Continuous Personal Dust Monitor Accuracy Testing 

6/23/08 

Introduction

New Continuous Personal Dust Monitors (CPDM) submitted to NIOSH for approval to 

sample coal mine dust must accurately measure respirable coal mine dust in mine 

environments. There are two steps in the process which may be done in any order. The 

manufacturer is required to submit the results of a comparative underground coal mine 

dust sampling study, where the candidate CPDM is compared to an approved coal mine 

dust sampling device (currently the Coal Mine Dust Personal Sampling Unit 

(CMDPSU)). This testing shall follow the guidelines outlined below and shall 

demonstrate through weighted regression analysis that the mean coefficient of variation 

with bias correction is equal to or less than 12.8%. The other step involves laboratory 

testing to determine the electronic and environmental stability. 

This testing must be conducted by a private, commercial, academic or other laboratory 

approved by NIOSH. 

Methods 

1.0 Comparative Underground Coal Mine Dust Sampling

The manufacturer shall submit evidence that the unit can perform satisfactorily in the 

underground mine environment. This may be demonstrated according to durability 

requirements set forth in § 74.7 (g). Coal mine dust sampling will be performed with the 

same instruments tested in § 74.7 (g) to compare the results of a candidate instrument 

to the performance of an approved CMDPSU. 

1.1 Criteria for mine selection 

A stratified random sampling design should be used to select mechanized mining units 

(MMUs) that are representative of all U.S. underground coal mines. The selected 

sample of MMUs should be partitioned into mutually exclusive strata that reflect the 

various coal seams and mining methods found in U. S. underground coal mines. 

Because of the mine selection process, any mine dust size distribution or coal type 

effects are accounted for, on average, in the data analyses. A proportionate allocation 

strategy with different sampling rates among the strata should be used to ensure
that the composition of the sampled MMUs is representative of the 

composition of the population. Sample size should be adequate to insure 

a statistically robust sample size but in no case be less than about 20% of 

the current mine workplaces. An example of this technique may be found 

in Page et al1

. 

1.2 Testing procedures 

To minimize spatial variability found in mine sampling environments, 

instrument sampling inlets should be located inside of a Lipmann type 

sampling container2,3

 with a single low velocity inlet. This procedure 

ensures that all samplers are exposed to the same atmospheric 

conditions. The Lipmann container will, at a minimum, include a 

NIOSH/MSHA approved CMDPSU, the instrument under evaluation and a 

size distribution measurement instrument -- intended to provide particle 

size distributions of sampled aerosol and capable of use in face areas of 

underground coal mines. 

Sampling will be conducted in underground coal mines in representative 

areas where miners normally work. These areas will include a statistically 

representative mix of longwall, continuous miner, roof bolter, haulage, and 

outby work sites. Samples will be collected for 8 hours over a range of 

equivalent concentrations of 10% to 200% of the occupational exposure 

limit of coal mine dust. Manufacturer recommended flow rates for all 

instruments will be used and verified through pre- and post-calibration. 

1.3 Analysis 

Weighted regression analysis is to be used to stabilize the variance for 

data analysis by estimating the relationship between the variance of the 

dependent variable and the independent variable. The CPDM testing 

shall demonstrate through weighted regression analysis that the mean 

coefficient of variation with bias correction is equal to or less than 12.8%. 

Appendix A 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 

candidate instrument, there is no need to specifically consider random 

measurement error in the predictor variable. Weighted regression should 

be performed using SigmaPlot v.9.04

 or equivalent statistical software. 

2
2.0 Laboratory Testing 

The laboratory test procedures will be used to determine the electronic and 

environmental stability under conditions that may only be rarely encountered in 

field sampling. Instruments used for this testing shall also be the same as those 

tested in § 74.7 (g). 

2.1 Zero Stability 

Demonstration of the zero mass measurement stability over 8 hours will 

be conducted and the instrument noise will be reported as the limit of 

detection and limit of quantification. The stability will be equivalent to or 

better than that of the CMDPSU. 

2.2 Electronic Stability 

Temperature stability of the electronics of the instrument will also be 

measured by subjecting the instrument to temperatures that fluctuate from 

-10 to +40o

 C. The continuous zero mass stability during the fluctuation 

conditions should remain equivalent to the ambient zero mass 

measurements in section 2.1. 

2.3 Environmental operating conditions 

Sampling in underground coal mines presents extreme environmental 

conditions. Laboratory testing must include the demonstration of 

candidate instrument dust measurement performance in the presence of 

relative humidity of approximately 95% and direct mist type water sprays. 

The CPDM will be expected to perform on a statistically equivalent basis 

as the CMPDSU. 

Report 

The manufacturer shall submit a complete test report in written and electronic 

format including all raw data, without omission of outlying data, valid data 

selection procedures, and analysis of the data according to the criteria listed 

above. 

3
Appendix A 

Mathematical representation 

Comparison of the CPDM to the CMDPSU will be made using regression 

analysis. Sampling data typically indicates an error term increasing with the 

independent variable, or multiplicative error, in addition to the required constant 

additive error term5

. As a result, the total sum of squares will largely be 

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

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 Muller6 to represent only 

multiplicative errors can be written as: 

Eq. A-1 Y = g(X)*(). 

In the present analysis, 

Y = a CMDPSU response variable, 

g(X) = a function of the CPDM predictor variable (X), 

 = a normally distributed random multiplicative error term, mean = 1 and 

variance resulting from spatial variation of the concentration within the sampling 

chamber, coupled with sampling and analytical error of the CMDPSU. 

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 with mean = 0, with inclusion of an 

additive error term, as 

Eq. A-2 Y = g(X)*(1+

) + 00 = g(X) + g(X)*() + 00,

where, 

00 = a normally distributed random additive error term with mean = 0 and 

constant variance (0)

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. 

4
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

).7,8 The data 

of this investigation will be used to internally estimate the variance relationship of 

the CMDPSU with the independent CPDM variable. Typical 1/X2 weighting 

assumes that dependent variable variance increases proportionally with X2

 over 

the entire range of independent variables. However, at low concentration values 

there is the limiting error term (00) due to weighing imprecision. The constant 

variance (0)

2 of this error term is known quite accurately for the CMDPSU 

samples. The proper weight variable is the reciprocal of the true total variance



2

, given by: 

Eq. A-3 

2 ≈ (0)

2 + (a*RSD)2

*X2, 

where the relative standard deviation (RSD) 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 the CMDPSU 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/

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. 

5
6

 

References 

1

 Page-SJ, Volkwein-JC, Vinson-RP, Joy-GJ, Mischler-SE, Tuchman-DP, 

McWilliams-LJ, J Environ Monit, 2008 Jan; 10(1):96-101 

http://www.cdc.gov/niosh/mining/pubs/pubreference/outputid2734.htm

2

 Blachman-MW, and Lippmann-M, Am Ind Hyg Assoc J, 1974, 35, 311-326. 

3

 Volkwein-JC, Vinson-RP, Page-SJ, McWilliams-LJ, Joy-GJ, Mischler-SE, 

Tuchman-DP, Reference: Pittsburgh, PA: U.S. Department of Health and Human 

Services, Public Health Service, Centers for Disease Control and Prevention, 

National Institute for Occupational Safety and Health, DHHS (NIOSH) Publication 

No. 2006-145, Report of Investigations 9669, 2006 Sep; :1-55 

http://www.cdc.gov/niosh/mining/pubs/pdfs/ri9669.pdf

4

 Systat Software, Inc. SigmaPlot v.9.0, Richmond, CA, 2005. 

5

 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. 

6

 Eagleson-GK, and Muller-HG, J Royal Stat Soc, 1997, 59, 173-189. 

7

 Neter-J, Wasserman-W and Kutner-MH, in Applied Linear Statistical Models, 

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

8

 SPSS, Inc. SPSS v.14.0, Chicago, IL., 2004.