sampling and analysis plan for sludge disposal area … · preparation and measurement* these will...

SAMPLINGAND ANALYSIS PLAN FORSLUDGE DISPOSAL AREA ATDIXIE CAVERNS LANDFILL

APPROVED

Prepared for

Roanoke County

Prepared by

Qlver IncorpoaatedCdnsulting Engineers andfinvircnmental Laboratories

1U6 South Main StreetBlackBburg, Virginia 24060

January 25, 1989tevised May 19, 1989

00655

TABLE OF CONTENTSPage Number

I. SAMPLING AND TESTING .................... 1

A. Sampling Locations ..................... 1

B. Sampling Methods ...................... 4

C. Tested Constituents. .................... 4

D. Threshold Values of Constituents .............. 6

E. Laboratory Techniques and Constituent Detection Limits ... 6

F. Quality Assurance/Quality Control ............. 8

G. Statistical Analysis .................... 8

H. Conclusion of Plan .................... 11

References ......................... 12

LIST OF TABLESPage Number

Table 1 Sludge Disposal Area Constituents For Analysis ....... 5

Table 2 Proposed Threshold Values Far Test Constituents ...... 7

LIST OF FIGURESPage Number

Figure 1 Bottom of Sludge Disposal Pit and SpillwayRandan Sample Location Grid ................. 2

Figure 2 Side mils of Sludge Disposal PitRandom Sample Location Grid. ................ 3

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points have been numbered consecutively and the actual sampling locations

will be determined by using a randan number generator or table. EPA SW-846

outlines a procedure based upon previous analyses for determining the number

of samples to be collected.

B. Sampling Methods

The methods used to obtain a representative sample from the sludge pit

area will be the appropriate method as identified in Appendix I, 40 CFR,2 3Part 261 . This reference specified the ASTM Standard D 420-69 for

soil or rock-like material which will be utilized in the field collection of

data. Sample preservation and handling techniques shall correspond to those

outlined and required in EPA SW-846._

C. Test Constituents

Sludge disposal pit soil samples will be analyzed for the following six

conpounds: bis (2-ethylhexyl) phthalate, di-n-fcutylphthalate, napthalene,

ethylbenzene, 1,1-dichloroethene, and toluene. The first three are semi-vol-

atile compounds while the remaining are volatile compounds. In selecting

these compounds as the basis of the statistical analysis, data compiled pre-

viously by the EPA .Region III and Roanoke County and their Contractor were

utilized. This data was examined for compounds that were frequently detect-

ed as well as those which occurred in relatively high concentrations at the

sludge disposal site. SOUP compounds were not considered for various rea-

sons. For example, Methlylene Chloride is a very 0:1111111. laboratory solvent

which could easily contaminate a sample before analysis and hence was

dropped from further consideration. Other conpounds occurred in such minute

amounts (in the parts per billion range) that the detection limits of the

analysis used could be questioned. The final compounds selected f

sampling and analyses plan are listed in Table 1 with a brief

._.__._ _. ..._..___..._.... ..... 4

TABLE 1

SLUDGE DISPOSAL AREA CONSTITUENTS FOR ANALYSIS

Constituent

1. Bis (2-ethylhexyl) phthalate

2. Di-n-butylphthalate

3. EthylLenzene

4. Napthalene

5. 1,1-Dichloroethene

6. ^toluene

Notes

Possible Source/Use£1)

Also referred to as Di (2-ethylhexyl)phthalate. Used as a plasticizer forresins and in the manufacture of organ-ic pump fluids.

Used in plasticizing vinyl acetateemulsion and cellulose esters/ and isalso used in insecticides.

Used in the manufacture of celluloseacetate, styrene, and synthetic rub-ber, as a solvent or diluted agent,and as a component of aviation andautomobile fuels. Found in signifi-cant quantities in mixed xylenes whichare used in the paint industry, inagricultural sprays for insecticidesand in gasoline blends (with concentra-tions as high as 20% ethyl benzene.

Used in the manufacture of syntheticresins, smokeless powder/ celluloid/and an intermediate in the manufactureof various dyes. Also used as a mothrepellant.

Used as a solvent and as a cleaningand degreasing agent. Also used as anintermediate in organic syntheses.

Used as an intermediate or feed fororganic synthesis, in the manufactureof benzene, as a solvent for paintsand coatings, or as a component ofautomobile and aviation fuels.

(1) Source of information: Sittig, M., 1985, Handbook of Ttaxic andHazardous Chgnicals and Carcinogens. Noyes Publications/ Park Ridge/N.J., 9SO pp. (4)

Job Number 10897January 26, 1989

possible sources and uses of each compiled from information gathered on po-

tential generators of waste found at the site.

D. Threshold Values of Constituents

Based upon detailed sampling and analytical work already corpleted at

the site during the removal phase and discussions with EPA Region in, it is

recoimended that the soil sanples collected at the sludge disposal pit for

the determination of clean closure should be compared to threshold values

for those six test constituents described herein. Threshold values for the

six constituents are presented in Table 2 and are based upon the EPA

Superfund Target Compound List (TCL) dated July, 1987, for said constitu-

ents. The threshold values proposed are Medium Soil/Sediment Contract Be-

quired Quantitation Limits (CEQL) for semi-volatile and volatile compounds.

These values will be the basis for the statistical conparison presented here-

in to determine if the sludge pit area has been cleaned to a level accept-

able for closure or whether further cleanup or contingent closure is re-

quired.

E. Laboratory Techniques and Constituent Detection Limits

Laboratory methods used for analysis of proposed constituents will be

those specified in EPA SW-846. The records, including calibration and main-

tenance records, shall be ma-infra-iTwi for .three years. These records shall

specify: (1) the dates, exact place, and times of sampling and measurement;

(2) the individuals who performed the sanpling or measurement; (3) the dates

analyses were performed; (4) the individuals who performed the analyses; (5)

the analytic techniques or methods used; and (6) the results of such analy-

ses. Chain of custody forms will be anticipated and completed by field and

lab testing personnel. The projected detection limits forecast for the con-

stituents to be tested are as follows:

TABEJ3 2

THRESEOUD VALUES FOR TEST CONSTITUENTSAT DIXIE CAVERNS LANDFILL

Constituent

A. Send-Vc-latiles

1) Bis (2-ethylhexyl) phthalate2} Di-n-butyl phtbalate3) Naptbaiene

B. Volatile

1} Eth^Uaenzene2) 1, IHDichloroethene3} Toluene

Level Considered AcceptableFor Closure of Site *

19.819.819.8

625300 ppb625

Hate;

Madimi Soil/Sediment Contract Required Quantitation Limit

Jcb NiniDer 10897January 25, 1989&cvid@d May 13, 1989

Compound Detection Limit (ran)

Bis (2-ethylhexyl) phthalate

Di-n-butyl phthalate

Napthalefte

1,1- dichloroetheneEthylbenzene

Toluene

0.001

0.001

0.001

0.00001

0.00001

0.00001

F. Quality Assurance/Quality Control

Quality Assurance/Quality Control (QA/QC) methods employed during analy-

sis will comply with EPA requirements. T3ie general, components of the QA/QC

program used in the soil sampling plan are outlined below:

1. Procedural blanks shall be used throughout the entire samplepreparation and analytical process to assess sample contamina-tion.

2. Duplicate samples shall be processed at an average frequency of10% to assess precision of test methods.

3. Standard reference materials shall be employed to determineaccuracy.

4. Calibration standards shall be verified against a QC sampleobtained from an outside source.

5. Fortified samples shall be carried through all stages of samplepreparation and measurement* These will be analyzed to vali-date the sensitivity and accuracy of the analysis. Sensitivityof the instrument shall be increased for the extract subjectedto additional clean-up to obtain the necessary detection limits,

G. Statistical AnalysisThe statistical analysis proposed herein will be based upon the compari-

son of the sludge pit sample population and the proposed threshold valuesfor the six test constituents. Preliminary data must be examined '—' -fj"U.yto determine both the feasibility and the number of soil samples to be taken

for the final analysis. A minimim of 4 preliminary sludge pit samples will

be taken; the locations of these samples being determined by simple randan

sampling as described previously.

After these preliminary sludge pit samples have been collected and ana-

lyzed, the proposed threstold constituent and sludge pit sample concentra-

tions will be compared before continuing further. If the sludge pit sample

concentrations are considerably grater than the proposed threshold concen-

trations/ say tenfold, then the statistical analysis should be put on hold

until further cleanup. At this point, collecting more samples for statisti-

cal analysis could prove fruitless, time consuming, and expensive. If, how-

ever, the sample concentrations are within an acceptable range, the test

will continue by calculating the required number of samples for the final

analysis.

Referring to SPA document SW-846, the required number of sludge pit

samples can be calculated ffrom Bq. 1.8 in Section 1 of that document by:

Nizfcer of Samples, n « (ts O.2O) (SP2)A2

flfcere A» PT - Xp*de term delta, A , is calculated from the proposed threshold, PS, and

the preliminary sludge pit sanple mean, X . 3 is the standard devia-

tion of tba preliminary sludge pit samples taken while tQ 2Q is the 0.20

level of significance specified by ERA.

After the rozober of required samples have been calculated and the sam-

ples collected and analyzed, a one sample t-test using the previously col-

lected background samples and the newly collected sludge pit samples will be

performed as oztlined in the EPA document SW-846. The null hypothesis-

H , and its alternative hypothesis, H-, will be defined for this analy-

sis as:

H CIu 1 -CIu > PT

ste upper limit of the confidence interval bounding the

sludge pit concentration mean.

PT-- de proposed threshold.

null hypothesis states that the upper limit of the confidence inter

val about the mean of the sludge pit constituent concentration is less than

or equal to the proposed threshold value. The alternative hypothesis states

that antithesis of the null hypothesis.

Should the upper limit of confidence, d , be greater than the regula-

tory threshold, ET, as proposed herein, then the null hypothesis will be

rejected, otherwise, the null hypothesis will be accepted and the sludge

disposal pit will be deemed acceptable for closure.

In any sampling and testing scheme, many different factors, both fore-

seeable and unforeseeable, affect the accuracy of the final results. Alter-

nate plans should be developed for factors which are foreseeable or predict-

able. Cbe such factor, non-normal data distribution, will be specifically

considered.

Based on previous experience and on many references in soil testing

literature, the results from sampling of many, if not most, components of

the soil are expected to be non-normal. 1ftat is, the data will not be dis-

tributed about a normal bell-shaped curve. 3he curve may be skefctea

the lower or upper end of the range of data collected. All data will, there-

fore, be examined for departures from the normal distribution. In accor-

dance with SW-846, a square root transformation or an arcsin transformation

will be performed on the data in an attempt to achieve normality. A log

normal transform will also be examined for normality* If none of these

transforms are successful, then the t-test methodology will have to be aban-

doned for nonparametric analysis of the data.

H. Conclusions of Plans

The results of the sampling and analysis plan presented herein will be

summarized upon completion and presented in a letter report to EPA Region

HI for their concurrence and approval. Work on the sampling/analysis plan

will not be initiated until written approval of this plan has been received

from EPA Eegion

AB10066?

REFERENCES

1. U.S. Environmental Protection Agency, SW-846, Test Methods Used ForEvaluating Solid Waste: Physical/Chemical Methods, November 1986, ThirdEdition.

2. Code of Federal Regulations Volume 40, Part 261, Appendix I, July 1, 1987.

3. American Society For Testing and Materials Standards, Volume 4, D 420-69, 1986

4. Sittig, M., Handbook of Toxic and Hazardous Chemicals and Carcinogens. NoyesPublications, Park Ridge, NJ, 1985.

MM 8

SECTION ONE

SAMPLING OF SOLID WASTES

The initial and perhaps most critical element in a program designed toevaluate the physical and chemical properties of a solid waste is the planfor sampling the waste. It is understandable that analytical studies, withtheir sophisticated instrumentation and high cost, are often perceived asthe dominant element in a waste characterization program. Yet, despite thatsophistication and high cost, analytical data generated by a scientificallydefective sampling plan have limited utility, particularly in the case ofregulatory proceedings.

This section of the manual addresses the development and implementationof a scientifically credible sampling plan for a solid waste and the documen-tation of the chain of custody for such a plan. The information presented inthis section is relevant to the sampling of any solid waste, which has beendefined by the ERA in its regulations for the identification and listing ofhazardous wastes to include solid, semi sol id, liquid, and contained gaseousmaterials. However, the physical and chemical diversity of those materials,as well as the dissimilar storage facilities (lagoons, open piles, tanks,drums, etc.) and sampling equipment associated with them, preclude a detailedconsideration of any specific sampling plan* Consequently, since the burdenof responsibility for developing a technically sound sampling plan rests withthe waste producer* it is advisable that he seek competent advice beforedesigning a plan. This is particularly true in the early developmentalstages of a sampling plan, which require at least a basic understanding ofapplied statistics. Applied statistics Is the science of employing techniquesthat allow the uncertainty of Inductive Inferences (general conclusionsbased on partial knowledge) to be evaluated.

1.1 Development of Appropriate jampling PlansAn appropriate sampling plan for a solid waste must be responsive to

both regulatory and scientific objectives. Once those objectives have beenclearly identified, a suitable sampling strategy, predicated upon fundamentalstatistical concepts, can be developed. The statistical terminology associatedwith those concepts Is reviewed in Table 1.

1.1.1 Regulatory and Scientific ObjectivesThe EPA, in Its hazardous waste management system, has required that

certain solid wastes be analyzed for physical and chemical properties. It ismostly chemical properties that are of concern, and, in the case of a numberof chemical contaminants, the EPA has promulgated levels (regulatory thresholds)that cannot be equaled or exceeded. The regulations pertaining to the

2 / SAMPLING - DevelopmentTAILS 1. BASIC STATISTICAL TERMINOLOSr APPLICABLE TO SAMPLING PLANS FOR SOLID WASTES

Terminology Synod Mathematical equation (Equation)

* Variable (e.g., bariuaor endrln)

• Individual MasureMntof variable

• Heen of all poiilbUmaiurotnts of variable(population **an)

• Mean of acasureMntsgenerated by luplt

Mtn)

X

X,

, with N « nuabtr ofpoifiblt (ntisurtmcnts

Pindoiii and

(1)

"^ , wltlt tt • nuabcr ofn saapli ntisurtotnts

Stnt<f1«d randoa

(2a)

• Variance of saaplc

x • r W,xk , with xk • stratufl)£•} flMn and Wfc - fraction

of population rtprtunttdby Stratm k (nuabtr ofstrata [k] ran ts fron1 to r)

rifldoa and1 1 c randoai

- (Z Xijz/n

• SUndars dtviatien ofsaaplc

• Standard error(also standard trrorof Man and standarddeviation of awn)of saaplc

a Confldtnee Inttmlfor £«

» Regulatory threshold*

Appropriate m*o*r ofsaopies to collect fro*a solid Miteconstraints not

CI

(i -lStratified randcet saapllng

rHL s| , with s| • stratuo varianceK * and Mfc*- fraction of

population represented byStratiM k (niMber of strataIk] ranges from 1 to r)

*-iV"

CI • £ + t »n s; with t 20 obtained" f fro* Table 2 In thlii p

section for appropitmtedegrees of freedM

Defined by EPA (e.g.. 100 PDB forbarlui In elutriate of £P t ox t dty test)

, with A « XT - x

(3a)

(3b)

(4)

(5)

(6)

W

(8)

Objectives / 3TABLE I (Continued)

Mathematical equationTerminology Symbol (Equation

• Degrees of freedom df

• Square root transformation --

t Arcsln transformation

df « n - 1

ArcsinJTT"; 1f necessary, refer to anytext on basic statistics;measurements must be con-verted to percentages (p)

(9)

(10)

(11)

*The upper Unit of the CI for u, Is compared to the applicable regulatory threshold (RT) to determineif a solid waste contains the variable {chemical contaminant) of concern at a hazardous level. The con-taminant of concern is not considered to be present in the waste at a hazardous level if the upper limitof the CI is less than the applicable RT. Otherwise, the opposite conclusion is reached.

4 / SAMPLING - Development

TABLE 2. TABULATED VALUES OF STUDENT'SSOLID WASTES

t" FOR EVALUATING

Degrees offreedom (n-l)a

1234567891011121314151617IS1920212223242526272829304060120••

Tabulated"t" valueb

3,0781.3861.6381.5331.4761.4401.4151.3971.3831.3721.3631.3561.3501.3451.3411.3371.3331.3301.3281.3251.3231.3211.3191.3181.3161.3151.3141.3131.3111.3101.3031.2961.2891.282

^Degrees of freedom (df) are equal to the number of samples (n)collected from a solid waste less one*

tabulated "t* values are for a two-tailed confidenc^J J^eg\@land a probability of 0.20 (the same values are applicable to a one-tailed confidence Interval and a probability of 0.10).

Objectives / 5

management of hazardous wastes contain three references regarding the samplingof solid wastes for analytical properties. The first reference, which occursthroughout the regulations, requires that representative samples of waste becollected and defines representative samples as exhibiting average propertiesof the whole waste. The second reference, which pertains just to petitionsto exclude wastes from being listed as hazardous wastes, specifies thatenough samples (but in no case less than four samples) be collected over aperiod of time sufficient to represent the variability of the wastes. The ~third reference, which applies only to groundwater monitoring systems,mandates that four replicates (subsamples) be taken from each groundwatersample intended for chemical analysis and that the mean concentration andvariance for each chemical constituent be calculated from those four subsamplesand compared to background levels for groundwater. Even the statisticaltest to be employed in that comparison is specified (Student's t-test).

The first of the above-described references addresses the issue ofsampling accuracy, while the second and third references focus on samplingvariability or,conversely, sampling precision (actually the third referencerelates to analytical variability, which, in many statistical tests, cannotbe distinguished from true sampling variability). Sampling accuracy (thecloseness of a sample value to its true value) and sampling precision (thecloseness of repeated sample values) are also the issues of overridingImportance in any scientific assessment of sampling practices. Thus,from both regulatory and scientific perspectives, the primary objectives of asampling plan for a solid waste are twofold - namely, to collect samples thatwill allow sufficiently accurate and precise measurements of the chemicalproperties of the waste. If the chemical measurements are sufficientlyaccurate and precise, they will be considered reliable estimates of thechemical properties of the waste.

It is now apparent that a judgment must be made as to the degree ofsampling accuracy and precision that is required to reliably estimate thechemical characteristics of a solid waste for the purpose of comparing thosecharacteristics to applicable regulatory thresholds. Generally, high accuracyand high precision are required if one or more chemical contaminants of asolid waste is present at a concentration that 1s close to the applicableregulatory threshold. Alternatively, relatively low accuracy and low pre-cision can be tolerated 1f the contaminants of concern occur at levels farbelow or far above their applicable thresholds. However, a word of caution1s in order. Low sampling precision Is often associated with considerablesavings In analytical, as well as sampling, costs and 1s clearly recognizableeven in the simplest of statistical tests. On the other hand, low samplingaccuracy may not entail cost savings and Is always obscured (cannot beevaluated) in statistical tests. Therefore, while it is desirable to designsampling plans for solid wastes to achieve only the minimally requiredprecision (at least two samples of a material are required for any estimateof precision), it Is prudent to design the plans to attain the greatestpossible accuracy.

ftit00673


The roles that inaccurate and imprecise sampling can play in causinga solid waste to be inappropriately judged hazardous are illustrated inFigure 1* When evaluating Figure 1, several points are worthy of consid-eration. Although a sampling plan for a solid waste generates a mean con-centration (x) and standard deviation (s, a measure of_the extent to whichindividual sample concentrations are dispersed around x) for each chemicalcontaminant of concern, it is not the variation of individual sample con-centrations that is of ultimate concern, but rather, the variation thatcharacterizes x itself. That measure of dispersion is termed the standarddeviation of the mean (also, the standard error of the mean_or standarderror) and is designated as sj. Those two samples values, x and s£» areused to estimate the interval (range) within which the true mean (n) ofthe chemical concentration probably occurs, assuming that the individualconcentrations exhibit a normal (bell-shaped) distribution. For the purposesof evaluating solid wastes, the probability level (confidence interval) ofSOS has been selected. That is, for each chemical contaminant of concern,a confidence interval (Cl) is described within which u occurs if the sample isrepresentative, which is expected of about 80 out of 100 samples. The upperlimit of the 805 CI is then compared to the appropriate regulatory threshold.If the upper limit is less than the threshold, the chemical contaminant isnot considered to be present in the waste at a hazardous level; otherwise,the opposite conclusion is drawn. One last point merits explanation* Evenif the upper limit of an estimated SOS CI 1s only slightly less than theregulatory threshold (the worst case of chemical contamination that would bejudged acceptable), there is only a 10S (not 20%) chance that the thresholdis equaled or exceeded. That is because values of a normally distributedcontaminant that are outside the limits of an SOS CI are equally distributedbetween the left (lower) and right (upper) tails of the normal curve.Consequently, the CI employed to evaluate solid wastes is, for all practicalpurposes, a 90S interval.

1.1.2 Fundamental Statistical Concepts

The concepts of sampling accuracy and precision have already been Intro-duced along with some measurements of central tendency (x) and dispersion(standard deviation [ s ] and sj) for concentrations of a chemical contaminantof a solid waste* The utility of x and s« 1n estimating a confidence inter-val that probably contains the true mean (u) concentration of a contaminanthas also been described* However, It was noted that the validity of thatestimate is predicated upon the assumption that individual concentrations ofthe contaminant exhibit a normal distribution.

Statistical techniques for obtaining accurate and precise samples arerelatively simple and easy to Implement. Sampling accuracy is usuallyachieved by some form of random sampling. In random sampling, every unit inthe population (e.g., every location in a lagoon used to store a solid waste)has a theoretically equal chance of being sampled and measured.

&RIQOS7U

Objectives / 7

ACCURATE AND PRECISE SAMPLE(Wtttt AoproDnatffiv Judgad Nonhazardousi

ACCURATE AND IMPRECISE SAMPLE{Want InaDproonataiy Judged Hazardous)

, RagulatoryThreshold (RT)

T70

r75

I80 as 90 95 too 105 no

CONCENTRATION OF BARIUM (ppm)as t

7Si i I 195 100 10S 11070 75 90 35 90

CONCENTRATION OF BARIUM tppml

INACCURATE AND PRECISE SAMPLE(Wan* Jnappfoociatrty Judgad Hazardous)

INACCURATE AND IMPRECISE SAMPLE(Watta Inaopropnanty Judgad Hazardous)

O4- 0.4-

atui

S

T 188 90 98 100 108 110

CONCENTRATION OF BARIUM <ppm)

I98

I 1 I100 108 11068 70 78 80 88 90

CONCENTRATION OF BARIUM Ippmt

NOTE: In All CftMt, Confldtnn Inttrvat for » • 2 ± t.2o «f.

Figur* 1.—Important theoretical relationship* batwtan sampling accuracy and precision andregulatory objecthrtt for a chemical contaminant of a solid waste that occurs at a concentrationmarginally last tnan its regulatory threshold. In this example, barium is the chemical contaminant.The true mean concentration of barium in the elutriate of the EP toxkaty test is SS pom, as comparedto a regulatory threshold of 100 ppm. The upper limit of the confidence interval for the truemean concentration, which is estimated from the sample mean and standard error,the regulatory threshold if barium is judged to be present in the wist*, at a nonhazardous level.


statistics generated by the sample (e.g., x, and, to a lesser degree, s*)are unbiased (accurate) estimators of true population parameters (e.g., theCI for u.). In other words, the sample is representative of the population.One of the commonest methods of selecting a random sample is to divide thepopulation by an imaginary grid, assign a series of consecutive numbers tothe units of the grid, and select the numbers (units) to be sampled throughthe use of a random numbers table (such a table can be found in any text onbasic statistics). It is important to emphasize that a haphazardly selected 'sample is not a suitable substitute for a randomly selected sample.That isbecause there is no assurance that a person performing undisciplined samplingwill not consciously or subconsciously favor the selection of certain unitsof the population, thus causing the sample to be unrepresentative of thepopulation.

.Sampling precision is most commonly achieved by taking an appropriatenumber of samples from the population. As can be observed from the equationfor calculating $£, precision increases (sj< and the CI for u. decrease)as thi number of samples (n) increases, although not in a 1:1 ratio. Forexample, a 100% increase in the number of samples from two to four causes theCI to decrease by approximately 62% (about 31% of that decrease is associatedwith the critical upper tail of the normal curve). However, another 100%increase in sampling effort from four to eight samples results in only anadditional 39% decrtase in the CI. Another technique for increasing samplingprecision Is to maximize the physical size (weight or volume) of the samplesthat are collected.that has the effect of minimizing between-sample variationand, consequently, decreasing $£• Increasing the number or size of samplestaken from a population, in addition to increasing sampling precision, has thesecondary effect of increasing sampling accuracy.

In summary, reliable information concerning the chemical properties of asolid waste is needed for the purpose of comparing those properties toapplicable regulatory thresholds. If chemical information is to be consideredreliable, it must be accurate and sufficiently precise. Accuracy is usuallyachieved by incorporating some form of randomness into the selection processfor the samples that generate the chemical Information. Sufficient precisionis most often obtained by selecting an appropriate number of samples.

There art a few ratifications of the above-described concepts that meritelaboration. If, for example, as in the case of semiconductor etchingsolutions, each batch of a waste is completely homogeneous with regard to thechemical properties of concern and that chemical homogeneity is constant(uniform) over tine (from batch to batch), a single sample collected from thewaste at an arbitrary location and time would theoretically generate anaccurate and precise estimate of the chemical properties. However, mostwastes are heterogeneous in terms of their chemical properties. If a batchof waste Is randomly heterogeneous with regard to its chemical charac-teristics and that random chemical heterogeneity remains constant from batchto batch, accuracy and appropriate precision can usually be achievedsimple random sampling. In that type of sampling, all units in the

100676

Statistics / 9

(essentially all locations or points in all batches of waste from which asample could be collected) are identified, and a suitable number of samplesis randomly selected from the population. More complex stratified randomsampling is appropriate if a batch of waste is known to be nonrandomlyheterogeneous in terms of its chemical properties and/or nonrandom chemicalheterogeneity "Is known to exist from batch to batch. In such cases, thepopulation is stratified to Isolate the known sources of nonrandom chemicalheterogeneity. After stratification, which may occur over space (locationsor points in a batch of waste) and/or time (each batch of waste), the unitsin each stratum are numerically identified, and a simple random sample istaken from each stratum. As previously intimated, both simple and stratifiedrandom sampling generate accurate estimates of the chemical properties of asolid waste. The advantage of stratified random sampling over simple randomsampling is that, for a given number of samples and a given sample size, theformer technique often results in a more precise estimate of chemical propertiesof a waste (a lower value of sj) than the latter technique. However, greaterprecision is likely to be realized only if a waste exhibits substantialnonrandom chemical heterogeneity and stratification efficiently "divides"the waste into strata that exhibit maximum between-strata variability andminimum within-strata variability. If that does not occur, stratifiedrandom sampling can produce results that are less precise than in the case ofsimple random sampling. Therefore, it Is reasonable to select stratifiedrandom sampling over simple random sampling only If the distribution ofchemical contaminants in a waste 1s sufficiently known to allow an intelligentidentification of strata and at least two or three samples can be collected,in each stratum. If a strategy employing stratified random sampling isselected, a decision must be made regarding the allocation of sampling effortamong strata. When chemical variation within each stratum can be estimatedwith a great degree of detail, samples should be optimally allocated amongstrata, i.e., the number of samples collected from each stratum should bedirectly proportional to the chemical variation encountered in the stratum.When detailed Information concerning chemical variability within strata isnot available, samples should be proportionally allocated among strata, i.e.,sampling effort in each stratum should be directly proportional to the sizeof the stratum.

Simple random sampling and stratified random sampling are types ofprobability sampling, which, because of a reliance upon mathematical andstatistical theories, allows an evaluation of the effectiveness of samplingprocedures. Another type of probability sampling 1s systematic randomsampling. In which the first unit to be collected from a population israndomly selected, but all subsequent units are taken at fixed space or timeintervals. An example of systematic random sampling 1s the sampling of awaste lagoon along a transect in which the first sampling point on thetransect is 1 m from a randomly selected location on the shore and subsequentsampling points are located at 2-m Intervals along the transect. Theadvantages of systematic random sampling over simple random sampl1gLand^«stratified random sampling are the ease in which samples are IdentftSeiUnAcollected (the selection of the first sampling unit determines the remainder

SRI 00677


of the units) and, sometimes, an increase in precision. In certain cases,for example, systematic random sampling might be expected to be a little moreprecise than stratified random sampling with one unit per stratum becausesamples are distributed more evenly over the population. As will be demon-strated shortly, disadvantages of systematic random sampling are the pooraccuracy and precision that can occur when unrecognized trends OP cyclesoccur in the population. For those reasons, systematic random sampling isrecommended only when a population is essentially random or contains at mosta modest stratification. In such cases, systematic random sampling would beemployed for the sake of convenience, with little expectation of an increasein precision over other random sampling techniques.

Probability sampling is contrasted with authoritative sampling, in whichan individual who Is well acquainted with the so]id waste to be sampledselects a sample without regard to randomization. The validity of datagathered in that manner is totally dependent on the knowledge of the samplerand, although valid data can sometimes be obtained, authoritative sampling isnot recommended for the chemical characterization of most wastes*

It may now be useful to offer a generalization regarding the foursampling strategies that have been identified for solid wastes. If little orno information is available concerning the distribution of chemical contami-nants of a waste, simple random sampling 1s the most appropriate samplingstrategy. As more information is accumulated for the contaminants of concern,greater consideration can be given (In order of the additional informationrequired) to stratified random sampling, systematic random sampling, and,perhaps, authoritative sampling.

The validity of a CI for the true mean (u.) concentration of a chemicalcontaminant of a solid waste is, as previously noted, based on the assumptionthat individual concentrations of the contaminant exhibit a normal distribu-tion. This is true regardless of the strategy that is employed to sample thewaste. Although there are computational procedures for evaluating thecorrectness of the assumption of normality, those procedures are meaningfulonly if a large number of samples are collected from a waste. Since samplingplans for most solid wastes entail just a few samples, one can do little morethan superficially examine resulting data for obvious departures from normality(this can be done by simple graphical methods), keeping In mind that even ifindividual measurements of a chemical contaminant of a waste exhibit a consid-erably abnormal distribution, such abnormality is not likely to be the case forsample meansi which are our primary concern. One can also compare the mean ofthe sample (x} to the variance of the sample (s2). In a normally distributedpopulation, x would be expected to be greater than s2 (assuming that the numberof samples [n] is reasonably large). If that is not the case, the chemicalcontaminant of concern may be characterized by a Poisson distribution (x isapproximately equal to s2-) or a negati ve bl noroi al di stri butl on (S TsHess thans2). in tne former circumstance, normality can often be achieved by ± BUS A <forming data according to the square root transformation. In the latmipxlrcumstance, normality may be realized through use of the arcsine transformation.

Statistics; Strategies / 11

If either transformation is required, all subsequent statistical evaluationsmust be performed on the transformed scale.

Finally, it is necessary to address the appropriate number of samples tobe employed in the chemical characterization of a solid waste.As hasalready been emphasized, the appropriate number of samples is the leastnumber of samples required to generate a sufficiently precise estimate of thetrue mean (ji) concentration of a chemical contaminant of a waste. From the -perspective of most waste producers, that means the minimal number of samplesneeded to demonstrate that the upper limit of the CI for n is less than theapplicable regulatory threshold (RT). The formula for estimating appropriatesampling effort (Table 1, Equation 8) Indicates that increased samplingeffort is generally justified as s2 or the Mt.2Q" value (probable error rate)- - - - - - - - ' '-- -* In a we11-designed samplingincreases and as A (RT - x) decreases. ____________plan for a solid waste, an effort 1s made to estimate the values of xand s* before sampling is Initiated. Such preliminary estimates,whichmay be derived from information pertaining to similar wastes, processengineering data, or limited analytical studies, are used to identify theapproximate number of samples that must be collected from the waste. It isalways prudent to collect a somewhat greater number of samples than indicatedfay preliminary estimates of x and s* since poor preliminary estimatesof those statistics can result In an underestimate of the appropriate numberof samples to collect. It is usually possible to appropriately process andstore the extra samples until analysis of the Initially identified samples iscompleted and it can be determined If analysis of the additional samples iswarranted.

1.1.3 Basic Sampling Strategies

It is now appropriate to present general procedures for implementing thethree previously introduced sampling strategies (simple random sampling,stratified random sampling, and systematic random sampling) and a hypotheticalexample of each sampling strategy. The hypothetical examples Illustrate thestatistical calculations that must be performed. 1n most situations likely tobe encountered by a waste producer and, also, provide some insight into theefficiency of the three sampling strategies 1n meeting regulatory objectives.

The following hypothetical conditions are assumed to exist for all threesampling strategies. First, barium, which has a RT of 100 ppm as measured inthe EP elutriate test, is the only chemical contaminant of concern. Second,barium Is discharged In particulate fora to a waste lagoon and accumulatesin the lagoon In the form of a sludge, which has built up to approximatelythe same thickness throughout the lagoon* Third, concentrations of bariumare relatively homogeneous along the vertical gradient (from the water-sludgeInterface to the sludge-lagoon interface), suggesting a highly controlledmanufacturing process (little between-batch variation in barium concentrations).

A n <


Fourth, the physical size of sludge samples collected from the lagoon is aslarge as practical, and barium concentrations derived from those samples arenormally distributed (note that we do not refer to barfum'levels in thesamples of sludge since barium measurements are actually made on tHe elutriatefrom EP toxicity tests performed with the samples). Last, a preliminarystudy of barium levels in the elutriate of four EP toxicity tests conductedwith sludge collected from the lagoon several years ago identified values of86 and 90 ppm for material collected near the outfall (in the upper third) ofthe lagoon and values of 98 and 104 ppm for material obtained from thefar end (the lower two-thirds) of the lagoon.

For all sampling strategies, it is important to remember that bariumwill be determined to be present in the sludge at a hazardous level if theupper limit of the CI for u, is equal to or greater than the RT of 100 ppm(Table 1, Equations 6 and 7).

1.1.3.1 Simple Random Sampling

Simple random sampling (Box 1) is performed by general procedures inwhich preliminary estimates of x and $2, as well as a knowledge of the RT,for each chemical contaminant of a solid waste that is of concern are employedto estimate the appropriate number of samples (n) to be collected from thewaste. That number, of samples is subsequently analyzed for each chemicalcontaminant of concern. The resulting analytical data are then used todefinitively conclude that each contaminant is or is not present in thewaste at a hazardous concentration or, alternatively, to suggest a reiterativeprocess, involving increased sampling effort, through which the presence orabsence of hazard can be definitively determined.

In the hypothetical example for simple random sampling (Box 1), prelimi-nary estimates of x and s2 indicated a sampling effort consisting of sixsamples. That number of samples was collected and initially analyzed,generating analytical data somewhat different from the preliminary data (s2was substantially greater than was preliminarily estimated). Consequently,the upper Halt of the CI was unexpectedly greater than the applicable RT,resulting in a tentative conclusion of hazard. However, a reestimatlon ofappropriate sampling effort, based on statistics derived from the six samples,suggested that such'a conclusion might be reversed through the collection andanalysis of just one more sample* Fortunately, a resampling effort was notrequlrtd because of the foresight of the waste producer In obtaining three .extra samples during the initial sampling effort, which, because of theirInfluence In decreasing the final values of xt sj, t.gO» and» conse-quently, the upper limit of the CI - values obtained'frora all nine samples -resulted 1n a definitive conclusion of nonhazard.

680

Strategies / 13

BOX 1. STRATEGY FOR DETERMINING IF CHEMICAL CONTAMINANTS OF SOLID WASTESARE PRESENT AT HAZARDOUS LEVELS -, SIMPLE RANDOM SAMPLING OF WASTES

3.

4.

General Procedures

Obtain preliminary estimates of x and s2 for each chemical con-taminant of a solid waste that is of concern. The two above-identifiedstatistics are calculated by, respectivel-y, Equations 2a and 3a (Table 1).

Estimate the appropriate number of samples (nj) to be collected fromthe waste through use of Equation 8 (Table 1) and Table 2. Deriveindividual values of HI for each chemical contaminant of concern.The appropriate number of samples to be taken from the waste is thegreatest of the individual n^ values.

Randomly collect at least nj samples (or 03 - n\9 n3 - ng» etc. samples,as will be indicated later in this box) from the waste (collection of afew extra samples will provide protection against poor preliminaryestimates of x and s2}. Maximize the physical size (weight orvolume) of all samples that are collected.

Analyze the nj (or r\2 - nj, n3 - n2, etc.) samples for each chemical con-taminant of concern. Superficially (graphically) examine each set ofanalytical data for obvious departures from normality.

5. Calculate x, s2, the standard deviation (s), and sj? for each set ofanalytical data by, respectively, Equations 2a, 3a, 4, and 5 (Table 1).

6. If x for a chemical contaminant is equal to or greater than theapplicable RT (Equation 7; Table 1)} and is believed to be an accurateestimator of u, the contaminant is considered to be present in thewaste at a hazardous concentration and the study is completed. Otherwise,continue the study. In the case of a set of analytical data that doesnot exhibit obvious abnormality and for which x is greater than s2,perform the following calculations with nontransformed data. Otherwise,consider transforming the data by the square root transformation (ifx is about equal to s2) or the arcsine transformation (If x is lessthan s2) and performing all subsequent calculations with transformeddata. Square root and arcsine transformations are defined by, respect-ively, Equations 10 and 11 (Table 1).

7. Determine the CI for each chemical contaminant of concern by Equation 6(Table 1) and Table 2. If the upper limit of the CI is less than theapplicable RT (Equations 6 and 7; Table 1), the chemical contaminant isnot considered to be present in the waste at a hazardous concentrationand the study is completed. Otherwise, the opposite conclusion istentatively reached.


8. If a tentative conclusion of hazard 1s reached, reestimate the totalnumber of samples (n£) to be collected from the waste by use ofEquation 8 (Table 1} and Table 2. When deriving ng, employ the newlycalculated (not preliminary) values of x and s2. If an additional ng -samples of waste cannot reasonably be collected, the study Is completedand a definitive conclusion of hazard is reached. Otherwise, collectan extra ng - r\i samples of waste.

9. Repeat the basic operations described in Steps 3-8 until the waste isjudged to be nonhazardous or, if the opposite conclusion continues tobe reached, increased sampling effort is Impractical.

Hypothetical Example

I. The preliminary study of barium levels 1n the elutriate of four EPtoxlcity tests conducted with sludge collected from the lagoon severalyears ago generated values of 86 and 90 ppm for sludge obtained fromthe upper third of the lagoon and values of 98 and 104 pom for sludgefrom the lower two-thirds of the lagoon. Those two sets of values arenot judged to be indicative of n on random chemical heterogeneity (stratificttion) within the lagoon. Therefore, preliminary estimates ofx and s2 are calculated as:

nI Xf

x - 1^— - 86 * 90 * 98 * 104 m ^Q, and (Equation 2a)

n o n yI X* - (i XjJVn

s* " — —— JTTl ——— (Equation 3a)

m 35.916.00 - 35.721.00 . « nnm i .in. i.r, ..,.-!...— • O3«UU.

2* Baitd on the preliminary estimates of x and s2, as well asthe knowledge that the RT for barium is 100 ppm,

(1.63a*)(66.00) . 5>77. (Equat1on 8)5.5CT

RRIQ0682

Strategies / 15

As indicated above, the appropriate number of sludge samples (nj) tobe collected from the lagoon is six. That number of samples (plusthree extra samples for protection against poor preliminary estimatesof x and s^) is collected from the lagoon by a single randomizationprocess (Figure 2). All samples consist of the greatest volume ofsludge that can be practically collected. The three extra samples aresuitably processed and stored for possible later analysis.

The six samples of sludge (nj) designated for immediate analysisgenerate the following concentrations of barium in the EP toxicitytest: 89, 90, 87, 96, 93, and 113 ppm. Although the value of 113 ppmappears unusual as compared to the other data, there is no obviousindication that the data are not normally distributed.

New values for x and s2 and associated values for the standarddeviation (s) and s£ are calculated as:

89 + 90 + 87 + 96 + 93 •*• 113

n ? n ?Z Xf - (E Xfr/n1-1 1 1*1 *__

n - 154.224.00 - 53.770.67

5

94.57, (Equation 2a)

90.67,

9.52, and

Sr - s/Vn" 3.89.

(Equation 3a)

(Equation 4)(Equation 5)

The new value for x (94.67) is less than the RT (100). Inaddition, x 1s greater (only slightly) than s2 (90.67) and, aspreviously Indicated, the raw data are not characterized by obviousabnormality* Consequently, the study is continued, with the followingcalculations performed with nontransformed data.

CI 94.67 ± (1.476)(3.89)

94.67 + 5.74.

(Equation 6)

Since the upper Halt of the CI (100.41) 1s greater than theRT (100), It Is tentatively concluded that barium 1s presentsludge at a hazardous concentration.


WASTE

i I

T8

36

52

60

tt

103-^

238

~

~

——

N

_

I~

113

——

_

—

^

~

—

——

87

———

———

*^/>

~••B

__

****

••HAW*

~

•M

m^m

————

I i

^ •

————

90

pnI"

_

^^^H

•V--H

__

______

~

91

—

/

M.————

~

JOW

-

ou

•"•»

_

••••

____

~

TFALL

1 89

s_

~

i

_

J

I

I I

I

1 1

VL_

~rii•f ^**

•P^ ^ ^H^W

~rii

—

—

——————

—————

•jA^

K*f

HW

90•B

i— —

ji I I I U i Ui i i i i i iTi

WASTE LAGOON 1 1

OVERFLOW PIPE

—————

—————

_••"*

m*m*m

~

——

——

——

v^

96

s

17

34

——

——

^

2SS

|

—

—

J~l•PHB

^^^^

^ •H*

\

UO

/\

LtO

>PER THIRD= LAGOON

3WCR TWO-THIRDS» LAGOON

VIMAGINARY SAMPLING GRID

LEGEND

1-421 Units in

S iariumAnodai

Samplim Grid

Concentration•dwHhNlMl

i(ppm)UmgJMptSluda*

Figure 2.—Hypothetical sampling conditions in waste lagoon containing sludge contiminatad with barium.Barium cancantrations asaociated with samples of sludge refer to levels measured In the elutriate of EP toxicitytens conducted with the simples.

3. n is now reestimated as:

Strategies / 17

(Equation 8)

The value for n2 h*7) indicates that an additionalsludge sample should be collected from the lagoon.

= 1)

9. The additional sampling effort is not necessary because of the threeextra samples that were initially collected from the lagoon. All extrasamples are analyzed, generating the following levels of barium for theEP t oxi city test: 93, 90, and 91 ppm. Consequently, x, s2, the stan-dard deviation (s), and s£ are recalculated as:

89 + 90 91 M ff93.56, . .(Equation 2a)

«I X? - (

n - 1

79,254.00 - 78,773.78——————— - ———————8

60.03,

7s2 « 7.75, and

7.75//T- 2.58.

(Equation 3a)

(Equation 4)

(Equation 5)

The value for x (93.56) is again less than the RT (100), and there is noindication that the nine data points, considered collectively, are abnor-mally distributed (in particular, x 1s now substantially greater than s?}.Consequently, CI, calculated with nontrans formed data, Is determined to be:

CI - x + t 9ns5 « 93.56 + (1.397)(2.58) (Equation 6)^ «£U X *~

- 93.56 + 3.60.

The upper limit of the CI (97.16) 1s now less than the RT of 100.Consequently, it 1s definitively concluded that barium Is not presentin the sludge at a hazardous level.


1.1.3.2 Stratified Random Sampling

Stratified random sampling (Box 2) 1s conducted by general proceduresthat are slmilafr to the procedures described for simple random sampling. Theonly difference is that, in stratified random sampling, values of x and s2are calculated for each stratum in the population and then integrated intooverall estimates of those statistics, the standard deviation (s), sj,and the appropriate number of samples (n) for all strata.

The hypothetical example for stratified random sampling (Box 2) is basedon the same nine sludge samples previously identified in the example ofsimple random sampling (Box 1) so that the relative efficiencies of the twosampling strategies can be fully compared. The efficiency generated throughthe process of stratification is first evident in the preliminary estimate ofn (Step 2 in Boxes 1 and 2), which is six for simple random sampling and fourfor stratified random sampling. {The lesser value for stratified samplingis the consequence of a dramatic decrease in s2, which more than compen-sated for a modest increase in A.) The most relevant indication of samplingefficiency 1s the value of s£, which is directly employed to calculatethe CI. In the case of simple random sampling, sj is calculated as 2.58 (Step 9in Box 1), while, for stratified random sampling, sj 1s determined to be 2.35(Steps and 5 and 7 in Box 2). Consequently, the gain in efficiency attributableto stratification is approximately 9% (0.23/2.58). (

1.1.3.3 Systematic Random Sampling

Systematic random sampling (Box 3) Is implemented by general proceduresthat are identical to the procedures identified for simple random sampling.The hypothetical example for systematic random sampling (Box 3) demonstratesthe bias and imprecision that are associated with that type of sampling whenunrecognized trends or cycles exist in the population.

1.1.4 Special Considerations

The preceding discussion has addressed the major Issues that are criticalto the development of a reliable sampling strategy for a solid waste. Theremaining discussion focuses on several "secondary" Issues that should beconsidered when designing an appropriate sampling strategy. These secondaryIssues are applicable to all three of the basic sampling strategies that havebetn Identified.

•Mil 00686

Strategies / 19

BOX 2. STRATEGY FOR DETERMINING IF CHEMICAL CONTAMINANTS OF SOLID WASTES AREPRESENT AT HAZARDOUS LEVELS - STRATIFIED RANDOM SAMPLING OF WASTES

Step

1.

4.

6.

General Procedures

Obtain preliminary estimates of x and s2 for each chemicalcontaminant of a solid waste that 1s of concern. The two above-Identified statistics are calculated by, respectively, Equations 2band 3b (Table 1).

Estimate the appropriate number of samples (HI) to be collectedfrom the waste through use of Equation 8 (Table 1) and Table 2.Derive individual values of n\ for each chemical contaminant ofconcern. The appropriate number of samples to be taken from thewaste is the greatest of the individual n\ values.Randomly collect at least nj samples (or ng - nt, 03 - ngt etc.samples, as will be Indicated later in this box) from the waste(collection of a few extra samples will provide protection againstpoor preliminary estimates of x and s2). If s for each stratum(see Equation 3b) is believed to be an accurate estimate, optimallyallocate samples among strata (I.e., allocate samples among strataso that the number of samples collected from each stratum is directlyproportional to sfc for that stratum). Otherwise, proportionallyallocate samples among strata according to size of the strata*Maximize the physical size (weight or volume} of all samples thatare collected from the strata.Analyze the ni (or ng • ni, 03 - ng, etc.} samples for each chemicalcontaminant of concern. Superficially (graphically) examine eachset of analytical data from each stratum for obvious departures fromnormality.

Calculate x, s2, the standard deviation (s), and sj for each setof analytical data by, respectively, Equations 2b, 3b, 4, and 5(Table 1).If x for a chemical contaminant 1s equal to or greater thanthe applicable RT (Equation 7; Table 1) and Is believed to be anaccurate estimator of jx, the contaminant Is considered to be presentIn the waste at a hazardous concentration and the study 1s completed.Otherwise, continue the study. In the case of a set of analyticaldata that does not exhibit obvious abnormality and for which xIs greater than s2, perform the following calculations withnontransformed data. Otherwise, consider transforming the data bythe square root transformation (If x Is about equal to s2)or the arcsine transformation (if x Is less than s2) andperforming all subsequent calculations with transformed datftSquare root and arcsine transformations are defined by, respectively.Equations 10 and 11 (Table 1).


7. Determine the CI for each chemical contaminant of concern by Equation6 (Table 1) and Table 2. If the upper limit of the CI is less thanthe applicable RT (Equations 6 and 7; Table 1), the chemical contaminantis not considered to be present in the waste at a hazardous concen-tration and the study is completed. Otherwise, the opposite conclusion1s tentatively reached.

8. If a tentative conclusion of hazard is reached, reestimate the totalnumber of samples (ng) to be collected from the waste by use ofEquation 8 (Table 1) and Table 2. When deriving r\2, employ thenewly calculated (not preliminary) values of x and s2. If anadditional n£ - ni samples of waste cannot reasonably be collected,the study 1s completed and a definitive conclusion of hazard isreached. Otherwise, collect an extra ng - n^ samples of waste.

9. Repeat the basic operations described in Steps 3-8 until the waste isjudged to be nonhazardous or, if the opposite conclusion continues tobe reached, increased sampling effort is impractical.

Hypothetical Example____B^____ I • •••~l-l___ll___. .•.!__. 4__B__^~

LThe preliminary study of barium levels in the elutriate of four EP ^toxicity tests conducted with sludge collected from the lagoon severalyears ago generated values of 36 and 90 ppm for sludge obtained fromthe upper third of the lagoon and values of 98 and 104 ppm for sludgefrom the lower two-thirds of the lagoon. Those two sets of values arejudged to be Indicative of nonrandom chemical heterogeneity (two_strata) within the lagoon. Therefore, preliminary estimates of xand s2 are calculated as:

x - £ W,xu - (1?(88.001 + l?)(101«QO). , g6.67f and (Equation 2b)UK 0 0

k-1

S , r W S . . + . . 14-67- (£quation 35,]em\

2. Based on the preliminary estimates of x and s2, as well as theknowledge that the RT for barium is 100 ppm,

„. -i°!! . <1-3682)(14.67) . 3.55. (Equation , -1 j 3.33*

Strategies / 21

3. As indicated above, the appropriate number of sludge samples (n^J tobe collected from the lagoon is four. However, for purposes ofcomparison to simple random sampling (Box 1), six samples (plusthree extra samples for protection against poor preliminary estimatesof, x and s2) are collected from the lagoon by a two-stage random-ization process (Figure 2). Because sjc for the upper (2.12 ppm) andlower (5.66 ppm) strata are not believed to be very accurate estimates,.the nine samples to be collected from the lagoon are not optimallyallocated between the two strata (optimum allocation would require twoand seven samples to be collected from the upper and lower strata,respectively). Alternatively, proportional allocation is employed -three samples are collected from the upper stratum (which representsone-third of the lagoon), and six samples are taken from the lowerstratum (two-thirds of the lagoon). All samples consist of thegreatest volume of sludge that can be practically collected.

4. The nine samples of sludge generate the following concentrationsof barium in the EP toxidty test: upper stratum - 89, 90, and 87 ppm;lower stratum - 96, 93, 113, 93, 90, and 91 ppm. Although the valueof 113 ppm appears unusual as compared to other data for the lowerstratum, there 1s no obvious Indication that the data are not normallydistributed.

5. New values for x and s? and associated values for the standarddeviation (s) and s£ are calculated as:

93.56,k-1

+ I2H73.601 .s » and

sx s//n • 7.06/./9 - 2-35.

(Equation 2b)

(Equation 3b)

(Equation 4)

(Equation 5}

6. The new value for x (93.56) 1s less than the RT (100). In addition,x Is greater than s? (49.84) and, as previously indicated, the rawdata are not characterized by obvious abnormality. Consequently, thestudy 1s continued, with the following calculation performed withnontransformed data.

7. CI - ?±t.20sx * 93.56 i (1.397}(2.35)

- 93.56.+ 3.28.

The upper limit of the CI (96.84) is less than the applicable RT (100).Therefore,.it 1s concluded that barium 1s not present in the sludge ata hazardous concentration*


BOX 3. STRATEGY FOR DETERMINING IF CHEMICAL CONTAMINANTS OF SOLID WASTESARE PRESENT AT HAZARDOUS LEVELS - SYSTEMATIC RANDOM SAMPLING

General Procedure

1. Follow general procedures presented for simple randomsampling of solid wastes (Box 1).

Hypothetical Example

1. The example presented in Box 1 1s applicable to systematic randomsampling with the understanding that the nine sludge samples obtainedfrom the lagoon would be collected at equal intervals along a tran-sect running from a randomly selected location on one bank of thelagoon to the opposite bank. If that randomly selected transectwere established between Units 1 and 409 of the sampling grid(Figure 2) and sampling were performed at Unit 1 and, thereafter,at three-unit intervals along the transect (I.e., Unit 1, Unit 52,Unit 103, .... and Unit 409), it is apparent that only twosamples would be collected in the upper third of the lagoon, whileseven samples would be obtained from the lower two-thirds of thelagoon. If, as suggested by the barium concentrations Illustratedin Figure 2, the lower part of the lagoon is characterized bygreater and more variable barium contamination than the upper partof the lagoon, systematic random sampling along the above-identifiedtransect, by placing undue (disproportionate) emphasis on the lowerpart of the lagoon, might be expected to result in an inaccurate(overestimation) and imprecise characterization of barium levels inthe whole lagoon, as compared to either simple random samplingor stratified random sampling. Such inaccuracy and Imprecision,which is typical of systematic random sampling when unrecognizedtrends or cycles occur in the population, would be magnified if, forexample, the randomly selected transect were established solely inthe lower part of the lagoon, e.g., between Units 239 and 255 of thesampling grid.

Strategies / 23

1.1.4.1 Composite Sampling

In composite sampling, a number of random samples are initially collectedfrom a waste and combined into a single sample, which is then analyzed forthe chemical contaminants of concern. The major disadvantage of compositesampling as compared to noncomposite sampling is that information concerningthe chemical contaminants is lost, i.e., each initial set of samples generatesonly a single estimate of the concentration of each contaminant. Consequently,since the number of analytical measurements (n) is small, S£ and t.gQ are

large, thus decreasing the likelihood that a contaminant will be judged tooccur in the waste at a nonhazardous level (refer to appropriate equations inTable 1 and to Table 2). A remedy to that situation is to collect andanalyze a relatively large number of, composite samples, thereby offsettingthe savings In analytical costs that'are often associated with compositesampling, but achieving better representation of the waste than would occurwith noncomposite sampling.

The appropriate number of composite samples to be collected from a solidwaste 1s estimated by use of Equation 8 (Table 1) as previously described forthe three basic sampling strategies. In comparison to noncomposite sampling,composite sampling may have the effect of minimizing between-sample variation(the same phenomenon that occurs when the physical size of a sample ismaximized), thereby reducing somewhat the number of samples that must becollected from the waste.

1.1.4.2 Subsampling

The variance (s2) associated with a chemical contaminant of awaste consists of two components 1n that:

.*+£'s IT(Equation 12)

with s| * a component attributable to sampling (sample) variation, s| aa component attributable to analytical (subsample) variation, and m - numberof subsamples. In general, s| should not be allowed to exceed one-ninthof s|. If a preliminary study indicates that s| exceeds that threshold,a sampling strategy Involving subsampling shoula be considered. In such astrategy, a number of replicate measurements are randomly made on a relativelylimited number of randomly collected samples. Consequently, analyticaleffort 1s allocated as a function of analytical variability. The efficiencyof that general strategy 1n meeting regulatory objectives has already beendemonstrated 1n the previous discussions of sampling effort.


The appropriate number of samples (n) to be collected from a solid wastefor which subsampling will be employed is again estimated by Equation 8(Table 1). In the case of simple random sampling or systematic randomsampling with an equal number of subsamples analyzed per sample:

nx * s iq/n, (Equation 13)

1-1

with X} * sample mean (calculated from values fop subsamples) and n = number ofsamples. Also,

n nE x* - (E x /n

S2 .1-1 isl____ . (Equation 14)n"-"l

The optimum number of subsamples to be taken from each sample (m Q^u ) isestimated as:

sa (Equation 15)) -^

when cost factors are not considered. The value for sa is calculated fromavailable data as:

n m - -I Z Xf- - (I X . . ) V m

s . flLLlLJ_____-___ » (Equation 16)a / n (m - 1)

and ss, which can have a negative characteristic, is defined as:

2« , (Equation 17)

ss " J m

with s2 calculated as Indicated in Equation 14.

In the case of stratified random sampling with subsampUng, criticalformulas for estimating sample size (n) by Equation 8 (Table 1) are:

- m i u ; (Equation Zb)x ,_, Vk* * — -

Special Considerations / 25

with X[< = stratum mean and W^ s fraction of population represented by Stratum K(number of strata, k» ranges from 1 to r). In Equation 2b, xfe for each stratumis calculated as the average of all sample means in the stratum (sample meansare calculated from values for subsamples). In addition:

sfc * i w,k*l >(Equation 3b)

with sic for each stratum calculated from all sample means in the stratum.The optimum subsampling effort when cost factors are not considered and allreplication is symmetrical is again estimated as:

m(opt.) =-rr , with (Equation 15)

sa =

n m

rn (m - 1), and (Equation 18)

with s2 derived as shown in Equation 3b.

(Equation 17)

1.1.4.3 Cost and loss__Funct_io_nsThe cost of chemically characterizing a waste Is dependent on the

specific strategy that is employed to sample the waste. For example, in thecase of simple random sampling without subsampling, a reasonable cost functionmight be:

'(n) (Equation 19)

with C(n) « cost of employing a sample size of n, Co * an overhead cost(which Is Independent of the number of samples that are collected and analyzed),and Cj » a sample-dependent cost. A consideration of C(n) mandates anevaluation of L(n)» which is the sample-size-dependent expected financialloss related to the erroneous conclusion that a waste is hazardous. A simpleloss function Is:


L(n) "as' (Equation 20)

* a constant related to the cost of a waste management program if thewaste Is judged to be hazardous, s^ - sample variance, and n - number ofsamples, A primary objective of any sampling strategy is to minimize C ( n )+ L{n). Differentiation of Equations 19 and 20 indicates that the number ofsamples (n) which minimize C(n) +• L(n) is:

(Equation 21)

As is evident from Equation 21, a comparatively large number of samples (n)is justified if the value of a or s2 is large, whereas a relatively smallnumber of samples is appropriate If the value of C\ is large. Thesegeneral conclusions are valid for any sampling strategy for a solid Waste.

AR!

sampling and analysis plan for sludge disposal area … · preparation and measurement* these will...

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