P.1 

OAR Box 1126 

Prepped by Ollie Stewart 

Document Number: 

26) 11-1-148 

Docket Number: 

A-83-22 

Printed 4/18/2008 9:58:22 AM Sheet 26 of 182 
P.2 

USB. 

* t PBO ^ y 

UNITED STATES ENVIRONMENTAL PROTECTION AGENCY 

Office of Air Quality Planning and Standards 

Research Triangle Park, North Carolina 27711 

13 APR 1989 

MEMORANDUM 

SUBJECT: 

FROM: 

Alternative Forms of a Revised NAAQS for Lead 

Neil Frank "/itU" &*-'' 

Bob Faoro 0f(r <$&#*"' 

Data Analysis Section (MD-14) 

TO: John Haines, Chief 

Standards Development Section B (MD-12) 

Attached is our revised report "Evaluation of Alternative 

Forms of a Revised NAAQS for Lead", which was referenced as a 

December draft in the OAQPS Draft Staff Paper for Lead (March, 

1989). Our report, dated April 1989, does not contain any 

changes to the conclusions presented earlier. However, the body 

of the report contains some new material and graphs. 

Specifically, it contains additional discussion of a monthly form 

based on the second highest monthly average per year. As you 

know, this is already reflected in the Staff Paper. Our report 

also contains some additional clarifying material suggested by 

you and your staff. In particular, it reflects the thought 

provoking comments provided by Gail Bryon. 

Attachment 

cc: B. Laxton (w/o attachment) 

B. Hunt 

T. Curran 

N. Berg 

G. Bryon 

J. Cohen 
P.3 

EVALUATION OF ALTERNATIVE FORMS OF A REVISED NAAQS FOR LEAD 

Neil Frank and Bob Faoro 

April 1989 

INTRODUCTION 

While the current Lead (Pb) standard is expressed as a 

quarterly average, not to be exceeded, the new health data 

supporting a shorter equilibrium time between the individual and 

their Pb contaminated environment, suggest that sensitive 

populations should be protected against monthly average 

concentrations. In this report, several alternative forms of a 

revised NAAQS for Pb are examined, all of which emphasize peak 

monthly average concentrations. The analyses are conducted 

independent of a specific concentration level for the standard. 

Each form was based on statistics computed during a three-year 

period to be consistent with the multi-year format adopted for 

ozone and particulate matter NAAQSs. If attainment was only based 

on a single year's data, an area could alternate between attainment 

and nonattainment on an annual basis. Thus, a three-year period is 

used to provide stability, additional monitoring data and 

additional confidence in the determination of NAAQS attainment. 

Six alternative monthly average NAAQS forms are considered: 

1. Maximum month 

2. Expected maximum calendar month 

3. Expected maximum month 

4. Expected highest three months 

5. Second highest month 

6. Maximum second highest month per year 

The first four forms were previously outlined in the 1985 memo 

entitled "Comparison of Four Alternative Lead Air Quality Standards 

Using Modelled Data at a Secondary Lead Smelter and a Battery 

Plant", (October 22, 1985), and will not be described in detail 

here. Number 1 (Maximum month) is deterministic, and is similar 

to the current quarterly form. The next three forms are 

statistical in nature, that they define expected values derived 

from averages of annual values. These forms are based on averages 

of individual monthly averages. The last two forms are also 

deterministic, but are based on a second highest observed monthly 

average. 

The maximum month form is the most stringent of all possible 

monthly forms. With this form, the standard would be exceeded more 

often and would require more emission reduction to achieve. It 

obviously would provide the greatest degree of health protection. 

However, maximum values, not to be exceeded, are judged to be 

statistically difficult to achieve; they do not allow for rare 

conditions in which high concentrations can be observed. With the 

expected value forms and the second max forms, allowance is made 
P.4 

for such exceedances. With the expected maximum forms, the impact 

of one or two high monthly averages are reduced by averaging with 

other lower monthly average concentrations. With the second max 

forms, the highest month is simply not considered. The first of 

these second max forms (number 5), termed the second highest 

monthly average in three years, explicitly allows for one monthly 

exceedance in three years. The next second max form (number 6), 

termed the maximum second highest month per year, is less stringent 

and allows one exceedance each year (up to three in three years). 

It is primarily included in this examination of alternative 

standards because other short term standards (eg. TSP, S02, CO) 

have been expressed with this form. 

In order to evaluate the statistical characteristics of each 

form, two types of analyses were conducted. First, a computer 

simulation was performed, using generated daily Pb concentrations, 

over a three-year period. This permitted the examination of a wide 

range of possible data sets with identical, known characteristics. 

The second type of analysis involved the examination of actual Pb 

data observed at point source oriented sites. This second analysis 

provided additional perspective for currently monitored situations 

and verification of the hypothetical results. 

All of the comparisons are based on the statistic with which 

attainment would be judged. This is the so-called design value 

(also called the design concentration). When this statistic is 

less than, or equal to, the concentration level of the NAAQS, the 

data would indicate attainment with the NAAQS for the three-year 

period considered. The design value also reflects the amount of 

air pollution control necessary to attain the standard. As used 

in this evaluation, as the design value increases, the stringency 

of the standard also increases due to the need for more control. 

Most of the results are presented as relative values, normalized 

to the expected maximum monthly average concentration. By using 

a reference indicator and presenting the results as relative 

values, the conclusions are independent of the concentration level 

selected for the standard. 

DISCUSSION AND CONCLUSIONS 

Suggested Form. Among the alternative forms examined, the 

form based on the second highest monthly value in three years is 

suggested for a revised Pb NAAQS, because it is easy to comprehend 

and does not involve any fancy statistical calculations. Although 

this form is less stringent than the maximum monthly value, it 

produces design values comparable to the expected maximum monthly 

value. With this second max form, at most one monthly value in a 

three-year period would be permitted to exceed the stated level of 

the NAAQS. The exceedances could occur in adjacent months or in 

separate years. In this way, it allows for explicit discounting 

of one "bad" month which may be caused, for example by unusual 
P.5 

for such exceedances. With the expected maximum forms, the impact 

of one or two high monthly averages are reduced by averaging with 

other lower monthly average concentrations. With the second max 

forms, the highest month is simply not considered. The first of 

these second max forms (number 5), termed the second highest 

monthly average in three years, explicitly allows for one monthly 

exceedance in three years. The next second max form (number 6), 

termed the maximum second highest month per year, is less stringent 

and allows one exceedance each year (up to three in three years).. 

It is primarily included in this examination of alternative 

standards because other short term standards (eg. TSP, S02, CO) 

have been expressed with this form. 

In order to evaluate the statistical characteristics of each 

form, two types of analyses were conducted. First, a computer 

simulation was performed, using generated daily Pb concentrations, 

over a three-year period. This permitted the examination of a wide 

range of possible data sets with identical, known characteristics. 

The second type of analysis involved the examination of actual Pb 

data observed at point source oriented sites. This second analysis 

provided additional perspective for currently monitored situations 

and verification of the hypothetical results. 

All of the comparisons are based on the statistic with which 

attainment would be judged. This is the so-called design value 

(also called the design concentration). When this statistic is 

less than, or equal to, the concentration level of the NAAQS, the 

data would indicate attainment with the NAAQS for the three-year 

period considered. The design value also reflects the amount of 

air pollution control necessary to attain the standard. As used 

in this evaluation, as the design value increases, the stringency 

of the standard also increases due to the need for more control. 

Most of the results are presented as relative values, normalized 

to the expected maximum monthly average concentration. By using 

a reference indicator and presenting the results as relative 

values, the conclusions are independent of the concentration level 

selected for the standard. 

DISCUSSION AND CONCLUSIONS 

Suggested Form. Among the alternative forms examined, the 

form based on the second highest monthly value in three years is 

suggested for a revised Pb NAAQS, because it is easy to comprehend, 

does not involve any fancy statistical calculations. Although this 

form is less stringent than the maximum monthly value, it produces 

design values comparable to the expected maximum monthly value. 

With this second max form, at most one monthly value in a threeyear period would be permitted to exceed the stated level of the 

NAAQS. The exceedances could occur in adjacent months or in 

separate years. In this way, it allows for explicit discounting 

of one "bad." month which may be caused, for example by unusual 
P.6 

meteorology. This approach is more stringent than the alternative 

maximimum second max form in which one monthly exceedance is 

allowed in each and every year. 

The suggested standard would be stated "deterministically", 

in terms of a three-year period with no more than one monthly 

average exceedance. It is deterministic in the sense that the 

observed data explicitly determines the attainment status. Because 

the second max form ignores the magnitude of the highest average 

monthly value (in three years), health protection against worst 

case exposure would not be explicitly incorporated into the form 

of the standard. However, additional protection from high average 

concentrations could be provided by a significant harm level. 

Precision vs. Sampling Frequency. Since attainment is 

to be based on peak monthly averages, the precision of the monthly 

average Pb concentrations is critical. This is because, with 

imprecision, peak values selected from a set of data tend to be 

overestimated. One source of imprecision is measurement error. 

Another source is incomplete sampling. Although, averages of 

measurement concentrations have less measurement error than 

individual 24-hour samples, these errors still persist with small 

sample sizes. With once in six day (1/6), or even every other day 

(1/2) sampling (coupled with the inevitable missing samples), 

monthly averages would be based on few values. For example, there 

would be at most 5-6 values with 1/6 sampling. Consequently such 

averages would be highly variable (imprecise), causing the 

potential for higher than normal monthly average concentration 

estimates. The peak values selected from these highly variable 

monthly averages would yield overestimates of the true peak average 

concentrations. The simulation analyses confirmed this, and showed 

very large overestimates in design concentrations are possible with 

1/6 sampling, and moderate overestimates are still possible even 

with 1/2 sampling. Therefore, incomplete sampling does not appear 

to be a viable monitoring strategy with which to judge 

attainment/nonattainment with a peak monthly average NAAQS for Pb 

for any case close to the standard. 

Recommended Sampling Frequency. Everyday sampling is viewed 

as being highly desireable, and is generally recommended in order 

to judge attainment / nonattainment for a revised Pb NAAQS. To 

reduce imprecision of the monthly average concentrations, general 

minimum data completeness criteria (say, 75 percent) would also be 

needed and should be explicitly stated in the NAAQS. Nevertheless, 

attainment or nonattainment could still be determined with less 

precise estimates for those cases in which the true peak averages 

were sufficiently far from the level of the NAAQS. This could be 

handled, as exceptions, on a case-by-case basis. These analyses 

suggest that everyday sampling and highest data capture would only 

be needed when the true design value is within a factor of two of 

the NAAQS level; this will maintain errors of 

attainment/nonattainment misclassification below 5 percent. 

Finally, where comparisons to the NAAQS on a site-by-site basis are 
P.7 

not important, incomplete sampling could also be utilized. For 

example, for those roadway Pb sites not expected to violate the 

NAAQS, 1/6 sampling would be sufficient to continue the study of 

aggregate national trends in average concentrations at these 

locations. 

COMPUTER SIMULATIONS 

Data usage. Pb concentration distributions derived from 

actual source oriented monitoring sites were used as the generating 

models for the simulations. Data in the vicinity of an ASARCO 

refinery in Omaha, Nebraska and a lead oxide manufacturer in 

Philadelphia were used. In both cases, everyday sampling was 

performed at Pb monitoring sites, permitting the estimation of the 

underlying concentration distribution. The simulation analyses 

were primarily used to examine the relative stringency among the 

alternative forms, and the potential effects of incomplete 

sampling. The simulation analyses also considered some effects of 

the underlying concentration distribution and seasonality. The 

simulation analyses are based on 50 - 100 sets of 1080 values, each 

set representing three years of simulated Pb data. The smaller 

simulations were used to explore the more specialized data cases 

and are only based on 50 sets in order to reduce computer costs. 

Relative Stringency. The first simulation analysis examined 

the relative stringency of each potential form in terms of average 

design values. For these comparisons, the concentration 

distribution shown in Figure 1 was assumed. The lower part of the 

distribution is lognormal1 and the upper tail is normal2. The shape 

of this distribution was derived from actual daily 1984 Pb 

concentrations in the vicinity of an ASARCO lead refinery, as 

reported by the State of Nebraska during their high concentration 

months of April to November. The site is located at Abott Drive. 

The 1984 maximum monthly average concentration, 3.86 p.g/m3, was 

recorded in September. 

Within each month, the concentrations were assumed to be 

independent and were randomly generated from the specified 

concentration distribution. The resulting average design values 

for the six alternative forms are presented in Table 1. Ratios to 

the reference indicator of the expected annual maximum month 

(three-year average, option 3) are also presented. 

The design values from the alternative three-year forms range 

from 2.97 to 3.89 \iq/vuii, with the maximum month in three years 

1 m, = 0.8; sgd = 4 

2

 |i = -2; a = 7.4 
P.8 

yielding the highest value and the maximum three-year calendar 

month yielding the lowest value. These are 11 percent above and 

15 percent below the reference indicator, respectively. The maximum 

annual second high month produces a relatively low value of 3.09 

p.g/m3. The other three alternatives, including the reference 

indicator, yield similar values which are each within 3 percent of 

each other. Among these three "middle" indicators, the simplest 

is the second maximum month in three years. This statistic 

corresponds to a standard which allows a single exceedance of a 

monthly average Pb level in a three year period and is a 

deterministic form. The other two forms - average of the three 

high months and the average of the annual max month - can be 

expressed as statistical (ie. expected value) standards. This 

property is desireable since attainment can be judged on the basis 

of more than three years of data, which is perhaps more useful for 

modeling which is typically based on 5 years of data. The use of 

more than three years of data is also useful to help adjust for the 

effect of an unusual month. With the three-year deterministic 

form, however, the number of monthly average values above the 

specified concentration level for the standard within a specified 

(i.e. three-year) time period is known and the design concentration 

is actually observed/measured. This property is very desireable, 

permits the standard to be simple and easily understood. 

Effect of Incomplete Sampling. The next simulation analysis 

examined the effect of incomplete sampling on the estimation of 

design values, again by using the concentration distribution 

representing the data from the ASARCO plant. For each simulation 

of the six alternative forms of the NAAQS, monthly average values 

were also generated for subsamples corresponding to every other 

day and every sixth day sampling. With every sixth day sampling, 

each monthly average was based on 5 generated values; with every 

other day sampling, each monthly average was based on 15 values. 

Table 2 presents the results in terms of the average design 

values. For each alternative form, the average design value 

increases with less complete sampling. This resulting average 

design value "bias" is a consequence of (1) the focus on the peak 

monthly average concentrations (in this case, the second highest 

month), and (2) the larger variability in potentially observable 

monthly averages which are the product of fewer samples. Due to 

this general effect, true attainment sites could appear to be 

nonattainment (so called false positive), unless some adjustment 

could be made to the standard level. Since this type of adjustment 

would depend on a variety of site specific factors including the 

variability of Pb concentrations at a Pb site, and these factors 

are different among sites, a universal adjustment would not be 

possible. Although the average design values increase with less 

complete sampling, some chance for attainment misclassification 

(false negative) also exists. The chance for false negatives, 

however, is in general considerably less than the chance for false 
P.9 

positives. 

With incomplete sampling, the relative ranking among the six 

alternatives remains the same. The following discussion now 

focuses more closely on the effect of incomplete sampling, using 

the form based on the second maximum monthly value in three years. 

For the sake of brevity, this design value will simply be called 

the three-year design value. 

With incomplete sampling, the average three-year design values 

were 18 and 57 percent higher with every other and every sixth day 

sampling, respectively. The ratio distribution of incomplete to 

complete sampling design values is illustrated in Figure 2, using 

box-plots. With 1/6 sampling, the entire box-plot is greater than 

one. In fact, the probability is 0.98 that the every sixth day 

design value is greater than the complete sampling design value. 

This is the chance for nonattainment misclassification. The 95th 

percentile of this ratio distribution is approximately two. 

Therefore, until the 1/6 design value is twice the standard level, 

it would not be a statistically significant violation (at the 5% 

significance level). Another interpretation of these data is that 

if a "true" attainment design value was greater than one half the 

level of the NAAQS, the chance of appearing to be nonattainment 

would exceed 5 percent. In other words, with monthly averages 

generated by 1/6 sampling, a large range of possible values are 

statistically indistinguishable from the standard level. With 1/2 

sampling, the range of uncertain values is much smaller, but 

nevertheless still exists. As shown in Figure 2, the chance that 

the 1/2 design value is greater than the complete sampling value 

is 0.90 (chance for false positive). The smallest value that is 

a statistically significant violation of the NAAQS would have to 

be 36 percent higher than the standard level. Finally, the chance 

for nonattainment misclassification with 1/2 day sampling exceeds 

.05 when the true attainment design value is greater than 74 

percent of the NAAQS level. 

Effect of underlying distributional model. The bias caused 

by incomplete sampling was studied for several underlying 

distributional models. The concern was that the wide range of 

uncertainty in 1/6 and even 1/2 samples could be a function of the 

within month variability characteristic of the underlying ASARCO 

distribution. In order to determine other appropriate distributions 

for further study, almost complete every day Pb data from a 

monitoring site in Philadelphia was selected. This site is in the 

vicinity of a lead oxide manufacturer. The concentration 

distribution from this site can be closely approximated by a 

lognormal distribution (a) with m, = 0.34 and sgd = 2.3. Two 

additional lognormal distributions were also considered, with the 

following geometric means and standard geometric deviations: 

(b) m=.10, sgd=2.3; (c) m,= .10, sgd=4.0 
P.10 

These two distributions were included to explore the effects of 

change in concentration (i.e. m,) and change in variability (i.e. 

sgd), separately. A fourth distribution to be considered was 

another "hybrid" distribution, whose lower portion has lognormal 

parameters m,=.32, sgd=4.3; and whose upper tail corresponds to a 

normal with p. = 7.2 and a = -7.2. This distribution represents 

low concentration months observed in the vicinity of the ASARCO 

plant. These distributions were selected in order to represent a 

wide range of conditions possible at Pb point sources. 

The results of the simulation using these distributions are 

presented graphically for 1/6 and 1/2 sampling in Figures 3 and 

4, respectively. Two statistics of interest are summarized in 

Table 3: (1) the average ratio of 1/6 design value to that of 

complete sampling and (2) the 95th percentile "critical value" used 

to define statistical significance for nonattainment determination. 

The results for the four new distributions bracket those 

presented earlier. Two distributions yield lower ratios (less 

bias) and two distributions yield higher ratios (more bias). The 

least bias corresponds to the underlying distribution with the 

lowest concentrations (m,=0.10, sgd=2.3). Here, the critical value 

for statistical significance is 1.7 (i.e. 170 percent). The bias 

increases with average concentration, and even more with greater 

within month variability. The highest critical value for 

statistical significance is 2.6 (i.e. 260 percent). A crude 

indicator of the potential for bias is the ratio between the peak 

monthly values and the overall (annual) average concentration. 

For these last four simulations, this ratio was 1.4 for the 

distributions corresponding to less bias and the ratio was 1.7-1.8 

for the distributions generating more bias. For the simulation 

discussed at the beginning of this paper, this ratio was 1.5. 

Correspondingly, the results for 1/2 sampling show less bias 

with the same underlying distributions. In the best cases studied, 

the average bias was reduced to 1.08 (8 percent), with a critical 

value of 1.27 (27 percent). Thus misclassification errors exceed 

.05 when the site is greater than 80 percent of the NAAQS. These 

results are similar to those presented earlier.. 

Effect of Seasonality. The next simulation analysis examined 

the effect of seasonal Pb concentrations on the observed bias in 

peak monthly statistics. The results indicate a reduction in bias 

with seasonal differences in Pb concentrations, but the improvement 

depends on the length of season, concentration gradients, as well 

as within month concentration distribution. 

Since the bias in peak monthly statistics is caused by the 

imprecision of estimated monthly average concentrations, 

seasonality in Pb concentrations affects the number of months with 
P.11 

potential for observed peak monthly averages. When there are fewer 

months with potential for high values, then the bias introduced 

by incomplete sampling can be less. Two analyses were performed 

to illustrate this phenomenon. Seasonal models were employed 

wherein data were generated from one concentration distribution for 

part of the year and from a different distribution for the other 

part. These analyses were first performed in terms of the lognormal 

distributions (a) and (b), and the two "hybrid" distributions 

described earlier. The gradients in average concentration between 

the high and low seasons are 3.6:1 and 2.5:1, respectively. These 

two cases are used to model large seasonality and moderate 

seasonality. 

The results of these analyses are presented in Figures 5 and 

6, where statistics describing the ratios of 1/6 sampled design 

value to the complete sampled value are presented by the number of 

months with the high concentration season. Figure 5 displays the 

95th percentile of the ratio distribution (i.e. critical value for 

statistical significance). Figure 6 presents the probability of 

exceeding, and not exceeding, the true design value. The results 

for 1/2 sampling displayed similar patterns and are not presented. 

The results of these seasonal analyses for 1/6 sampling show 

that: 

(1) the positive design value bias was generally observed, although 

it disappeared for the most extreme case - a single high 

concentration month combined with the larger seasonal concentration 

gradient. 

(2) As the length of the Pb season increases, peak monthly values 

and relative bias increase, until approximately 8 months when a 

leveling off occurs. 

(3) The chance for exceeding the true design value (false positive) 

was generally large. The probability for not exceeding the true 

value (false negative) increased with fewer true high concentration 

months, and with the larger seasonal concentration gradient. For 

the hybrid distributions representing the moderate seasonal 

concentration gradient, the largest probability of not exceeding 

the true design value was 0.14 for the single high month case. 

(4) With the larger concentration gradient with the two lognormals, 

the chance for not exceeding the true design value was larger, but 

still less than 0.10 with 6 or more months with high 

concentrations. It also increased with fewer high concentration 

months, and ultimately achieved a false negative probability value 

of 0.65 for the extreme case with a single high concentration 

month. This was because with the higher seasonal concentration 

gradient, the high season was less likely to produce a maximum 

monthly concentration greater than the true maximum monthly value. 
P.12 

EXAMINATION OF ACTUAL PB DATA 

All point source oriented lead monitoring sites, which had 

violations of the present lead standard in more than one calendar 

year in the 1985-1987 time period, were selected for comparisons 

to the six alternative forms of the revised Pb NAAQS. Ten sites 

from seven different States were selected for these comparisons. 

These sites include the ASARCO and lead oxide manufacturer 

discussed earlier. In order to compute the design value statistics 

from available data, two out of the three years had to be 

available. The results are presented in Table 4 and Figures 7, and 

confirm the relative stringency findings developed from the 

computer simulation. 

Figure 7 shows the average design values for each alternative 

form expressed as a ratio to the expected maximum month. The 

results show that the most stringent is the maximum month form, 

which is also the most sensitive to a single "atypical" month. The 

ratio shown is 1.31 for this form of the standard. The next most 

stringent is the expected maximum three months, whose ratio is 1.07 

or 7 percent higher than the expected maximum month. The average 

design value for the second highest month in three years is only 

slightly higher than the expected maximum month - the ratio is 

1.01. The maximum second highest month per year and the expected 

maximum calendar month were the least stringent, with ratios of 

0.86 and 0.73, respectively. 
P.13 

Table 1. Relative stringency of alternate forms of a monthly NAAQS 

for Pb, based ori a simulation of Pb data in the vicinity of ASARCO 

Pb refinery (annual average = 2.36 ng/m3). 

OPTION 

Average Design 

Value ((ig/m3) 

Ratio to 

Reference Indicator 

1) Max Month 3.89 1.11 

2) Expected Max 

Calendar Month 2.97 0.85 

3) Expected Max 

Month* 3.51 1.0 

4) Expected High 

Three Months 3.60 1.03 

5) Second Highest 

Month 3.54 1.01 

6) Max 2nd High 

Month Per Year 3.09 0.88 

"Reference indicator 

10 
Table 2. Effect of incomplete sampling on estimated design values 

for alternative forms of a monthly NAAQS for Pb based on a 

simulation of ASARCO Pb refinery data. 

I DESIGN VALUE CONCENTRATION (ng/m3) i 

P.14 

Sampling 

Frequency 

1/1 

1/2 

1/6 

1/1 

1/2 

1/6 

1 

3.8 9 

4.6 4 

6.4 6 

1 

1.1 1 

1.3 2 

1.8 4 

2 

2.9 7 

3.2 6 

3.9 5 

2 

0.8 5 

0.9 3 

1.1 3 

O P T 

3* 

3.5 1 

4.0 3 

5.3 2 

3* 

1 . 0 

1.1 5 

1.5 1 

I O N 

4 

3.6 0 

4.1 6 

5.5 9 

4 

1.0 3 

1.1 9 

1.5 9 

5 

3.5 4 

4.0 9 

5.4 4 

5 

1.0 1 

1.1 7 

1.5 5 

6 

3.0 9 

3.4 2 

4.1 7 

6 

0.8 8 

0.9 7 

1.1 9 

t RATIO TO REFERENCE INDICATOR OF 3.51 ng/m3 t 

*Reference Indicator (Option 3) 

11 
P.15 

Table 3. Selected statistics associated with the ratio of 

incomplete to complete sampling design values for various 

underlying concentration distributions. 

Ratio of 

1/6 to 1/1 design vals. 

Ratio of 

1/2 to 1/1 design vals. 

Distribution* 

lognormal 

a 

b 

c 

hybrid 1 

hybrid 2 

average 

1.41 

1.36 

1.65 

1.52 

1.71 

critical 

value 

1.83 

1.70 

2.60 

1.95 

2.38 

average 

1.12 

1.08 

1.21 

1.15 

1.19 

critical 

value 

1.30 

1.27 

1.64 

1.36 

1.43 

'See text for description of distributions 

12 
Table 4. Comparison of Alternative Lead Standards Applied to Point 

Source Oriented Monitoring Data (1985-1987). 

DESIGN VALUES FROM OBSERVED DATA (ng/m3) 

AIRS SITE 

OPTIO N 

1 2 3 4 5 6 

Max Ex Max ExMax ExMax 2ndMx Mx2nd 

Month Cal Mnth Month 3 Mon Month MxMth 

010732004 

011090003 

180892013 

290990005 

290990011 

300490714 

300490719 

310550042 

421010028 

481410031 

Leeds, AL1 

Troy, AL1 

Hammond,IN2 

Jeff.Co.MO3 

Jeff.Co.MO3 

Lewis & Clrk 

Lewis & Clrk 

Omaha, NE* 

Phil., PA2 

El Paso, TX3 

MT3 

MT3 

Average 

2.6 

7.6 

4.1 

7.4 

5.7 

7.2 

5.2 

5.0 

4.3 

4.3 

5.34 

1.6(Nov) 

3.8(Mar) 

2.4(Jul) 

3.5(Sep) 

2.2(Jan) 

5.1(Oct) 

3.4(Oct) 

2.3(Dec) 

2.5(Jan) 

2.8(Apr) 

2.96 

2.0 

4.0 

3.8 

5.5 

4.7 

6.3 

4.8 

3.7 

3.1 

2.8 

4.08 

2.2 

4.7 

3.8 

5.5 

5.1 

6.4 

4.8 

3.9 

3.4 

3.8 

4.36 

2.1 

3.9 

3.5 

4.8 

5.3 

6.1 

4.8 

3.9 

3.3 

3.7 

4.13 

1.8 

3.8 

2.6 

3.6 

4.2 

6.0 

3.6 

2.9 

2.6 

3.7 

3.49 

1 Secondary Lead Smelter 

2 Lead Oxide Manufacturer 

3 Primary Lead Smelter 

* Lead Refinery 

13 
P.17 

FIGURE 1 LEAD CONCENTRATION 

DISTRIBUTION FROM ASARCO 

REFINERY DATA 

I 

Z 

O 

UJ 

o o 

ffi 

CL 

to 

10 

5 

4 

2 

2 

1 

05 

0.4 

0.3 

0-2. 

0.1 

0.05 

-

-

-

1 

O 

» 

PB CONCENTRATION DISTRIBUTION 

OBSERVED FROM MONITORING DATA 

HYBRID DISTRIBUTION 

LOWER TAIL LOGNORMAL 

UPPER TAIL NORMAL 

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Figure Z Ratio Distribution of incomplete to complete sampling 

design vdues fbr the 2nd highest mcrithSy value 

In 3 years based on a simulation of ASARCO Pb Refinery 

y/2 DAY 

SAMPLING 

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L m O 

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RATIO 

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Figure 3. Variability In second highest irrcn^ crverage In three years 

Ratios of Incomplete (y& to complete sampling design values 

based on a smiatton of various lead ccricentration dstributfons. 

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Lognormal Distributions 

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Hybrid Distributions 
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Rgure 4. VariabflHy In second highest monthly average tn three years 

Ratios of incomplete (1/2) to complete sampling design values 

based on a simulation of various lead concentration distributions. 

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Hybrid Distributions 
FIGURE 5 EFFEC 

SECOND HIGHEST 

YEARS WITH INCO 

CRITICAL RATIO FOR NONATTAINMENT 

2.4 

OF SEASONALITY ON VARIABIL1 

ONTHLY AVERAGE OBSERVED IN THREE 

PLETE(t/(8) SAMPLING 

2.2 

2 -

1.8 

1.6 

1.4 

\ / 

J I I L. 

* RATIO OF OBERVED TO TRUE 

DESIGN VALUES FOR STATISTICAL 

SIGNIFICANCE 

J L J I I L 

1 2 3 4 5 6 7 8 • 9 10 11 12 

NUMBER OF MONTHS WITH HIGH LEAD SEASON 

SEASONAL CONCENTRATIONS GRADIENT «o 

MODERATE 

LARGE 

oo SEE TEXT 

TJ 

ho 
6 EFFECT QF.SE 

EXCEEDING TRUE SECOND 

PROBABILITY OF EXCEEDING TRUE DESIGN VALUE 

(1/ 6 SAMPLING) 

ONAL1TY ON PROBABILITY OF 

H MONTH IN THREE YEARS 

0.2 

0.1 

0 I L ml. I i - J L. J l_ -i—.J 

SEASONAL CONCENTRATIONS GRADIENT o« 

MODERATE 

LARGE 

oo SEE TEXT 

1 2 3 4 5 6 7 8 9 10 11 12 

NUMBER OF MONTHS WITH HIGH PB SEASON 
RATIO OF ALTERNATIVE FORMS 

ONTH BASED ON DATA FROM TEN POINT 

MONITORING SITES 

TO THE EXP MAX 

SOURCE LEAD 

ALTERNATIVE FORMS 

OF LEAD STANDARD 

MAX MONTH 

EXP MAX CAL MONTH 

EXP MAX MONTH 

EXP MAX 3 MONTHS 

2ND MAX MONTH 

MAX 2ND MAX MONTH 

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 

AVERAGE RATIO OF ALTERNATIVE FORMS TO THE EXP MAX MONTH