Equivalency of a personal dust monitor to the current United States coal

mine respirable dust sampler

Steven J. Page, Jon C. Volkwein, Robert P. Vinson, Gerald J. Joy,

Steven E. Mischler, Donald P. Tuchman and Linda J. McWilliams

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

The United States National Institute for Occupational Safety and Health, through an informal

partnership with industry, labor, and the United States Mine Safety and Health Administration,

has developed and tested a new instrument known as the Personal Dust Monitor (PDM). The

new dust monitor is an integral part of the cap lamp that coal miners normally carry to work and

provides continuous information about the concentration of respirable coal mine dust within the

breathing zone of that individual. Previous laboratory testing demonstrated that there is a 95%

confidence that greater than 95% of individual PDM measurements fall within ± 25% of

reference measurements. The work presented in this paper focuses on the relationship between the

PDM and respirable dust concentrations currently measured by a coal mine dust personal

sampler unit utilizing a 10 mm Dorr Oliver nylon cyclone. The United Kingdom Mining

Research Establishment instrument, used as the basis for coal mine respirable dust standards, had

been designed specifically to match the United Kingdom British Medical Research Council

(BMRC) criterion. The personal sampler is used with a 1.38 multiplier to convert readings to the

BMRC criterion. A stratified random sampling design incorporating a proportionate allocation

strategy was used to select a sample of mechanized mining units representative of all US

underground coal mines. A sample of 180 mechanized mining units was chosen, representing

approximately 20% of the mechanized mining units in production at the time the sample was

selected. A total of 129 valid PDM/personal sampler dust sample sets were obtained. A weighted

linear regression analysis of this data base shows that, in comparison with the personal sampler,

the PDM requires a mass equivalency conversion multiplier of 1.05 [95% C.I. (1.03, 1.08)]

when the small intercept term is removed from the analysis. Removal of the intercept term

results in a personal sampler equivalent concentration increase of 2.9% at a PDM measurement

of 2.0 mg m-3

.

1. Introduction

Measurement of workplace respirable dust concentration is an

essential first step in eliminating lung disease caused by over

exposure to dust. In the United States (US), The Federal Coal

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

Federal Mine Safety and Health Act of 1977,1 mandates that

respirable coal mine dust levels be monitored and controlled to

a maximum of 2 -3 mg m or below for a working shift,

provided quartz levels remain at or below 5%. To date, this

monitoring process has relied upon a coal mine dust personal

sampler unit (hereafter referred to as personal sampler or

CMDPSU in figures and tables) utilizing a pre weighed

5 mm pore polyvinyl chloride (PVC) filter, preceded by a

10 mm Dorr Oliver nylon cyclone, operated at a flow rate

of 2.0 L min-1 to collect a sample in the mine environment.

The personal sampler historically includes an empirically de 2 rived 1.38 multiplier to convert readings to the United King

dom British Medical Research Council (BMRC) criterion.3

In consultation with labor, industry, and government, the US

National Institute for Occupational Safety and Health (NIOSH)

issued a contract to Rupprecht and Patashnick Co., Inc. (now

Thermo Fisher Scientific Corporation), Albany, NY, USA,

(CDC Contract 200 98 8004) to develop a Personal Dust Moni

tor (PDM). The PDM is based on existing environmental

ambient air monitoring instruments, the latter of which has

achieved global acceptance for use in air quality monitoring

networks. The key feature of this monitor is that it directly

measures the mass of dust on a filter, regardless of dust

composition, size, or physical characteristics. This contract work

successfully miniaturized the air quality monitor’s sensor and

incorporated the sensor into a prototype, person wearable dust

monitor that provides accurate end of shift respirable dust con

centration data to miners.4 Through a protocol developed by a

partnership of labor, government and industry, previous work5

verified that the PDM laboratory accuracy met the NIOSH
criterion.6 This report describes the underground full shift per

formance of the PDM compared to the personal sampler.

2. Methods

2.1 Criteria for mine selection

A stratified random sampling design was used to select me

chanized mining units that were representative of all US

underground coal mines. The sampling base was developed

using information extracted from the US Mine Safety and

Health Administration (MSHA) Standardized Information

System and reflected 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 type (MSHA bituminous coal district) and

mining method (potentially related to size distribution) of the

dust in underground coal mines. Because of the mine selection

process, any mine dust size distribution effects are accounted

for, on average, in the data analyses. Of the total mechanized

mining unit population, only a small percentage employed

longwall and other (e.g., scoop) mining methods (6% and

3.5%, respectively), with the balance being continuous mining

sections. A proportionate allocation strategy with different

sampling rates among the strata was used to ensure that the

composition of the sampled mechanized mining units was

approximately representative of the composition of the popu

lation. 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, USA).

2.2 Testing procedures

Planning and implementation of this segment of the testing

was performed by NIOSH, in close cooperation with MSHA

headquarters, district offices, and field offices. A sampling

schedule was developed after the list of candidate mines and

mechanized mining units was compiled. This schedule also

introduced a degree of randomness in that, whenever possible,

certain selected mines from different MSHA field offices and/

or districts were combined into one trip. The mine sampling

was conducted from October, 2004 through August, 2005.

Each sampling package contained (1) a PDM, pre pro

grammed to begin an 8 h sample at the selected mine’s shift

start time and operating at 2.2 L min-1

; (2) two dust samplers

using Dorr Oliver -1 cyclones, one operating at 2.0 L min and

the other at 1.7 L min-1

; and (3) a Marple cascade impactor

operating at 2.0 L min-1

. The Marple impactor is a miniatur

ized eight stage cascade impactor intended to provide particle

size distributions of sampled aerosol and sufficiently small as

to be wearable as a personal sampler. The cyclones, impactor,

and the PDM sampling inlet were mounted inside a specially

constructed Lippmann sampling 7,8 canister with a single inlet.

This procedure ensured that all samplers were exposed to the

same atmospheric conditions. Flow controlled Mine Safety

Appliances Escort s Elf pumps were calibrated to 2.0

 

±

0.02 L min-1 and 1.7 ± 0.017 L min-1 for the cyclone samplers

prior to each trip using a Gilibrator (Sensidyne Inc., Clear

water, FL, USA) primary standard flow meter. An equivalent

pressure restriction for the respective samplers was used dur

ing pump calibration. Flow rates for all samplers were checked

prior to each trip and post checked for proper calibration to

±1%. The post check calibration also served as pre calibra

tion for the following trip. Sampling locations were chosen

where miners typically worked. Data for the cascade impactor

and 1.7 L min-1 Dorr Oliver sampler will not be included in

this report because they are not pertinent to the present

objective. Analysis of those samplers will be the focus of a

future publication.

The PDM was pre programmed to automatically begin

sampling at the pre determined shift start time and turn off

eight hours later. Gravimetric samplers were manually started

and stopped within 3 min of the PDM start/stop times. In the

event that the PDM display indicated a projected end of shift

concentration of 1.5 mg m-3 or greater at any time during the

sampling period, a HEPA filter was placed into the inlet of the

Lippmann canister and all samplers finished running the 8 h

period without collection of additional airborne dust into the

canister. The purpose of the 1.5 mg m-3 concentration limit

was to minimize the possibility of overloading the impactor.

2.3 Samplers

2.3.1 PDM. The PDM4,5 is a pre commercial (not for

general sale) model 3600 PDM using a tapered element

oscillating microbalance (TEOMs) mass sensor. The PDM

s uses Teflon coated fiberglass (nominal 15 mm diameter)

filter media TX40H120WW, (Pallflex Products Corp.,

Putnam, CT, USA) manufactured into special plastic holders

that mount on the end of a vibrating hollow tapered element.

The device is intended to be virtually ‘‘invisible’’ to the miner,

as a replacement for the cap lamp and battery currently

employed in mines. Fig. 1(a) illustrates the PDM device with

accompanying charger/PC interface docking station. The

docking station is used to simultaneously communicate with

PC software for programming and retrieving stored data in the

instrument and to recharge its batteries for the next work shift.

Fig. 1(b) shows the PDM components. The enclosure of the

PDM is hardened to withstand the harsh conditions found in

the mine environment, with the system designed to meet

MSHA drop test requirements for cap lamps,9 as well as

intrinsic safety approval requirements.10 An illuminated data

display on the top of the PDM continuously shows the dust

concentration for the previous 30 min, cumulative mass con

centration to that point in the shift, and a projected end of

shift concentration. A full description of the PDM system

configuration, air flow path, flow measurement and control,

battery configuration, data acquisition, and mass measure

ment technique has been previously described5,11 and will not

be presented here. Additionally, extensive laboratory and

replicate sampling data from ten underground coal mines to

establish the accuracy and precision of the PDM have been

previously reported.5

The PDM instrument samples, analyzes, and calculates

mass based concentrations of respirable dust. It is acknowl

edged that there may be some negative bias (defined as

[measured concentration C true concentration] 1) in the
 

 

 

use of the PDM associated with particle losses that take place

in the sampling path between the cyclone exit and the sensing

zone of the instrument. This may be corrected empirically by

reference to experimental data in specific situations. Prior 5 testing of the pre commercial PDM instrument found that

the PDM consistently underestimated mass, based on com

parison to reference mass samples using identical inlet config

urations and Higgins Dewell cyclones. Established scientific

protocol requires measurement correction for systematic error

(bias) prior to analysis. Therefore, these systematic measure

ment errors were used to calculate an average bias correction

factor prior to regression analysis.12,13

Additionally, prior work has documented that the PDM

filter has a characteristic average positive thermally induced

filter bias during an 8 h sampling period. This value was

determined by random filter selection from various filter lots 14 and is due to heating effects acting on the filter. The data of

this work were also corrected for this bias, prior to regression

analysis. While this filter induced bias is trivial for an indivi

dual measurement, it is significant when many low mass

measurements are combined in the regression analysis.

Fig. 1 (a) Pre commercial PDM connected to docking station used

for charging and communication with a PC using an RS 232 interface.

(b) PDM internal components.

2.3.2 Cyclone gravimetric reference. Each sampler

consisted of a Mine Safety Appliances 37 mm diameter, pre

weighed 5 mm pore PVC filter, preceded by a 10 mm Dorr

Oliver nylon cyclone.

2.4 Analytical gravimetric imprecision

Gravimetric analysis was performed on a Mettler Toledo

UMT2 microbalance for the personal sampler samples.

Weighing was done in the NIOSH Pittsburgh Research

Laboratory at 22.8 + 0.4 1C (73 ± 0.7 1F) and 53 ± 2%

RH. All samples were pre and post weighed, employing

control filters. Two filter cassettes were used as controls for

the personal sampler. Average blank control filter masses were

used to correct the filter mass results for each test. Because

sampling packages were deployed to numerous mines simul

taneously, the control filters could not accompany the sam

pling packages to the mines. However, this is considered a

minor factor compared to differences in weighing room con

ditions between pre and post weighings. All sample and

control filters were desiccated and allowed to equilibrate to

room conditions. However, small cyclical fluctuations in room

conditions are not totally corrected by the control filters

because: (1) the control filters cannot be weighed at the same

moment as the sample filters, and (2) the pre and post

weighings are not performed at the same time in relation to

the cyclic variation of the room conditions. Since the pre and

post weighings are not time correlated with the cyclic varia

tion, there is an uncorrectable, but minor, random variation.

Therefore, several estimates for the weighing imprecision will

be provided.

2.5 Analysis

Weighted regression is the method of choice to stabilize the

variance for data analysis by estimating the relationship

between the variance and the independent variable. Appendix

Aw describes the mathematical representation and weight

variable estimation. It should be noted that, since the overall

purpose is to predict contaminant concentration from an

imprecise measurement in the PDM, there is no need to

specifically consider random measurement error in the pre

dictor variable. Additionally, it can be demonstrated that the

random error in the PDM can be classified as one of the

embodiments of the Berkson case. The Berkson case describes

several classes of measurement procedure in which random

error in the predictor variable has no effect on the regression

analysis. Weighted regression was performed using Sigma

Plot v.9.0.15

3. Results

3.1 PDM bias correction

A bias correction factor for internal dust loss within the PDM

was estimated 5 from previous empirical work. A negative bias

of 6.6% for laboratory data from instrument testing was

calculated. This bias correction is not applied to the tabular

data of Tables B 1 and B 2 in Appendix B.w However, all

subsequent data analysis will include this PDM bias correction

as well as the thermal zero drift bias correction of 25.5 mg -3 (0.024 mg m for an 8 h sample).14

3.2 Gravimetric limit of quantification

Determination of the traditional limit of quantification 6 (LOQ) requires determining the standard deviation (SW) in

nine consecutive weighings of a blank filter. It was determined

that SW 1.4 mg and LOQ 14 mg in a single weighing.

However, quality control procedures involving control room
 

 

 

 

 

 

 

 

 

 

 

filters used only in the balance room document that the total

standard deviation (ST) due to (SW) and the cyclic fluctuations

in weigh room conditions during the course of this study was

ST 4.1 mg. Applying traditional formulae for propagation of

error in the personal sampler filter dust mass gains (including

an average of 2 control filters) yields Sfilter 1.8478xST

7.6 mg. For an 8 h sample, this value corresponds to 0s

0.011 mg m-3

, suggesting an LOQ 0.11 mg m-3 for the

personal sampler.

3.3 In-mine testing results

Table B 1w lists all data included in the analysis, sorted in

order of increasing PDM measurements. Of 180 total pro

jected samples, 129 valid PDM/personal sampler pairs were

collected. Although the number of valid samples obtained was

less than the target value, the actual sample data base obtained

was closely proportional to the original mine distribution by

district. Table B 2w lists 9 entire data sets excluded for

technical or procedural errors. It is again noted that the

PDM values in Tables B 1 and B 2w do not include any bias

corrections.

3.4 Data analysis

3.4.1 Weight variable estimation. Analysis of the raw mine

 5 replicate sampling data of Volkwein et al. show that the

relative standard deviation (RSD) of the different samplers

can be generally described by the equation

RSD = 1 3 x 3 2 RSD0 A(mg m ) Xsampler(mg m ) (R o 0.1), (1)

with slopes (A) typically less than 0.05 in magnitude. The RSD

 2 is also called the coefficient of variation (CV). The low R and

the small slope of the data demonstrate general independence

of the RSD on sampler concentrations above Xmin E 0.3 mg -3 m . Constant RSD necessarily implies variance increasing

with the square of the mean. Given this relationship, a partial

weighting factor to correct the regression for the increasing

variance is (1/X2

). It should be noted that the magnitude of the

intercept constant (RSD0) in eqn (1) is not important in

establishing the weighting factor for two reasons. First, the

only statistical requirement is proportionality between stan

dard deviation and mean. Second, the intercept term incor

rectly implies constant RSD as the concentration approaches

zero.

The small negative slope indicates the presence of a constant

variance term becoming more prominent at sampler concen

trations less than 0.3 mg m-3

. Iteration of eqn (A 3) (see

Appendix A),w (0s)

2 with fixed by weighing imprecision,

converged quickly to a solution within 4 iterations, yielding.

s 2 3 2 2 T (0.011 mg m- ) + 0.0155X . (2)

3.4.2 Weighted regression. Fig. 2 shows the scatter plot

relationship between the personal sampler and the PDM. The

iterated weighted regression without the y intercept term is

included. In general, the data clearly indicate a linear relation

ship with multiplicative errors between the two instruments.

Regression weight variable estimates were obtained using

eqn (2).

 

 

 

 

Fig. 2 CMDPSU data plot with PDM bias corrections. CMDPSU

data incorporate 1.38 multiplier historically used to estimate BMRC/

MRE equivalency. Weighted regression statistics are presented in

Table 1.

Table 1 shows the regression statistics for analyses with and

without the intercept term. Although it is not quantifiable, the

y intercept 0.018 mg m-3 term is statistically significant at

the 0.05 significance level (tintercept 4.35 4 tcritical 1.98).

Removal from the regression can have a significant effect on

the slope and the calculation of respirable dust concentration.

For comparison, regression without the intercept yields

slope 1.05 [95% C.I. (1.03, 1.08)]. Because tslope

3.82, the hypothesis [slope 1.00] is rejected and the PDM

would use a 1.05 conversion factor to be an equivalent

measure of the personal sampler.

 

 

 

 

 

 

 

 

 

 

 

Table 1 CMDPSU (with 1.38 conversion factor) vs. PDM. Weighted

regression results on bias corrected PDM data

Statistic Value 95% C.I. 90% C.I.

PDM designated predictor (independent) variable

Intercept y0/mg m 3 0.018 (0.010, 0.026) (0.011, 0.025)

Sintercept 0.004

tintercept 4.35

Slope 1.01 (0.98, 1.04) (0.98, 1.04)

Sslope 0.017

tslope(wrt 1.0) 0.52

y0 removed

Slope 1.05 (1.03, 1.08) (1.03, 1.08)

Sslope 0.014

tslope(wrt 1.0) 3.82

Regression 0s/mg m 3 0.011

Regression CV 12.4%

tcritical(.05) 1.98

tcritical(.10) 1.66

N 129

3.4.3 Consideration of regression intercept terms. Ideally, in

the absence of bias one would expect both instruments to read

zero or to average zero for a very large data set when no dust is

present. When this does not occur, there are several different

schools of thought regarding treatment of an intercept term.

One philosophy is that, in many cases, the intercept is not

considered meaningful for two reasons. First, the intercept is

usually beyond the range of the data and assigning any
significance to an extrapolation beyond the data is suspect.

Second, the intercept can be highly influenced by error in

herent in the data. Therefore, a case could be made for simply

ignoring an unmeasurable intercept.

Another school of thought is that in a regression, the

intercept and slope are correlated. If, in particular, the inter

cept term is not statistically significant, it offers no useful

information and should be removed from a subsequent regres

sion. The issue is not quite so clear cut when the intercept is

statistically significant but unmeasurable. In this case, per

forming the regression without the intercept may have a

significant effect on the slope parameter, depending on the

level of significance associated with the intercept. Because

consideration of the intercept term is often an end user

decision, the analysis is presented with and without the inter

cept term in the regression.

Additional insight regarding the intercept term can be

obtained using independent data obtained by Volkwein 5 et al. This independent data set was obtained in the same

manner as the present data, with the exception that, although

data was collected in every mining district, the mines were not

selected in a proportional manner. Even though this propor

tionality is a very important consideration, the independent

data is useful. The weighted linear regression result was a

statistically significant intercept of 0.020 and slope of 1.05.

Given that the present work has an intercept of +0.018, it

could reasonably be inferred that the intercept terms are

merely a result of error inherent in the data and should be

removed from the regression. Removal of the intercept term in

the independent data results in a slope of 1.02. Although this is

slightly outside the present confidence interval (1.03, 1.08), the

difference is somewhat exaggerated by rounding error (1.024

vs. 1.026). In any case, being somewhat conservative would be

preferable to basing the health of miners on a statistical

consideration. This would provide justification for not includ

ing the intercept term in the regression.

4. Conclusions

An accurate, direct reading dust monitor for use in coal mines

has been demonstrated in underground coal mine environ

ments. In the current, as tested, PDM configuration and

calibration, weighted regression analysis indicates that a linear

relationship between the PDM and the personal sampler can

be established. The conversion factors are applicable only after

applying the PDM internal dust loss and filter thermal bias

corrections to the raw PDM measurements for an 8 h sampling

period. However, it is noted that the filter thermal bias

correction is negligible at most respirable dust concentrations

of interest, being only 2.4% at a concentration of 1.0 mg m-3

.

It is recommended that the manufacturer document and

implement the measured bias corrections to the mass concen

tration calculations of the PDM instrument.

The results indicate the suitability of the PDM for in mine

use to assess respirable dust concentrations defined in accor

dance with the currently used personal sampler. This fact,

together with the advantages of a direct reading end of shift

instrument, provides strong justification for adoption of the

PDM as a primary in mine sampling device.

In comparison to the personal sampler, the PDM would

require a mass concentration equivalency conversion multi

plier of 1.05 [95% C.I. (1.03, 1.08)] when the small intercept

term is removed from the analysis. Removal of the intercept

term results in a personal sampler equivalent concentration

increase of 2.9% at a PDM measurement of 2.0 mg m-3

.

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

the National Institute for Occupational Safety and Health.

Acknowledgements

The authors thank and acknowledge the support and technical

advice given by members of the PDM partnership, namely,

Dennis O’Dell of The United Mine Workers of America, Joe

Lamonica of the Bituminous Coal Operators and Bruce

Watzman of the National Mining Association. Additionally,

we would like to thank David Bartley, visiting scientist,

NIOSH, for his technical expertise and support during the

course of data analysis. We also thank MSHA for its active

support and participation in the collaborative research effort

by purchasing units for testing and collecting vital test data at

144 mechanized mining units around the country. We appreci

ate the generous engineering support provided by Erich Rup

precht, Business Development Manager and Dan Dunham,

PDM project manager, from Thermo Fisher Scientific Corp.

Finally, we thank the Pittsburgh Research Laboratory staff,

Cal Garbowsky, Shawn Vanderslice, Jeanne Zimmer, Erica

Hall, Randy Reed and Tom Mal for conscientious support in

managing the logistics of the equipment for the mine tests.

References

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

2 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, 28pp.

3 A. J. Orenstein, Proceedings of the Pneumoconiosis Conf., Johan

nesburg, 1960.

4 J. C. Volkwein, R. P. Vinson, L. J. McWilliams, D. P. Tuchman

and S. E. Mischler, Performance of a New Personal Respirable Dust

Monitor for Mine Use, US Department of Health and Human

Services, Public Health Services, Centers for Disease Control,

National Institute for Occupational Safety and Health, Report

RI 9663, 2004, 20pp.

5 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, 47pp.

6 E. R. Kennedy, T. J. Fischbach, R. Song, P. M. Eller and S. A.

Shulman, Guidelines For Air Sampling And Analytical Method

Development And Evaluation, US Department of Health and

Human Services, Public Health Services, Centers for Disease

Control, National Institute for Occupational Safety and Health,

Report 1995, pp. 95 117.

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

35, 311 326.
8 J. C. Volkwein and E. D. Thimons, Proceedings of VIIth Interna

tional Ventilation Symposium, Kracow, 2001.

9 US Code of Federal Regulations 30 CFR Part 19.

10 US Code of Federal Regulations 30 CFR Part 18.

11 Rupprecht & Patashnick Co., Inc., Operating Manual TEOM

Series 3600/3700 Personal Dust Monitor, Revision A, R&P Part

Number 42 009904, September 2004.

12 National Institute of Standards and Technology, http://www.

itl.nist.gov/div898/handbook/mpc/section6/mpc632.htm, 2006.

13 Intergovernmental Panel on Climate Change, http://www.grida.

no/climate/ipcc_tar/wg1/192.htm, 2006.

14 S. J. Page, D. P. Tuchman and R. P. Vinson, J. Environ. Monit.,

2007, 9, 760 767.

15 Systat Software, Inc. SigmaPlot v.9.0, Richmond, CA, USA.
Equivalency of a personal dust monitor to the current 

United States coal mine respirable dust sampler 

 

 

 

 

 

Appendix A 

Mathematical representation 

Comparison of the PDM to the personal sampler was made using regression analysis. The data 

indicate an error term increasing with the independent variable, or multiplicative error, in addition to 

the required constant additive error term. As a result, the total sum of squares will largely be 

influenced by the large dependent variable values and lead to an analysis bias. This situation is 

typical of data collected with dust sampling instrumentation1 and there are several different remedial 

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

The general equation used by Eagleson and Muller2

 to represent only multiplicative errors can be 

written as: 

Eq. A-1 Y = g(X)*(ε1). 

In the present analysis, 

Y = a personal sampler response variable, 

g(X) = some function of the PDM predictor variable (X), 

ε1 = a normally distributed random multiplicative error term, mean = 1 and variance resulting from 

in-canister spatial variation in the concentration, coupled with sampling and analytical error of the 

personal sampler. 

The only requirement is that g(x) be a smooth function. Eq. A-1 can also be expressed in terms of the 

usual error term ε0 with mean = 0, with inclusion of an additive error term, as 

Eq. A-2 Y = g(X)*(1+ε0) + 0ε0 = g(X) + g(X)*(ε0) + 0ε0,

where 

0ε0 = a normally distributed random additive error term with mean = 0 and constant variance (0σ)

2

, 

resulting from weighing imprecision as the true concentration approaches zero. 
A decision for g(X) representing the true underlying model for the data must be made. The model 

should agree with similar published data, previous experience, and be based on sound statistical 

arguments. Intuitively, one would expect, in the absence of measurement bias, a linear and 

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

designed and developed to measure the same true but unknown quantity. In this case, that quantity is 

the airborne respirable coal mine dust concentration. 

Weight variable estimation 

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

There are numerous weighting factors that can be used in regression analysis, the more common of 

which are (1/X) and (1/X2).3,4 The data of this investigation were used to internally estimate the 

variance relationship of the personal sampler with the independent PDM variable. Typical 1/X2 

weighting assumes that dependent variable variance increases proportionally with X2 over the entire 

range of independent variable. However, at low concentration values there is the limiting error term 

(0ε0) due to weighing imprecision. The constant variance (0σ)

2 of this error term is known quite 

accurately for the personal sampler samples and is presented in the Results section. It is readily seen 

that the proper weight variable is the reciprocal of the true total variance σΤ

2

, given by 

Eq. A-3 σΤ

2 ≈ (0σ)

2 + (RSD)2

*X2, 

where RSD can be considered to be the variation of the dependent variable about the regression. 

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

the personal sampler data: 

Step 1: An initial regression of Eq. A-2 using 1/X2 weighting is performed to establish initial weight 

variables, where g(X) = Y0 + a*X. 

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

2

, 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. A-3. The second weight estimation 

is then approximated point-by-point as 1/σΤ

2

. 

Step 4: Perform a weighted regression 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. 
Appendix B

Table B-1 Valid area sample raw data without PDM bias corrections -3 mg m 

MSHA Field Office PDM Void CMDPSU Void Notes District 

6 Whitesburg, KY 0.041 - 0.047 - 

4 Pineville, WV 0.050 - 0.055 - 

7 Barbourville, KY 0.050 - 0.048 - 

6 Whitesburg, KY 0.073 - 0.063 - 

6 Elkhorn City, KY 0.076 - 0.097 - 

5 Norton, VA 0.080 - 0.078 - 

6 Elkhorn City, KY 0.080 - 0.114 - 

6 Pikeville, KY 0.080 - 0.088 - 

4 Logan, WV 0.095 - 0.088 - 

5 Norton, VA 0.100 - 0.124 - 

5 Norton, VA 0.100 - 0.065 - 

2 Indiana, PA 0.115 - 0.109 - 

6 Martin, KY 0.119 - 0.098 - 

2 Kittanning, PA 0.126 - 0.104 - 

9 Delta, CO 0.129 - 0.129 - 

5 Norton, VA 0.130 - - 0.004 (a) 

2 Ruff Creek, PA 0.134 - 0.132 - 

5 Norton, VA 0.140 - 0.112 - 

2 Kittanning, PA 0.143 - 0.113 - 

9 Craig, CO 0.155 - 0.220 - 

9 Castle Dale, UT 0.158 - 0.205 - 

4 Princeton, W VA 0.180 - 0.160 - 

11 Hueytown, AL 0.186 - 0.208 - 

5 Norton, VA 0.190 - 0.149 - 

4 Logan, WV 0.204 - 0.224 - 

2 Ruff Creek, PA 0.213 - 0.257 - 

8 Benton, IL 0.220 - 0.282 - 

7 Jacksboro, TN 0.222 - 0.195 - 

2 Kittanning, PA 0.240 - 0.180 - 

8 Hillsboro, IL 0.240 - 0.276 - 

9 Castle Dale, UT 0.248 - 0.301 - 

11 Hueytown, AL 0.253 - 0.331 - 

2 Ruff Creek, PA 0.254 - 0.220 - 

10 Beaver Dam, KY 0.254 - 0.308 - 

9 Craig, CO 0.265 - 0.246 - 

4 Logan, WV 0.265 - 0.262 - 

4 Madison, WV 0.272 - 0.244 - 

4 Pineville, WV 0.280 - 0.233 - 

6 Whitesburg, KY 0.284 - 0.295 - 

2 Johnstown, PA 0.292 - 0.246 - 

3 Morgantown, WV 0.323 - 0.387 - 

8 Benton, IL 0.330 - 0.441 - 

11 Hueytown, AL 0.348 - 0.408 - 

3 Morgantown, WV 0.355 - 0.303 - 

5 Norton, VA 0.360 - 0.415 - 

6 Pikeville, KY 0.360 - 0.352 - 

8 Hillsboro, IL 0.360 - 0.346 - 

8 Vincennes, IN 0.360 - 0.390 - 

4 Madison, WV 0.369 - 0.404 - 

4 Logan, WV 0.376 - 0.368 - 

4 Madison, WV 0.379 - 0.369 - 
7 Hindman, KY 0.380 - 0.354 - 

3 St. Clairsville, OH 0.383 - 0.429 - 

7 Harlan, KY 0.440 - 0.392 - 

10 Madisonville, KY 0.449 - 0.546 - 

6 Martin, KY 0.451 - - 0.395 (b) 

7 Hazard, KY 0.452 - 0.459 - 

6 Martin, KY 0.455 - 0.482 - 

4 Madison, WV 0.475 - 0.558 - 

5 Vansant, VA 0.480 - 0.612 - 

7 Hindman, KY 0.485 - 0.543 - 

6 Phelps, KY 0.490 - 0.520 - 

5 Vansant, VA 0.500 - 0.503 - 

8 Benton, IL 0.500 - 0.587 - 

4 Logan, WV 0.513 - 0.434 - 

3 Morgantown, WV 0.540 - 0.599 - 

9 Delta, CO 0.563 - 0.614 - (c) 

4 Madison, WV 0.570 - 0.595 

-

2 Ruff Creek, PA 0.579 - 0.588 - 

7 Barbourville, KY 0.588 - 0.644 - 

10 Beaver Dam, KY 0.596 - 0.565 - 

6 Pikeville, KY 0.610 - 0.601 - 

5 Norton, VA 0.620 - 0.612 - 

2 Kittanning, PA 0.628 - 0.600 - 

8 Hillsboro, IL 0.630 - 0.819 - 

4 Pineville, WV 0.640 - 0.689 - 

2 Johnstown, PA 0.644 - 0.533 - 

6 Phelps, KY 0.660 - 0.650 - 

11 Hueytown, AL 0.686 - 0.875 - 

3 Bridgeport, WV 0.689 - 0.888 - 

9 Delta, CO 0.741 - 0.965 - 

5 Norton, VA 0.760 - 0.717 - 

6 Phelps, KY 0.760 - 0.703 - 

8 Vincennes, IN 0.820 - 0.841 - 

9 Craig, CO 0.842 

- 0.805 

-

10 Beaver Dam, KY 0.852 - 1.046 - 

9 Price, UT 0.888 - 1.156 - 

4 Mt. Carbon, WV 0.890 - 1.070 - 

6 Whitesburg, KY 0.914 - 0.822 - 

3 Morgantown, WV 0.921 - 0.872 - 

4 Mt. Hope, WV 0.960 - 1.076 - 

9 Price, UT 0.979 - 1.059 - 

6 Pikeville, KY 1.020 - 1.035 - 

7 Barbourville, KY 1.041 - 1.203 - 

7 Jacksboro, TN 1.058 - 1.100 - 

7 Harlan, KY 1.070 - 1.280 - 

7 Jacksboro, TN 1.103 - 1.255 - 

3 Bridgeport, WV 1.103 - 1.271 - 

10 Madisonville, KY 1.171 - 1.528 - 

10 Madisonville, KY 1.244 - 1.435 - 

4 Logan, WV 1.285 - 1.473 - 

4 Madison, WV 1.297 

- 1.607 - 

7 Harlan, KY 1.330 - 1.491 - 

6 Whitesburg, KY 1.362 - 1.301 - 

6 Martin, KY 1.401 - 1.428 - 

3 Morgantown, WV 1.419 - 1.420 - 

4 Madison, WV 1.482 - 1.680 - 

5 Norton, VA 1.520 - 1.291 - 
6 Phelps, KY 1.520 - 1.445 - 

8 Vincennes, IN 1.520 - 1.930 - 

4 Logan, WV 1.522 - 1.705 - 

3 Oakland, MD 1.529 - 1.956 - 

5 Vansant, VA 1.530 - 1.746 - 

6 Elkhorn City, KY 1.570 - 1.681 - 

6 Pikeville, KY 1.590 - 1.455 - 

4 Mt. Hope, WV 1.610 - 1.543 - 

7 Harlan, KY 1.620 - 1.586 - 

5 Norton, VA 1.630 - 1.680 - 

8 Vincennes, IN 1.650 - - 0.481 (d) 

7 Jacksboro, TN 1.669 - 1.700 - 

7 Hazard, KY 1.670 - 2.074 - (c) 

7 Harlan, KY 1.680 - 1.496 - 

7 Barbourville, KY 1.720 - 1.697 - 

4 Mt. Hope, WV 1.740 - 1.993 - 

7 Barbourville, KY 1.742 - 1.616 - 

7 Harlan, KY 1.840 - 2.012 - 

7 Hindman, KY 1.934 - 2.702 - 

7 Hindman, KY 1.972 - - 1.515 (b) 

6 Martin, KY 2.042 - 2.250 - 

4 Mt. Carbon, WV 2.060 - 2.020 - 

6 Pikeville, KY 2.100 - 2.666 - 

4 Pineville, WV 2.320 - 2.715 - 

4 Logan, WV 2.415 - 2.550 - 

4 Pineville, WV - 0.610 1.370 - (e) 

4 Pineville, WV - 0.120 0.209 - (e) 

(a) Cyclone hose off when opened can 

(b) Cyclone pump out of calibration 

(c) light rockdusting 

(d) possible pre-weigh error on 2.0 L min-1 filter--outlying data point 

(e) PDM flow restriction 

 
Table B

 

MSHA 

District 

 

-2 Excluded area sample 

 

Field Office 

raw data withou

-3 mg m

 PDM 

 

 

CMDPSU 

t PDM bias corrections

Notes 

2 

3 

3 

3 

4 

4 

5 

6 

6 

(a) 

(b) 

(c) 

(d) 

(e) 

(f) 

(g) 

Ruff Creek, PA 

Bridgeport, WV 

Bridgeport, WV 

Bridgeport, WV 

Mt. Carbon, WV 

Mt. Hope, WV 

Norton, VA 

Martin, KY 

Whitesburg, KY 

PDM failed 

PDM filter overload e

PDM TE fail/remove 

PDM did not start. 

PDM greater than twi

Sample terminated ea

heavy rockdusting 

 - 

 16.465 

 0.885 

 1.842 

 - 

 3 930 

 1 340 

 0.174 

 0.520 

 

rror after 4 hr 42

error after 7 hr 1

 

ce the protocol li

rly, mine shut do

 

- 

14.361 

0.778 

1.911 

- 

4.714 

1.406 

0.228 

0.411 

 

 min 

0 min 

mit. 

wn by inspector.

(a) 

(b) 

(c) 

(a) 

(d) 

(e) 

(a) 

(f) 

(g) 

 

References 

 

1

 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. PB-85-220721, 1984. 

2. G. K. Eagleson and H. G. Muller, J. Royal Stat. Soc. 1997, 59, 173-189. 

3. J. Neter, W. Wasserman and M. H. Kutner, in Applied Linear Statistical Models, Richard D. 

Irwin, Inc. 3rd edn., 1990, ch.11, p. 420. 

4. SPSS, Inc. SPSS v.14.0, Chicago, IL.