A revised conversion factor relating respirable dust concentrations

measured by 10 mm Dorr-Oliver nylon cyclones operated

 -1 at 1.7 and 2.0 L min

Steven J. Page* and Jon C. Volkwein

US Department of Health and Human Services, Public Health Service,

Centers for Disease Control and Prevention, National Institute for

Occupational Safety and Health, Pittsburgh Research Laboratory, 626

Cochrans Mill Road, Pittsburgh, PA, 15236, USA

Accurate measurement of workplace respirable dust concentration is an essential step in eliminating 

lung disease in any occupational setting. In the United States (U.S.) coal mining industry, this 

measurement process has relied upon a personal sampler that includes a 10 mm Dorr-Oliver (DO) 

nylon cyclone operated at a flow rate of 2.0 L min-1 to collect a respirable dust sample. Dust 

concentrations measured with this sampler are multiplied by 1.38, which was empirically derived, to 

convert them to measurements approximating the United Kingdom British Medical Research Council 

(BMRC) definition of respirable dust upon which the health effects of coal mine dust are based. The 

International Organization for Standardization (ISO) subsequently refined the respirable dust 

definition and the U.S. National Institute for Occupational Safety and Health (NIOSH) 1995 Criteria 

for a Recommended Standard presented a conversion multiplier of 0.857 to apply to the 2.0 L min-1 

DO (in addition to the1.38 multiplier) to obtain equivalent ISO concentrations, as approximated by the 

1.7 L min-1 DO. However, the conversion multiplier 0.857 was derived indirectly from a limited size 

distribution data set rather than a direct comparison of the DO samplers. The present analysis focuses 

on providing a more accurate conversion multiplier derived from direct comparisons of the 2.0 L min-1 

(with 1.38 BMRC equivalency multiplier) and 1.7 L min-1 DO cyclones. A weighted linear regression 

analysis of this database suggests that a more accurate estimate of the conversion multiplier is 0.815. 

1. Introduction

Accurate measurement of workplace respirable dust concentration is an essential first step in eliminating lung disease caused by 

overexposure to dust in any occupational setting. More accurate 

measurements can be made by minimizing random error and, 

perhaps more importantly, minimizing measurement bias. In the 

United States (U.S.), The Federal Coal Mine Health and Safety 

Act of 1969, the predecessor of the Federal Mine Safety and 

Health Act of 19771 mandates that respirable coal mine dust 

levels be monitored and controlled to a maximum of 2 mg m-3 or 

below for a working shift, provided the quartz content of the 

airborne respirable dust remains at or below 5%. To date in the 

U.S. coal mining industry, this measurement has relied upon 

a personal sampler unit that includes a 10 mm diameter DorrOliver (DO) nylon cyclone operated at a flow rate of 2.0 L min-1 

to collect a respirable mine dust sample. 

Particle collection according to size by the DO cyclone operated at 2 L min-1 sampling airflow rate was initially considered in 

the U.S. to approximate particle deposition in the human lung 

and became an early definition of respirable dust for the U.S. 

coal mining industry. However, earlier studies relating the 

prevalence of lung disease to exposure to respirable coal mine 

dust were conducted in the United Kingdom (U.K.) using 

a different type of sampler. The horizontal plate elutriator 

associated with the U.K. sampler classified mine dust according 

to a different particle size function, which came to be known as 

the British Medical Research Council (BMRC) definition2 of 

respirable dust and adopted by the U.K. Mining Research 

Establishment (MRE) as the method used to relate coal mine 

dust concentrations to worker health effects. Subsequent 

comparison studies3 arrived at a multiplier of 1.38 to convert the 

U.S. personal sampler [2.0 DO] estimates of respirable dust 

concentrations to equivalent BMRC estimates (hereafter referred 

to as [2.0 DO] 3 BMRC, measured in mg m- ). It is understood that 

[2.0 DO]BMRC 1⁄4 1.38 x [2.0 DO]. The U.S. coal industry has 

retained use of the BMRC definition. 

More recently, Soderholm4 developed a theoretical model to 

characterize human lung penetration of all dust sizes. This model 

was adopted by the International Organization for Standardization5 (ISO) and is that organization’s definition of respirable 

dust. This definition of respirable dust has also been adopted by 

the European Committee for Standardization6 (CEN),the 

American Society for Testing and Materials7 (ASTM) and the 

American Conference of Governmental Industrial Hygienists8

(ACGIH). 

No cyclone sampler collects dust strictly according to either 

the BMRC or ISO definition of respirable dust, and specific 

cyclones that are used will exhibit varying degrees of bias, 

depending on the size distributions of challenge aerosols. The 

[2.0 DO]BMRC sampler currently used in the U.S. has bias relative 
to both the ISO and the BMRC definitions of respirable dust.9

The same DO cyclone operated at a flow rate of 1.7 L min-1 and 

without the 1.38 multiplier (hereafter referred to as [1.7 DO], 

measured in mg m-3

) has been previously reported9–11 to have 

low bias relative to the ISO definition. However, it must be 

observed that this reported low bias is based on idealized laboratory tests utilizing particle counting at very low levels of 

challenge aerosol directly from the cyclone outlet. Performance 

of [1.7 DO] under actual dust sampling conditions could exhibit 

negative bias, for example, due to particulate loss or loading 

within the cyclone itself12 and possibly within the cyclone/filter 

transition zone. 

To relate cyclone performance with international definitions of 

respirable dust, the National Institute for Occupational Safety 

and Health (NIOSH) document, Criteria for a Recommended 

Standard,13 presents a conversion multiplier of 0.857 to apply to 

[2.0 DO]BMRC measurements to obtain equivalent [1.7 DO] 

values as an approximation of the ISO definition. At the time the 

0.857 conversion multiplier was calculated, the best available 

data was limited size distribution data from eleven underground 

coal mine sections obtained using a Marple 298 personal cascade 

impactor. This is a miniaturized eight-stage cascade impactor 

intended to provide particle size distributions of sampled aerosol 

and it is sufficiently small so as to be a wearable personal 

sampler. The conversion multiplier was derived indirectly by first 

using the ISO respirable definition to calculate an equivalent 

respirable mass concentration to associate with each impactor 

stage. The cumulative result of this calculation was then 

compared to the cyclone-defined respirable mass concentration 

measured by [2.0 DO]BMRC. To support the analysis, the NIOSH 

Criteria Document13 cites another independent analysis14 of 

particle size distributions using Marple 298 and 260 impactors 

obtained from various studies over a 10-year time period. The 

resultant conversion multiplier obtained from that analysis was 

0.85, similar to the Criteria Document result. 

The present work represents a direct comparison between [2.0 

DO]BMRC and [1.7 DO] and should provide a more accurate 

conversion multiplier than previously derived. Such a relationship, however, has more significance than a mere conversion 

value between two different samplers. For example, it would 

permit conversion of historical U.S. Mine Safety and Health 

Administration (MSHA) coal mine respirable dust exposure data 

to near-ISO equivalency, as estimated by [1.7 DO], in the event 

that MSHA would make the transition to the ISO definition at 

some future time in the interest of regulatory enforcement. Also, 

the ISO definition of respirable dust is acknowledged to be 

a better approximation of alveolar deposition than the BMRC 

definition. Of epidemiological interest, the conversion multiplier 

provides consistency and a means to place the U.S. historical 

data on the same international basis with which exposure and 

epidemiological data from other countries could be compared. 

Although exposure limits themselves cannot be directly 

compared from country to country because of differences in 

measurement strategies, the current work does provide 

a common point of comparison adopted by the international 

community regarding the health effects of exposure to respirable 

coal mine dust. 

Of a more general and widespread concern, the Marple 

cascade impactor is used in many different industrial hygiene 

applications outside of mining and it has generally been accepted 

that data obtained with this impactor is more or less accurate. 

Therefore, this work presents the opportunity to examine the 

accuracy of the Marple cascade impactor. Additionally, the work 

presents an analytical method of sampler comparison which is 

beyond ordinary regression and is not limited only to dust 

samplers. This method is particularly useful when data exhibit 

constant coefficient of variation with an inherent constant variance term at small values of either variable. 

2. Methods

2.1 Criteria for mine selection

A stratified random sampling design was used to select mechanized mining units that were representative of all U.S. underground coal mines. The sampling base was developed using 

information extracted from the MSHA Standardized Information System, reflecting all producing mechanized mining units as 

of September 27, 2004. The selected sample of mechanized 

mining units was partitioned into mutually exclusive strata that 

reflected the coal type (MSHA bituminous coal district) and 

mining method. Therefore, because of the mine selection process, 

many potentially confounding effects such as mine dust size 

distribution or coal type are accounted for, on average, in the 

data analyses. Of the total mechanized mining unit population, 

only a small percentage employed longwall and other mining 

methods (6% and 3.5%, respectively) with the balance being 

continuous mining sections. A proportionate allocation strategy 

was used to ensure that the composition of the sampled mechanized mining units was approximately representative of the 

composition of the population. A sample of 180 was chosen to 

represent approximately 20% of all mechanized mining units in 

production at that time. The sample was randomly selected using 

the Survey Select procedure from the SAS system for the statistical analysis of data (SAS Institute, Inc., Cary, NC). 

2.2 Testing procedures

Sampling instruments were grouped into a sampling package. 

Each sampling package contained (1) a Personal Dust Monitor 

(PDM),15–17 pre-programmed to begin an 8 h sample at the 

selected mine shift start time and operated at 2.2 L min-1

; (2) two 

dust samplers using DO cyclones, one operated at 2.0 L min-1 

and the other at 1.7 L min-1; and (3) a Marple 298 cascade 

impactor prepared according to standard procedures and operated at 2.0 L min-1

. The PDM is a belt-wearable combination 

cap lamp and real-time sampling instrument using a tapered 

element oscillating microbalance (TEOM®) mass sensor. Dust 

classification in the PDM is performed by a Higgins-Dewell 

cyclone. Each DO cyclone sampler consisted of a Mine Safety 

Appliances (Cranberry, PA) 37 mm diameter, pre-weighed 5 mm 

pore PVC filter preceded by a 10 mm DO nylon cyclone. It 

should be noted that the PVC filter is contained within a plastic 

cassette so that wall deposits are retained with the filter and not 

lost. The DO cyclones, impactor, and the PDM sampling inlet 

were mounted inside a specially constructed Lippmann sampling 

canister16–18 with a single inlet to minimize spatial variability. 

This procedure ensured that all samplers were exposed to 

essentially the same atmospheric conditions by minimizing 
spatial variation. Flow-controlled Mine Safety Appliances 

Escort Elf ® pumps were calibrated to ± 1% for the DO cyclone 

and impactor samplers prior to each mine test using a Gilibrator 

(Sensidyne Inc.,Clearwater, FL) primary standard flow meter. 

An equivalent pressure restriction for the respective samplers was 

used during pump calibration. 

Sampling locations were chosen where miners typically worked. 

Data for the PDM has been previously analyzed and reported.17

2.2.1 Analytical gravimetric imprecision. Gravimetric analysis was performed on a Mettler-Toledo UMT2 microbalance. 

Weighing was done at controlled ambient conditions of 22.8 °±

0.4 °C (73 ± 0.7 F) and 53 ± 2% RH. All samples were pre- and 

post-weighed with control filters. Two filter cassettes were used 

as controls for each sampler. To correct for potential differences 

(e.g., temperature and humidity variations) in weighing room 

conditions between pre- and post-weighings, average blank 

control filter masses were used to correct the filter mass results 

for each test. All sample and control filters were desiccated and 

allowed to equilibrate to room conditions prior to weighing. 

2.2 Analytical model

An iterative weighted regression was the method of choice 

previously reported17 according to the model 

[1.7 DO] 1⁄4 (a[2.0 DO]BMRC)31 + 030 (1) 

where a 1⁄4 regression slope and assuming zero (statistically 

insignificant or unmeasurable) intercept, 31 1⁄4 a normally 

distributed random multiplicative error term with unity mean and 

constant variance (s1)

2 resulting from in-canister spatial variation 

in the concentration, coupled with sampling error of the personal 

sampler, and 030 1⁄4 a normally distributed random additive error 

term with zero mean and constant variance ( 2 0s) resulting from 

weighing imprecision as the true concentration approaches zero. 

Appendix B† presents the general analytical model and 

method of weight variable estimation. The [2.0 DO]BMRC was 

chosen as the independent predictor variable to correspond with 

the designation in the NIOSH Criteria Document.13

3. Results

3.1 Gravimetric limit of quantification

Quality control procedures, involving control room filters used 

only in the weighing room, document that the standard deviation 

(SW) due to weighing imprecision and the cyclic fluctuations in 

weighing room conditions during the course of this study was SW 

1⁄4 4.1 mg. Propagation of error in the personal sampler filter dust 

mass gains (including an average of 2 control filters, designated 

WC) using 

S2 S2 

2 W

p

C- ST 1⁄4 S2 

W W ffiffiffi pre þ S2 

post þ pre 

þ W

p

C-post

ffiffiffi (2) 2 2 

yields ST 1⁄4 1.848 x SW 1⁄4 7.6 mg. For an 8 h sample, this value 

corresponds to 0s 1⁄4 0.008 mg m-3 applicable to measured values of 

[1.7 DO]. This value was used to estimate 0s, necessary for estimating the appropriate weight variable in the regression analysis.17

3.2 Analysis

Tables 1 and 2 (see Appendix A) present the regression results and 

sampler data, respectively. Fig. 1(a) shows a scatter plot of the 

data with a high degree of linearity and a slight degree of the 

typical multiplicative error. An initial weighted regression yielded 

a very small intercept of -0.006 mg m-3

. Although statistically 

significant at the 95% significance level (t 1⁄4 -3.83), the intercept 

is below any level of measurement certainty and has very little 

effect on the slope when regression is performed without the 

intercept. Therefore, the iterative weighted regression was performed through the origin. The final result yielded a conversion 

multiplier of 0.815 (95% C.I. 1⁄4 [0.804, 0.824), which is statistically 

different (t 1⁄4 -7.48) from the value of 0.857 reported in the 

NIOSH Criteria Document.13 Table 1 additionally shows the 

regression value of d, from which s1 and the coefficient of variation (CV) are calculated, as per Appendix B,† from 

d 1⁄4 a2

CV2 1⁄4 s 2 

1 (3) 

Fig. 1 (a): Fitted line to the paired cyclone data. (b): Substitution of [1.7 

DO] data by the ISO calculation from impactor data. The regression line 

shown is that of part (a) to establish a common comparison. 

4. Discussion

Differences in particle size distribution between mines or coaltype bias likely are not contributing factors in the difference 

between the present direct comparison and the Criteria Document13 or the analysis by Hewitt.14 This is suggested by the fact 
 

 

 

that the Criteria Document and the Hewitt analysis obtained 

virtually identical results. Considering that the Hewitt analysis 

was based on some 400 impactor data sets collected over several 

years by different people and that the data base for the NIOSH 

Criteria Document had 52 impactor data sets from 11 sections in 

7 mines, it would seem extremely coincidental for both studies to 

have identical size and coal type biases and yielding identical 

conversion factors. The common denominator between those 

two studies was the Marple impactor. The 131 sample set of the 

present direct comparison was statistically representative of the 

mining industry and tends to average out size distribution and 

coal type effects uniformly when seeking a conversion multiplier 

to apply to the entire U.S. coal industry. 

Fig. 1(b) shows the respirable dust concentration calculated 

from the Marple impactor according to the ISO definition. The 

calculation was made in similar fashion as calculated in the 

NIOSH Criteria Document13 by assigning the appropriate ISO 

respirable fraction to each impactor stage. It should be noted 

that the particular method of estimating these ISO concentrations is not important in the context of this work because it 

would apply equally to all samples and any resulting bias 

incurred would be constant. Qualitatively, there is one notable 

and important point concerning Fig. 1(b) and that is a concentration-dependent negative bias producing the downward 

curvature. The observed non-constant negative bias occurs 

independently of the manner in which an ISO respirable 

concentration is estimated from the stage masses collected. The 

linear regression line shown in Fig. 1(b) is the same as in Fig. 1(a) 

to provide a common reference point. Because of evidence that 

the impactor data is biased, it is provided only in graphical form 

for the purpose of demonstrating that there is an increasing 

underestimation of the respirable dust concentration with 

increasing concentration as measured by [2.0 DO]BMRC. Size 

distribution information derived from the impactor data, such as 

median size and geometric standard deviation, are rendered quite 

meaningless because of the displayed negative bias increasing 

with increasing mass concentration. Extracting any useful 

information from impactor data requires the instrument to be 

operating properly, properly calibrated, and linear with respect 

to mass concentration. Because a linear relationship is expected 

with such data we presume that some concentration-related or 

mass loading bias is the source of the non-linearity. 

As noted above, it is observed that overall there is downward 

curvature in Fig. 1(b). This downward curvature is not likely to 

be the result of impactor overloading. If it is presumed that 

impactor overloading occurred, the expected effect on the data 

would produce a relationship that curves upward, not downward. 

One explanation in terms of overloading can be eliminated as 

follows. One must consider each impactor stage, beginning with 

the first, when excessive dust attempts to deposit on each 

substrate. The phenomenon generally has the result of an effect 

known as ‘‘particle bounce’’ or ‘‘blow off’’ within impactors.19

The high velocity air stream carrying the dust particles to the 

substrate will actually begin to dislodge the dust accumulated on 

the substrate, and a portion of this dislodged dust will be carried 

on to the following stage substrate(s). Since each subsequent 

stage corresponds to a smaller aerodynamic size, and therefore 

a larger respirable size fraction, it is obvious that a biased 

increase in accumulated mass on a subsequent stage would 

necessarily result in a positive, rather than negative, bias in 

measured impactor respirable dust concentration. In the absence 

of concentration-dependent impactor bias, one would reasonably expect a linear relationship instead of the apparent downward curvature indicated. It should be noted that this curvature 

is made apparent, in large part, by the preponderance of data 

obtained in this study. A much more limited set of data likely 

would not exhibit the curvature because the high degree of 

multiplicative error (variance increasing with concentration) in 

the impactor data could easily conceal any curvature. 

In addition to the direct vs indirect difference in sampler 

comparison, there is another problematic difference between the 

current and previous NIOSH studies. In using the impactor data, 

the total respirable mass calculation can be made in several ways. 

One is by assigning a respirable fraction to a single value, the 

stage cutpoint, for each impactor stage. However this method is 

at best a crude approximation because there are only nine size 

fractions in the impactor. Another more detailed method would 

be a numerical integration across all sizes associated with each 

impactor stage, weighted by the respirable fraction associated 

with each size. Although an improvement, this method is still an 

indirect calculation of ISO concentrations with the assumption 

that the [1.7 DO] is a close approximation to the ISO definition. 

Table 1 Regression results for cyclone comparison 

Statistic Value 95% CI 

[2.0 DO]BMRC designated predictor variable 

Intercept y0/mg m-3 -0.006 

Sintercept 0.002 

tintercept -3.83 

Slope a 0.828 

Sslope 0.008 

y0 removed

Slope a 0.815 (0.804, 0.826) 

Sslope 0.006 

tslope (wrt 0.857) -7.48 

tcritical(0.05) 1.98 

0s/mg m-3 0.008 

d 0.00187 

s1 1⁄4 Od 0.043 

CV 1⁄4 s1/a 5.3% 

N 131 

5. Conclusions

The work presented in this paper focuses on providing a more 

accurate conversion multiplier than previously reported in the 

literature, using an independent direct comparison of the 2.0 L 

min-1 Dorr-Oliver cyclone (BMRC equivalent) and the 1.7 L 

min-1 Dorr-Oliver cyclone. The sampler data were obtained in 

131 underground coal mines and proportionately distributed to 

be representative of the entire U.S. underground coal mining 

industry. The revised conversion multiplier of 0.815 (95% C.I. 1⁄4

[0.804, 0.824) is statistically different from the value of 0.857 

previously reported by NIOSH. Although the change is not 

large, conversion using the previous value of 0.857 would overestimate the respirable concentration by about 5%. For example, 

at [2.0 DO]BMRC 1⁄4 2.0 mg m-3 the ISO equivalent would be 
1.71 mg m-3 using 0.857, compared to 1.63 mg m-3 using the 

revised multiplier. 

Because of the industry-representative database and derivation of the conversion multiplier without use of the potentially 

biased Marple cascade impactor, the present result is considered 

to be more reliable. Therefore, historical U.S. coal mine respirable dust exposure data can be more accurately converted to 

near-ISO equivalency, as estimated by the 1.7 L min-1 DorrOliver cyclone. 

The Marple cascade impactor is used in many different 

industrial hygiene applications outside of mining and it has 

generally been accepted that data obtained with this impactor is 

more or less reliable. The current work is the first evidence 

known to the authors suggesting this may not be the case by 

demonstrating impactor negative bias which increases with 

increasing mass concentration. The source of the suggested bias 

is currently being investigated. 

The current work presents a statistically valid analytical 

method of sampler comparison which is beyond ordinary 

regression and is not limited only to dust samplers. This is 

particularly true when data exhibit constant coefficient of variation with an inherent constant variance term at small values of 

either variable. The analytical method also provides the means to 

estimate the coefficient of variation of the data about the 

regression function. 

5. Disclaimer

The findings and conclusions in this report are those of the 

authors and do not necessarily represent the views of the 

National Institute for Occupational Safety and Health. Mention 

of any company or product does not constitute endorsement by 

National Institute for Occupational Safety and Health. 

Appendix A

Table 2 Underground cyclone data 

MSHA district Field office 

mg m -3 

[2.0 DO]BMRC [1.7 DO] 

6 

4 

7 

6 

6 

5 

6 

6 

4 

5 

5 

2 

6 

4 

2 

9 

5 

2 

5 

2 

9 

9 

Whitesburg, KY 

Pineville, WV 

Barbourville, KY 

Whitesburg, KY 

Elkhorn City, KY 

Norton, VA 

Elkhorn City, KY 

Pikeville, KY 

Logan, WV 

Norton, VA 

Norton, VA 

Indiana, PA 

Martin, KY 

Pineville, WV 

Kittanning, PA 

Delta, CO 

Norton, VA 

Ruff Creek, PA 

Norton, VA 

Kittanning, PA 

Craig, CO 

Castle Dale, UT 

0.047 

0.055 

0.048 

0.063 

0.097 

0.078 

0.114 

0.088 

0.088 

0.124 

0.065 

0.109 

0.098 

0.209 

0.104 

0.129 

— 

0.132 

0.112 

0.113 

0.220 

0.205 

0.029 

0.028 

0.032 

0.052 

0.073 

0.068 

0.085 

0.048 

0.075 

0.085 

0.059 

0.060 

0.073 

0.161 

0.100 

0.114 

0.086 

0.121 

0.083 

0.083 

0.159 

0.154 

Table 2 (Contd.) 

MSHA district Field office 

mg m -3 

[2.0 DO]BMRC [1.7 DO] 

4 

11 

5 

4 

2 

8 

7 

2 

8 

9 

11 

2 

10 

9 

4 

4 

4 

6 

2 

3 

8 

11 

3 

5 

6 

8 

8 

4 

4 

4 

7 

3 

7 

10 

6 

7 

6 

4 

5 

7 

6 

5 

8 

4 

3 

9 

4 

2 

7 

10 

6 

4 

5 

2 

8 

4 

2 

6 

11 

3 

9 

5 

6 

8 

9 

10 

9 

4 

6 

Princeton, WV 

Hueytown, AL 

Norton, VA 

Logan, WV 

Ruff Creek, PA 

Benton, IL 

Jacksboro, TN 

Kittanning, PA 

Hillsboro, IL 

Castle Dale, UT 

Hueytown, AL 

Ruff Creek, PA 

Beaver Dam, KY 

Craig, CO 

Logan, WV 

Madison, WV 

Pineville, WV 

Whitesburg, KY 

Johnstown, PA 

Morgantown, WV 

Benton, IL 

Hueytown, AL 

Morgantown, WV 

Norton, VA 

Pikeville, KY 

Hillsboro, IL 

Vincennes, IN 

Madison, WV 

Logan, WV 

Madison, WV 

Hindman, KY 

St. Clairsville, OH 

Harlan, KY 

Madisonville, KY 

Martin, KY 

Hazard, KY 

Martin, KY 

Madison, WV 

Vansant, VA 

Hindman, KY 

Phelps, KY 

Vansant, VA 

Benton, IL 

Logan, WV 

Morgantown, WV 

Delta, CO 

Madison, WV 

Ruff Creek, PA 

Barbourville, KY 

Beaver Dam, KY 

Pikeville, KY 

Pineville, WV 

Norton, VA 

Kittanning, PA 

Hillsboro, IL 

Pineville, WV 

Johnstown, PA 

Phelps, KY 

Hueytown, AL 

Bridgeport, WV 

Delta, CO 

Norton, VA 

Phelps, KY 

Vincennes, IN 

Craig, CO 

Beaver Dam, KY 

Price, UT 

Mt. Carbon, WV 

Whitesburg, KY 

0.160 

0.208 

0.149 

0.224 

0.257 

0.282 

0.195 

0.180 

0.276 

0.301 

0.331 

0.220 

0.308 

0.246 

0.262 

0.244 

0.233 

0.295 

0.246 

0.387 

0.441 

0.408 

0.303 

0.415 

0.352 

0.346 

0.390 

0.404 

0.368 

0.369 

0.354 

0.429 

0.392 

0.546 

— 

0.459 

0.482 

0.558 

0.612 

0.543 

0.520 

0.503 

0.587 

0.434 

0.599 

0.614 

0.595 

0.588 

0.644 

0.565 

0.601 

1.370 

0.612 

0.600 

0.819 

0.689 

0.533 

0.650 

0.875 

0.888 

0.965 

0.717 

0.703 

0.841 

0.805 

1.046 

1.156 

1.070 

0.822 

— 

0.161 

0.125 

0.168 

0.201 

0.188 

0.154 

0.164 

0.198 

0.235 

0.276 

0.194 

0.234 

0.201 

0.223 

0.232 

0.216 

0.216 

0.225 

0.318 

0.320 

0.325 

0.264 

0.322 

0.282 

0.344 

0.314 

0.325 

0.308 

0.303 

0.373 

0.366 

0.279 

0.453 

0.327 

0.394 

0.378 

0.475 

0.441 

— 

0.403 

0.463 

0.469 

— 

0.458 

0.480 

0.452 

0.518 

0.523 

0.458 

0.500 

1.061 

0.468 

0.504 

0.581 

0.570 

0.466 

0.542 

0.741 

0.760 

0.825 

0.578 

0.626 

0.661 

0.703 

0.778 

0.907 

0.800 

0.661 
Table 2 (Contd.) 

MSHA district Field office 

mg m -3 

[2.0 DO]BMRC [1.7 DO] 

3 Morgantown, WV 0.872 0.790 

4 Mt. Hope, WV 1.076 0.881 

9 Price, UT 1.059 0.856 

6 Pikeville, KY 1.035 0.999 

7 Barbourville, KY 1.203 0.993 

7 Jacksboro, TN 1.100 0.939 

7 Harlan, KY 1.280 0.982 

7 Jacksboro, TN 1.255 0.999 

3 Bridgeport, WV 1.271 1.001 

10 Madisonville, KY 1.528 1.257 

10 Madisonville, KY 1.435 1.217 

4 Logan, WV 1.473 1.164 

4 Madison, WV 1.607 1.279 

7 Harlan, KY 1.491 1.187 

6 Whitesburg, KY 1.301 1.058 

6 Martin, KY 1.428 1.129 

3 Morgantown, WV 1.420 1.184 

4 Madison, WV 1.680 1.437 

5 Norton, VA 1.291 1.165 

6 Phelps, KY 1.445 1.248 

8 Vincennes, IN 1.930 1.472 

4 Logan, WV 1.705 1.281 

3 Oakland, MD 1.956 1.585 

5 Vansant, VA 1.746 1.410 

6 Elkhorn City, KY 1.681 1.461 

6 Pikeville, KY 1.455 1.153 

4 Mt. Hope, WV 1.543 1.311 

7 Harlan, KY 1.586 1.307 

5 Norton, VA 1.680 1.473 

8 Vincennes, IN — 1.507 

7 Jacksboro, TN 1.700 1.392 

7 Hazard, KY 2.074 1.692 

7 Harlan, KY 1.496 1.026 

7 Barbourville, KY 1.697 1.409 

4 Mt. Hope, WV 1.993 1.519 

7 Barbourville, KY 1.616 1.360 

7 Harlan, KY 2.012 1.627 

7 Hindman, KY 2.702 2.318 

7 Hindman, KY — 1.219 

6 Martin, KY 2.250 1.869 

4 Mt. Carbon, WV 2.020 1.645 

6 Pikeville, KY 2.666 2.115 

4 Pineville, WV 2.715 2.105 

4 Logan, WV 2.550 2.185 

References

1 http://www.msha.gov/REGS/ACT/ACT2.HTM#7. 

2 British Medical Research Council, ‘‘Recommendations of the MRC 

Panels Relating to Selective Sampling,’’ Inhaled Particles and

Vapours, Pergamon Press, Oxford, 1961. 

3 T. F. Tomb, H. N. Treaftis, R. L. Mundell and P. S. Parobeck, 

Comparison of Respirable Dust Concentrations Measured with MRE

and Modified Personal Gravimetric Sampling Equipment, U.S. 

Department of Interior, Bureau of Mines, RI 7772, 1973. 

4 S. C. Soderholm, Ann. Occup. Hyg., 1989, 33, 301–320. 

5 International Standards Organization, Air Quality-Particle Size

Fraction Definitions for Health-Related Sampling, Standard 7708, 

Geneva, Switzerland, 1995. 

6 CEN EN 481 Standard on Workplace Atmospheres. Size Fraction

Definitions for the Measurement of Airborne Particles in the

Workplace, Brussels, 1993. 

7		ASTM D 6062M Standard Guide for Personal Samplers of HealthRelated Aerosol Fractions, ASTM International, West 

Conshohocken, 2007. 

8 ACGIH, Threshold Limit Valuesfor Chemical Substances and Physical

Agents & Biological Exposure Indices, Cincinnati, 2007. 

9 D. L. Bartley, C. Chen, R. Song and T. J. Fischbach, Am. Ind. Hyg.

Assoc. J., 1994, 55, 1036–1046. 

10 A. D. Maynard, J. Aerosol Sci., 1993, (Suppl 1), S457–S458. 

11 G. Lideen and L. C. Kenny, Appl. Occup. Environ. Hyg., 1993, 8, 386–391. 

12 A. Gudmunsson and G. Lideen, AerosolSci. andTechn., 1998, 28, 197–214. 

13 NIOSH, Criteria for a Recommended Standard-Occupational Exposure

to Respirable Coal Mine Dust, US Department of Health and Human 

Services, Public Health Services, Centers for Disease Control, 

National Institute for Occupational Safety and Health, 1995, pp. 77–79. 

14 P. Hewett, 1993, Internal memorandum dated March 25, 1993. US 

Department of Health and Human Services, Public Health Services, 

Centers for Disease Control, National Institute for Occupational 

Safety and Health. Available upon request. 

15 J. C. Volkwein and E. D. Thimons, Proceedings of VIIth International

Ventilation Symposium, Kracow, 2001. 

16 J. C. Volkwein, R. P. Vinson, S. J. Page, G. J. Joy, S. E. Mischler, 

D. P. Tuchman and L. J. McWilliams. Laboratory and Field

Performance of a Personal Dust Monitor, US Department of Health 

and Human Services, Public Health Services, Centers for Disease 

Control, National Institute for Occupational Safety and Health, 

Report RI 9669, 2006. 

17 S. J. Page, J. C. Volkwein, R. P. Vinson, G. J. Joy, S. Mischler, 

D. P. Tuchman and L. J. McWilliams, J. Environ. Monit., 2008, 10, 

96–101. 

18 M. W. Blachman and M. Lippmann, Am. Ind. Hyg. Assoc. J., 1974, 

35, 311–326. 

19 V. A. Marple, K. L. Rubow and B. A. Olson, in Aerosol Measurement, 

eds. Willeke and Baron, Van Nostrand Reinhold, NY, 1993, ch.11, 

pp. 206–232. 
A Revised Conversion Factor Relating Respirable Dust Concentrations Measured 

by 10 mm Dorr-Oliver Nylon Cyclones Operated at 1.7 and 2.0 L min-1 

Appendix B 

B-1 General analytical model 

As a result of multiplicative errors arising from various errors associated with the personal samplerB1, 

the total sum of squares in regression analysis will primarily be influenced by the large dependent 

variable values and lead to an analysis bias. This situation is typical of data collected with dust 

sampling instrumentationB1, and there are several different remedial data transformations available to 

eliminate, or at least minimize, the non-constant variance problem. 

Weighted regression was the method of choice previously reportedB2 to stabilize the variance for data 

analysis according to the model 

Eq.B-1 Y = g(X)ε1 + 0ε0, 

where 

Y = a response variable, 

g(X) = aX, and 

a = regression slope, assuming zero (statistically insignificant or unmeasurable) intercept. 

The only requirement in Eq. B-1 is that g(X) be a smooth, arbitrary function of the predictor variable 

(X). Intuitively, one would expect, in the absence of measurement bias, a linear and monotonic 

relationship (ideally with zero intercept and unity slope) between different instruments designed and 

developed to measure the same true but unknown quantity. 

Weighted regression can directly stabilize the variance if the variance function can be estimated. 

Typical 1/X 2 weighting assumes that the dependent variable variance increases proportionally with 

X 2

 over the entire range of independent variable, resulting in constant coefficient of variation (CV). 

However, at low concentration values there is the limiting error term (0ε0) due to weighing 

imprecision. 

B-2 Weight variable estimation 

The constant variance (0σ)

2 of 0ε0 can usually be determined with sufficient accuracy. It can readily 

be shown by calculating Var(Y), using the method of expectation values, that the proper weight 

variable is the reciprocal of the total variance σ 2

Τ , given by 
Eq. B-2 σ 2 

Τ = (0σ)

2 + [(g(X)CV]2

, 

 = ( σ)

2 + ( )2

0 aCV X 2

, 

where 

From Eq. B-2, CV can be considered to be the variation of the dependent variable about the 

regression line. 

The process for estimating the proper weight variable is iterative, using the following procedure for 

estimating the relationship between the dependent variable variance and the independent variable: 

Step 1: An initial regression of Eq. B-1 using 1/X 2 weighting is performed to establish initial weight 

variables, where g(X) = aX + Y0. 

Step 2: Using the definition of variance, the values (Yi – Y 2

ip) , representing the variance between the 

measured Yi and predicted Yip from the initial regression of step 1, are calculated. 

Step 3: The plot of (Yi – Yip)

2

 vs. Xi is fit with the function of Eq. B-2, represented by the model 

Eq. B-3 (Y – Yip)

2

c

2

i = + dX 2 

 

using 1/X 2 weighting. The second weight estimation is then approximated point-by-point as 1/σ 2

Τ . 

Step 4: A weighted regression is next performed with the new weight variable. 

Steps 2-4 are then repeated with each new estimate of weight variable and (Yi – Yip)

2 until 

convergence to a solution. If intercept Y0 is shown to be irrelevant due to statistical insignificance, 

being an unmeasurable quantity, or some other justification, steps 1-4 are repeated with Y0 = 0. 
 

 

 

References 

B1 NIOSH, The Precision of Coal Mine Dust Sampling. US Department of Health and Human 

Services, Public Health Services, Centers for Disease Control, National Institute for Occupational 

Safety and Health, NTIS Pub. No. PB85220721, 1984. 

B2 S. J. Page, J.C. Volkwein, R. P. Vinson, G. J. Joy, S. Mischler, D. P. Tuchman, L. J. McWilliams, 

J Environ. Monit. 2008, 10, 96-101.