A fTlM United States
tfVPKA Envlroninerta! Protection
!¦£ ,e*A§siicy
Procedure for Safe Drinking Water Act Program
Detection Limits for Radionuclides
Office of Water (MS-140)
EPA 815-B-17-003
April 2017
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Questions concerning this document should be addressed to:
Glynda A. Smith, Ph.D.
U.S. EPA, Office of Ground Water and Drinking Water, Standards and Risk Management Division,
Technical Support Center, 26 W. Martin Luther King Dr., Cincinnati, OH 45268
Phone:(513)569-7652
smith.glvnda(a)epa.gov
Authors
Katie Adams, Inorganic Chemistry Technical Lead, USEPA Region 10 Laboratory, 7411 Beach Drive East,
Port Orchard, WA 98366
Gerald Dodo, Supervisory Chemist, USEPA Region 10 Laboratory, 7411 Beach Drive East, Port Orchard,
WA 98366
Barry V. Pepich, Ph.D., Director, USEPA Region 10 Laboratory, 7411 Beach Drive East, Port Orchard, WA
98366
Glynda A. Smith, Ph.D., U.S. EPA (Cincinnati, OH)
Acknowledgements
The following served as peer reviewers for the document:
John G. Griggs, Ph.D., National Analytical Radiation Environmental Laboratory (NAREL), Office of
Radiation and Indoor Air (ORIA), USEPA
Keith McCroan, Ph.D., National Analytical Radiation Environmental Laboratory (NAREL), Office of
Radiation and Indoor Air (ORIA), USEPA
Bahman Parsa, Ph.D., Environmental and Chemical Laboratory Services, PHEL/PHILEP, New Jersey
Department of Health
Bob Read, Ph.D., Environmental Chemistry Laboratory, Tennessee Department of Health, Division of
Laboratory Services
Andy Eaton, Ph.D., Eurofins Eaton Analytical, Inc., Monrovia, California
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TABLE OF CONTENTS
Contents
1.0 Introduction 1
1.1 Background and Objectives 1
1.2 Scope and Application 1
2.0 Overview 1
3.0 Calculating Detection Limits for Radiochemical Measurements 2
3.1 Definition of the Detection Limit for SDWA Radiochemical Measurements 2
3.2 Derivation of the SDWA Detection Limit Calculation 2
4.0 Performing Experimental Confirmation of SDWA Detection Limits for Radiochemical
Measurements 4
4.1 Experimental SDWA Detection Limit Studies 4
4.2 Statistical Evaluation of Detection Limit Studies 5
5.0 References 5
Appendix A: Example Calculations 6
Table 1. Experimental Values for Seven Spiked Replicates 7
Appendix B: Chi-Square Values at the 99th Percentile 9
Table 2. Chi-Square Values (99th Percentile) 9
Appendix C: Abbreviations and Acronyms 10
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1.0 I xluction
1.1 Background and Objectives
When analyzing radionuclides for the drinking water program, it is important to carefully evaluate
method performance at the lowest concentrations attainable for the method. Critical water testing and
treatment requirements impacting public health are made based on results that are often near the
limits of method detection capability.
The Code of Federal Regulations (CFR) specifies Required Detection Limits (RDLs) for radionuclides.
Laboratories must demonstrate their performance at those levels. Many radiochemistry laboratories are
accustomed to using a Minimum Detectable Activity (MDA) to achieve this requirement. The MDA is a
calculation that is based on counting precision that is scaled by multipliers to account for such factors as
sample volumes, chemical yields, and counting times, which may vary. It is therefore a useful, sample-
specific tool. However, MDA equations vary and may or may not account for the variability of the whole
system (including, for example, the sample separation steps, which often precede instrument counting).
Consequently, the Office of Ground Water and Drinking Water (OGWDW), in administering the National
Drinking Water Program, emphasizes the need for laboratories to capably and reproducibly
demonstrate system performance through detection limit studies. These experimental studies seek to
confirm that the system does, in fact, meet the method performance that can be derived
mathematically.
Because most radiochemistry methods are based on Poisson distributions rather than Gaussian
distributions (as in other chemistry fields), the mechanism of calculating the detection limit for
radionuclides differs from that described in 40 CFR 136 Appendix B, which is applied for inorganic and
organic analytes. This document provides the derivation of the Safe Drinking Water Act (SDWA)
program's radionuclide Detection Limit (herein after referred to as the "SDWA DL"), as well as practical
steps for executing the experimental DL study.
1.2 Scope and Application
The procedure provided in this document describes the basis for the SDWA DL for radionuclides and
provides an example calculation (see Appendix A) intended to assist laboratories conducting the DL
determination for the first time. This procedure describes in detail the calculations associated with the
radionuclide detection limit that is defined in 40 CFR 141.25(c). The DL procedure is one part of
demonstrating method capability. The evaluation and monitoring of laboratory reagent blanks (LRBs)
are also required to verify low system background, and method accuracy and precision are
demonstrated through the evaluation of laboratory fortified blanks (LFBs).
2.0 Overview
As an initial estimate, laboratories should calculate their theoretical ability to meet the DL requirement
of 40 CFR 141.25(c). Subsequently, they experimentally verify that their analytical system does actually
perform consistently with what has been demonstrated in theory. The experimental verification consists
of the analysis of at least seven standards spiked at or near the concentration of the RDL. These
standards are taken through the entire analytical process, and the results are evaluated against a Chi-
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square ( x2) distribution to determine if the experimental results compare favorably with the expected
values.
3.0 1 Ululating Detection Lin-ii t »r Radiochemical Measurements
3.1 Definition of the Detection Limit for 5DWA Radiochemical Measurements
The detection capability of radiochemical measurements used for SDWA drinking water compliance
monitoring is defined at 40 CFR part 141.25(c) as a detection limit with the following conditions:
"The detection limit shall be that concentration which can be counted with a precision of plus
or minus 100 percent at the 95 percent confidence level (1.96a, where a is the standard
deviation of the net counting rate of the sample)."
The SDWA Detection Limit according to this definition differs from other "detection limits/' such as the
method detection limit or MDL (defined in 40 CFR part 136, Appendix B), and the Minimum Detectable
Activity (MDA), which is commonly used by radiochemists. The RDLs for SDWA drinking water
compliance monitoring of radionuclides are expressed in terms of the definition given in 40 CFR
141.25(c).
For measurements involving simple nuclear counting with Poisson counting statistics, the procedure
given in Section 3.2 below is used to obtain a preliminary estimate of the SDWA DL.
3.2 Derivation of the SDWA Detection Limit Calculation
The definition of the SDWA DL may be expressed mathematically as follows:
RDl = 1-96 x aDL (1)
Where:
Rdl is the mean net count rate for a sample with concentration at the detection limit
oDL is the standard deviation of the net count rate
The relationship for the standard deviation of a radiochemical measurement is centered around the fact
the gross rate has a background rate subtracted from it to derive a net count rate:
Rdl = Rg ~ Rb (2)
Where:
Rq is the mean gross count rate for a sample (with concentration at the DL)
Rb is the mean background count rate for a sample measurement
However, each count rate is a calculated quantity as specified below:
RG = Cf and RB = C-f- (3)
Where:
Rq is the mean gross count rate for a sample (with concentration at the detection limit)
Rb is the mean background count rate for a sample measurement
CG is the mean total (gross) sample count
CB is the mean total background count
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tG is the time of the measurement used to accumulate the sample count
tB is the time of the measurement used to accumulate the background count
The standard deviation of a count rate is proportional to the square root of the mean of a measurement.
Assuming Poisson counting statistics, the standard deviations of the measured values of RG and RB are
given by:
oG=1—=— and oB=*—= — (4)
rG y rG y
Where:
oG is the standard deviation of the measured gross count rate
oB is the standard deviation of the measured background count rate
Since the net count rate, RDL, is the difference between Rc and RB, its standard deviation is given by:
°dl= JOg+(Tb) (5)
Where:
oDL is the standard deviation of the net count rate
Combining equations (4) and (5), one arrives at:
+ (6)
Substituting equation (6) into equation (1), one arrives at:
R»' = 1-96xJ(t+S) (7)
Equation (2) may now be used to eliminate the variable, RG, from the equation. Since RG = RDL + RB,
equation (7) may be rewritten as:
Rn, = 1.96 X "L " +
(Rdl+Rb i rb
"i) <8>
,e ¦
Equation (8) is then solved algebraically for the value of RDL. First, rewrite the radicand:
(v+R»x£+i)) (9)
RDl — 1-96 x
M
Squaring each side of the equation, one arrives at:
S1
tG " \tG tBj
Collecting all items on the left-hand side to put the equation in standard quadratic form, one arrives at:
Rdl =^xRDL + 1.962RBx{^ + f) (10)
p2 1^96^
KDL
xRDL- 1.962RBx(j- + f) = 0 (11)
2 tG D \tG tB
The quadratic formula gives two solutions to equation (11), one of which is positive and one of which is
negative. The positive solution is required and it is given by the following equation:
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x 1+J1+SxR»x(t + i) (12)
J
Equation (12) provides a reasonable estimate of the count rate at the DL for the net activity that is
based on counting statistics alone. This count rate is then divided by the product of the experimental
factors, H, which can include the following items: the method of detection's counting efficiency, the
sample volume, chemical recoveries (measured by gravimetric or tracer techniques), conversion factors
to picocuries, etc. The result is used to derive a specific DL of the radioanalyte of interest for a
radiochemical method of analysis that is used for SDWA compliance monitoring:
Where:
H is the product of the experimental factors (see example calculations in Appendix A)
SDWA DL is the SDWA Detection Limit
This SDWA DL is mathematically equivalent to the detection limit specified in 40 CFR part 141.25(c). It is
expected that the experimental factors will vary with specific method and sample conditions.
If an estimate of the SDWA DL described in equation (13) does not exceed the required DL, a DL study is
performed as described below to verify that laboratory performance in practice can be demonstrated
prior to analyzing drinking water samples for compliance. However, if the estimate of the DL exceeds
the required DL, the performance will be considered inadequate and there will be little value in
completing the experimental DL study. Conditions would need to be adjusted to meet the required DL
before proceeding to confirm the DL experimentally. This may entail using a larger sample volume or
longer sample counting time.
NOTE: Typical drinking water compliance samples will have very low activity levels and compliance
samples should be run under the same conditions as those used to confirm the DL.
4.0 Performing Exp* i if i a i ii. -1» «. >i,nrmation of - II11 II >i > ctlion Limits for
Radiochemical Measurements
4.1 Experimental SDWA Detection Limit Studies
The experimental SDWA DL study will verify that the method is capable of routinely achieving the
required detection capability.
The experimental SDWA DL study consists of seven replicate samples. Each sample is prepared with
ASTM II grade reagent water, or other blank matrix as appropriate for the method, and using the sample
volume described in the method. For example, gross alpha analyses are highly dependent on the total
dissolved solids content in the sample matrix. Reagent water can yield artificially low DLs due to higher
detector efficiencies. Thus, more realistic gross alpha DLs will be obtained using either laboratory tap
water or a synthetic water solids matrix to prepare the DL study samples. Each DL study sample is spiked
with NIST traceable source(s) of the method target radionuclide(s) to an activity concentration at or near
their RDL. The sample is mixed and then processed through sample preparation, processing and analysis
per the test method. The measurements of the DL study samples are then assessed by calculating a
precision statistic.
SDWA DL = —
H
(13)
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4.2 Statistical Evaluation of Detection Limit Studies
The assessment of the replicate results for each radionuclide uses a chi-square statistic to test whether
the relative standard deviation of the results exceeds the maximum value allowed at the RDL.
Where:
n is the number of replicate measurements (> 7)
ju is the spike concentration (at or near the RDL)
Xj is the result of the fh replicate measurement (j = 1,2,..., n)
To be deemed acceptable, the value of x2 must be less than or equal to the 99th percentile of the x2
distribution with (n-1) degrees of freedom. When n = 7, the value of this percentile is 16.812.
NOTE: Refer to Appendix A - Example Calculations. Refer to Appendix B for a table of Chi-square values.
5.0 References
1. 40 CFR 141: National Primary Drinking Water Regulations
2. ASTM D1193-99E01: Standard Specifications for Reagent Water. American Society for Testing and
Materials. March 1999, with editorial change made in October 2001.
3. MARLAP 2004. Multi-Agency Radiological Laboratory Analytical Protocols Manual. NUREG-1576, EPA
402-B-04-001C.
4. Chapter VI, Critical Elements for Radiochemistry. The Manual for the Certification of Laboratories
Analyzing Drinking Water. (EPA/815-R-05-004).
Calculate the mean, X, and a chi-square statistic, x2, as follows:
71
y=i
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Appendix A: Examp culations
The following section provides example calculations for the estimation and experimental confirmation
of the SDWA Detection Limit for radionuclide activity. The example uses gross alpha results obtained
using EPA Method 900.0. The data was generated by the New Jersey Department of Health (NJDOH)
Radioanalytical Services Laboratory, and is used with their permission1.
1.0 Example Detection Limit Calculation
Equations (12) and (13) in Section 3.2 state:
1.962
RDL = —o X
°L 2 tr.
1 +
4 tl /II
1 + , rZl X RB X b —
1.962 B \tG tB
And
SDWA DL =
R
DL
H
Combining these equations and considering the experimental factors relevant for gross alpha
determination, the following equation is obtained:
DL
c!"Ci/L) =
X Ru X
(Efficiency) (Volume) (Chemical Recovery) (2.22)
Where:
Rb is the mean background count rate for a sample measurement
tG is the time of the measurement used to accumulate the sample count
tB is the time of the measurement used to accumulate the background count
2.22 is the conversion factor from dpm to pCi
For this DL study, gross alpha recovery is assumed to be 100%. RB = 0.03 cpm, Volume = 1.0 L,
and tG =tB = 200 minutes. The detection efficiency was 0.177 cpm/dpm. Substituting these
values into the equation produces the following:
DL (PCi/L) =
1.96
(2 X 200)
x
1 + . 1 +
4(200)'
1.962
x 0.03 x
(200 + 20o)
(0.177)(1)(1)(2.22)
r\ r -1 r\— 3 l+Vl + 12.5
= 9.6x10 d x
0.393
= 2.44xl0-2 X 4.7
= 0.11 pCi/L
The Required Detection Limit (RDL) for gross alpha is 3 pCi/L. Because 0.11 pCi/L is a smaller
quantity than 3 pCi/L, it is theoretically true that the counting times, volumes, and efficiencies
assumed for this example would lead to acceptable precision at the RDL concentration.
2.0 Example Experimental SDWA Detection Limit Study
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The instructions for performing an experimental SDWA DL study are given in Sections 4.1 and
4.2. The following example illustrates how the evaluation criteria are applied.
1, Experimental Values for Seven Spiked Replicates
Replicates
Measured Gross Alpha (Th-230)
Activity (pCi/L)
Spike Amount (pCi/L)
BS 1
2.89 + 0.30
3.0
BS 2
5.51 + 0.45
3.2
BS 3
2.88 + 0.31
3.3
BS 4
3.72 + 0.36
3.2
BS 5
3.42 + 0.34
3.0
BS 6
3.11 + 0.32
3.1
BS 7
3.17 + 0.32
3.1
Average:
3.53
3.13
The mean gross alpha activity is calculated using the equation:
n
y=i
Substituting the data, this produces:
X = ^(2.89 + 5.51 + 2.88 + 3.72 + 3.42 + 3.11 + 3.17) = 3.53 pCi/L
The Chi-square statistic is calculated using the equation:
„ n
1.962\~> 2
x2=—2Sx<~x)
7 = 1
Where:
n is the number of replicate measurements (7)
ju is the spike concentration (at or near the RDL; in this case 3.13 pCi/L)
Xj is the result of the jth replicate measurement
Substituting the data, this produces:
1 962
X2 = ——7 X [(2.89 - 3.53)2 + (5.51 - 3.53)2 + (2.88 - 3.53)2 + (3.72 - 3.53)2
3.13/
+ (3.42 - 3.53)2 + (3.11 - 3.53)2 + (3.17 - 3.53)2]
3.84 ^ -v
= — x (5.1)
9.8 v J
= 2.0
This data set has seven replicates and thus, six degrees of freedom. So, the critical value for the
statistic is the 99th percentile of the x2 distribution with six degrees of freedom, which equals
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16.812. (see Chi-Square Table provided in Appendix B). Since the calculated x2 value of 2.0 does
not exceed 16.812, the method passes the experimental DL study.
1. Detection Limit Study, Gross Alpha, Evaporation, EPA Method 900.0. Dr. Bahman Parsa, NJDOH
Laboratory, 3 Schwarzkopf Drive, West Trenton, NJ 08628. June 14, 2011.
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Appeimdi > V ». Li-Sqi>»[ * * ''lne* jf 111
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Appenfii i -hbreviation Acronyms
ASTM
ASTM International
CFR
Code of Federal Regulations
DL
Detection Limit
EPA
U.S. Environmental Protection Agency
MARLAP
Multi-Agency Radiological Laboratory Analytical Protocols Manual
MDA
Minimum Detectable Activity
NJDOH
New Jersey Department of Health
NIST
National Institute of Standards and Technology
OGWDW
Office of Groundwater and Drinking Water
RB
Reagent Blank
RDL
Required Detection Limit
SDWA
Safe Drinking Water Act
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