quent discussion of statistical methods and error rates has meaning only
if the definition of homogeneous sampling areas is complete.
3. LOCATING SAMPLING POSITIONS WITHIN
HOMOGENEOUS AREAS
The sampling locations selected within a homogeneous sampling area
should be representative of the whole homogeneous area. If the sam-
pling area were truly homogeneous (i.e., if the asbestos were distributed
evenly throughout), samples could be taken from arbitrary locations in
the area. However, as a practical matter, the property of homogeneity
is difficult to establish. Asbestos is mixed with filler materials, usually
at the site, prior to application. It is reasonable to expect some uneven-
ness in the distribution of asbestos in the surfacing material. Therefore,
efforts to be sure that the sampled material is representative are justified.
^ The sampling rules proposed must satisfy three criteria. They must:
• produce representative data;
• be defensible to all interested parties (e.g., workers and other
building occupants); and
• be practical to implement.
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The first two criteria are inter-related and therefore must be con-
sidered together when designing a sampling strategy. Homogeneity of
the area to be sampled is a critical characteristic if the sample is to be
representative. Stating that an area is homogeneous assumes that all
information that could be used to distinguish one homogeneous area
from another has been exhausted. Any remaining deviation from unifor-
mity in the distribution of asbestos across the area (e.g., clustering of
fibers) is random. Then, a sample from one location in the homogeneous
area is as informative as a sample from any other location. However,
uniformity, or the lack thereof, is not a visible characteristic. To over-
come concerns about the actual distribution of asbestos in the
homogeneous sampling area and to further reinforce the represen-
tativeness concept, each area is divided into subareas and samples are
selected within each subarea.
Sampling from different subareas assures that the samples will be
spread across the homogeneous sampling area providing a greater
degree of representativeness.
The selection of locations within subareas remains. The designated
sampling locations within a subarea should produce a randomly selected
sample of the surfacing material. The sampling procedure needs to be
objective, assuring that the sample has not been selected for conve-
nience or to serve a special purpose, and repeatable. In addition, it needs
to be easy to implement (i.e., the selection can be made in the field quick-
ly, requiring little if any information beyond what is already available).
Since asbestos fibers, if present, are distributed randomly within a
subarea, any sampling location identified before inspecting the subarea
produces a randomly selected sample of the material. Therefore the
recommended solution, which satisfies the criteria discussed above is:
Step 1. Divide the homogeneous sampling area into subareas of
equal size.
Step 2. Sample from the center of each subarea.
(Guidance for constructing the subareas and locating the "center" is
found in the primary document, "Asbestos in Buildings: Simplified
Sampling Scheme for Friable Surfacing Materials.")
4. DETERMINING THE NUMBER OF SAMPLES FOR A
HOMOGENEOUS SAMPLING AREA
Technically, if asbestos is found in one or more samples then the
sampling area is classified as containing asbestos and no additional
sampling is needed. Note, however, that the May 27,1982 EPA "Friable
Asbestos-Containing Materials in Schools; Identification and Notifica-
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tion Rule" (40 CFR Part 763) currently requires the collection and
analysis of three samples from each "distinct type of friable materials"
found within a school building. It is also acceptable to assume that the
sampling area contains asbestos and dispense with the sampling and
analysis altogether. If this is done, the area must be treated as an
asbestos-containing area. The number of samples derived here (3, 5,
7 or 9) is the number required under various situations to support a claim
that the sampling area does not contain asbestos.
The number of samples required for a homogeneous sampling area
is related to the probability that the test for asbestos gives the correct
answer. The test determining whether or not asbestos is present is based
on the sampling scheme described above and a Polarized Light
Microscopic (PLM) search for asbestos fibers in the samples obtained.
Since statistical variability enters both the sampling and analysis steps,
the test result is subject to two sources of error:
(1) If asbestos is not distributed uniformly throughout the material,
one or more samples could miss asbestos even if it is present.
(2) The laboratory performing the analysis could make an incor-
rect determination.
The quantitation method employed with PLM has a very low error rate
in terms of detecting the presence or absence of asbestos. (Estimates
of percent asbestos can vary but that is not an issue here.) Based on
data collected in EPA's bulk asbestos sample quality assurance program,
the probability of correctly detecting the presence of asbestos in a sam-
ple is at least 0.975 (RTI 1985). Given that surfacing material in a
homogeneous sampling area consists of at least 1% asbestos, the
likelihood that a sample taken from the sampling area contains asbestos
has not been empirically characterized, but is believed to be typically
less than 0.975. The number of samples required is determined by speci-
fying the minimum acceptable probability of correctly identifying
asbestos, considering the uncertainty in both the sampling and the
analysis steps. As indicated above, the probability of finding asbestos
when it is present is the product of two component probabilities: the
probability that asbestos is in the sample selected when the
homogeneous sampling area surfacing material contains at least 1%
asbestos, and the probability of correctly determining that asbestos is
present with PLM. The former probability depends on the uniformity of
asbestos in the surfacing material. If asbestos is uniformly distributed
throughout the material (i.e., minimal clustering of asbestos fibers), the
probability that asbestos is in a sample selected at random will be large.
On the other hand, if asbestos, although at least 1% by weight, was
unevenly mixed or applied, the probability that it is in a randomly selected
sample will be small.
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The composite probability, P, of finding asbestos when it is present is
P = Q x Prob (correctly identifying asbestos with PLM), (1)
where Q is a measure of patchiness. Q is the probability that asbestos
is in the sample when the surfacing material in the homogeneous sam-
pling area contains at least 1% asbestos. Q equal to 1 means that the
material is so uniform that virtually every sample taken from the sam-
pling area will contain asbestos. Lower values of Q indicate a patchy
distribution of asbestos. If Q is small it is easy to miss asbestos by sam-
pling, by chance, from a location that does not contain asbestos.
Although there is no empirical information about the degree of
asbestos clustering or patchiness in surfacing materials, it is reasonable
to expect smaller homogeneous sampling areas to be less patchy than
larger areas. For example, in areas less than 1000 square feet, the pro-
bability of asbestos in an individual sample when the surfacing material
in the homogeneous area contains at least 1% asbestos may be greater
than 0.8. For larger areas, such as 1000 to 5000 square feet, the pro-
bability may be as low as 0.4, and for areas greater than 5000 square
feet, the probability may be as low as 0.3. Since none of these pro-
babilities are known, their values must be assumed for planning
purposes.
Assuming that individual samples are statistically independent (there
is no basis for assuming otherwise), the probability that at least one
of n samples will show asbestos is
pn = 1 - (i-p)n. (2)
Setting the right hand side of equation (2) equal to the desired pro-
bability level of finding asbestos and solving for n gives the number of
samples required.
Figure 1 displays the probability of finding asbestos when it is pre-
sent as a function of Q. This relationship is shown for values of n equal
to 3, 5, 7, and 9. The values 3, 5, and 7 were chosen because they are
the sample sizes recommended in previous EPA guidance (USEPA
1980a,b). A sample size of nine corresponds to current guidance which
recommends dividing a homogeneous sampling area into nine equal
subareas and taking at least one sample from the center of each. Nine
samples are recommended because they provide a high probability of
detecting asbestos for a broad range of values of Q.
Considering a probability of at least 0.95 satisfactory for detecting
asbestos when it is present, Figure 1 shows that three samples (n =
3) are adequate only if the asbestos is extremely uniform in the surfac-
ing material (i.e., a value of Q greater than 0.6). Using five samples (n
= 5), allows Q to be as low as 0.45, and for seven samples (n = 7),
Q could be as low as 0.35. When nine samples are used, as currently
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recommended, the uniformity of asbestos in the surfacing material as
reflected by Q could be slightly lower than 0.3. It is worth noting that
the value of P is not substantially increased when the probability of cor-
rectly identifying asbestos by PLM is increased to 0.99, 0.999 or 0.9999.
The choice of 0.975 used in the figure is conservative (i.e., the probability
of correctly detecting the presence of asbestos in a sample is at least
0.975).
0.2 0.4 0.6 0.8
Q (MEASURE OF PATCHINESS)
Figure 1. Probability of finding asbestos when it is present as a func-
tion of Q (where Q is the probability that asbestos is in the
sample when the surfacing material in the homogenous
sampling area contains at least (1% asbestos) for sample
sizes of 3, 5, 7, and 9.
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5. CONCLUSIONS
In a given situation, the uniformity of asbestos across the sampling
area is unknown. The basic question—how many samples—can be
answered only by considering various alternatives and balancing costs
against the risks of erring. Increasing the number of samples always
reduces the likelihood of error, but the cost of additional sampling and
analysis must be considered. Additional samples have a small effect
on the error rate once it is less than 0.05 (i.e., when the probability of
finding asbestos when it is present is greater than 0.95).
Considering the curves shown in Figure 1, a cautious person would
choose at least nine samples per homogeneous sampling area. Taking
nine samples provides a 0.95 probability of finding asbestos when it is
present for most reasonable assumptions about the uniformity of
asbestos in the sampling area. Since the combined process of sam-
pling and PLM analysis is relatively inexpensive, the recommended
number of samples is nine. Previous guidance indicated three, five or
seven samples depending on the number of square feet in the
homogeneous sampling area. Certainly for very small areas, fewer than
nine samples may be sufficient. Three, five or seven samples can be
justified by ascertaining the degree of uniformity.
If fewer than nine samples are used, the sampling locations should
be selected in an unbiased and objective manner. The primary docu-
ment provides a scheme, based on random numbers, for selecting
samples from a subset of the nine subareas. Following this scheme
removes the potential for criticism when no asbestos is found; that is,
the samples were selected for the convenience of the building owner.
In general, once all systematic factors have been used to define
homogeneous sampling areas and subareas, selection by a random
number scheme should follow. Such schemes are objective because
a third party not involved in the design can follow the documentation
that has been prepared and arrive at the same selections.
Finally, none of the sample size recommendations or probability com-
putations are meaningful if the search for surfacing materials that could
contain asbestos has been inadequate. Surfacing materials containing
asbestos that go undetected will never be sampled. Also, all available
information must be used to define homogeneous sampling areas. If
an area defined as homogeneous is known to consist of two or more
material formulations, the sampling scheme proposed has a much
greater chance of erring than planned. There are no statistical principles
to guide the search. However, if the search is not complete, or the defini-
tion of homogeneous sampling areas is applied haphazardly, the recom-
mended sampling approach will not achieve the intended objective.
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References
USEPA. 1980a.
USEPA. 1980b.
USEPA. 1985.
RTI. 1985.
U.S. Environmental Protection Agency. Asbestos-
containing materials in school buildings, guidance
for asbestos analytical programs. Washington, DC:
Office of Toxic Substances, USEPA. EPA
560/13-80-017a.
U.S. Environmental Protection Agency. Asbestos-
containing materials in school buildings, guidance
for asbestos analytical programs. Statistical
Background Document. Washington, DC: Office of
Toxic Substances, USEPA. EPA 560/13-80-017b.
U.S. Environmental Protection Agency. Asbestos in
buildings: simplified sampling scheme for friable sur-
facing materials. Washington, DC: Office of Toxic
Substances, USEPA. EPA 560/5-85-030a.
Research Triangle Institute. Commercial laboratories
with polarized light microscope capabilities for bulk
asbestos identification. Interim Listing Number 19,
EPA Bulk Analysis Round 12. Prepared for U.S. En-
vironmental Protection Agency, Research Triangle
Park, NC: Environmental Monitoring Systems
Laboratory and Office of Toxic Substances.
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50373-101
REPORT DOCUMENTATION »• REPORT NO.
PAGE [EPA 560/5-85-30b
4. THIe and Subtitle
Statistical Support Document for
"Asbestos in Buildings: Simplified Sampling Scheme for
_ Friable Surfacing Materials" _.
7. Authord)
.Toan
9. Performing Organization Name and Addrm
Bprrram P. Price, Ted Bemer
Battelle Columbus Laboratories
2030 M Street, NW
Suite 800
Washington, DC 20036
S. Reclplent'a Accaatlon No
S. Raporl Data
December 1985
«. Performing Organization Rapt. No.
10. Prolact/Teik/Work Unit No.
11. Contract(C) or Cranl(O) No.
(0 68-02-3938
«>subcontract #107-7900-3
IS. Type of Raport * Parlod Covarad
14.
12. Sponsoring Organization Name end Address Battelle Columbus Laboratories
Midwest Research Institute 2030 M Street NW
425 Volker Boulevard Sulte 800
Kansas City, MO 64110 Washington, DC 20036
(subcontractor to MRI) _
15. Supplementary Notes
This report was prepared for the Exposure Evaluation Division of the Office of Toxic
Substances. Copies of the document can be obtained by calling toll-free 800—424-9065.
(Call 554-1404 in the District of Columbia.)
It. Abstract (Limit: 200 words)
This document provides the statistical support for the EPA document "Asbestos In
Buildings: Simplified Sampling Scheme for Friable Surfacing Materials." The document
is designed to supplement the sampling scheme document by demonstrating the statistical
basis for the scheme.
17. Documant Analyela e. Descriptor*
D. Identlflera/Open-Cnded Tarmc
Asbestos
Asbestos-Containing Materials
Asbestos Sampling Scheme
Asbestos Analytical Program
Statistical Support
c. COSATI Field/Group
il. Availability Statamant
Available to the Public
19. Sacurlty Cla» (Thlt Raport)
Unclassified
20. Security Clan (Thli Page)
Unclassified
21. No. of Pafa*
_14
22. Prlca
(Saa ANSI-Z39.1D
Saa fnafrucMons on Havana
OPTIONAL TOHM 272 (4-77)
(Formerly NTIS-35)
Department of Commerce
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