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NBSIR 78-1574

A Suggested Experimental Plan

for the Determination of the

Accuracy and Reliability of Coal

Mine Dust Measurements

Harry H. Ku

Joan R. Rosenblatt

Center for Applied Mathematics

National Bureau of Standards

Washington, D C. 20234

June 30, 1 979

Issued October 1979

Final

Contract No. J0177013

°repared for Jnited States Department of the Interior

100 bureau of Mines

,U56

78-157

1979

C.2

nsirn^sr

NBSIR 78-1574

l « I A SUGGESTED EXPERIMENTAL PLAN

FOR THE DETERMINATION OF THE

ACCURACY AND RELIABILITY OF COAL

MINE DUST MEASUREMENTS

Harry H. Ku

Joan R. Rosenblatt

Center for Applied Mathematics

National Bureau of Standards

Washington, D.C. 20234

June 30, 1 979

Final

Issued October 1979

Prepared for United States Department of the Interior

Bureau of Mines

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
' .

s, ' • p'r'r • • • v £
TABLE OF CONTENTS

Page

0. Introduction 1

1. Accuracy and Reliability of the Coal Mine Dust Measurements.... 2 1.1 Accuracy/Uncertainty of the Coal Mine Dust Measurements.. 2 1.1.1 Reference Base for the Coal Mine Dust

Measurements 2 1.1.2 Possible systematic errors in the Coal Mine

Dust Measurement Program 3 1.1.3 Imprecision of the Coal Mine Dust Measurements.... 9 1.2 Reliability of the Coal Mine Dust Measurements 11

2. Some Unit Designs Appropriate for the Estimation of the

Error Variance of Interest 13

2.1 The 5x5 Latin Square 13

2.2 Other Unit Designs that may be Considered 15

2.3 Advantages and Limitations of the Design 16

2.4 Checking the Performance of the Sampler in the

Laboratory 16

3. Dry Run and the Pilot Experiments 17

3.1 Treatment of Void Samples 18

3.2 Protocol for Monitored Experiments 18

3.2.1

Unmonitored Experiments 19

3.3 Estimate of time required for each unit experiment 19

3.4 Experimental Plans at Different Levels of Funding 19

4. General Remarks on the Coal Mine Dust Sampling Program 20

4.1 A Generalized Model 22

5. Acknowledgement 23

References 24

Appendix A: Statistical Model and Analysis of the 5x5 Latin

Square Design

i

0. Introduction

In December 1975, a report entitled "An Evaluation of the Accuracy

of the Coal Mine Dust Sampling Program Administered by the Department of

Interior" [1] was prepared by the Analytical Chemistry Division of the

National Bureau of Standards (NBS) , in response to a request by Senator

Harrison A. Williams, Chairman, Committee on Labor and Public Welfare.

The report attempted to evaluate the adequacy of (1) the personal

sampler unit used to measure the coal dust concentration in the mines,

(2) the procedures used by the Department of Interior (DOI) to analyze

the dust samples obtained from mine operators, and (3) any recent

studies made by the Department or private industry concerning the coal

dust sampling equipment. Recommendations in the report of NBS included

continued research efforts by the appropriate organization to correct

the personal sampler deficiencies and to consider the use of area or stationary samplers as a supplement to the personal samplers.

Concurrent with the NBS report cited above, the General Accounting

Office (GAO) also issued a report in December, 1975 [2], suggesting that

improvements are still needed in coal mine dust sampling programs and

procedures relating to penalty assessments and collections. Among

recommendations made by GAO, the following paragraph specifically called

for actions by the agencies involved:

"GAO further recommends that the Secretary of the Interior

instruct the Mining Enforcement and Safety Administration

[MESA, now MSHA] and the Bureau of Mines and the Secretary

of HEW instruct the National Institute for Occupational Safety

and Health to conduct a joint study to determine quantitatively

the accuracy and reliability of dust measurements when taken

with the current equipment by coal miners in underground

mines. GAO suggests that the assistance of the equipment

manufacturers and the National Bureau of Standards be

solicited .

To implement the above recommendations, an interagency agreement

[3] was made between the Bureau of Mines (BOM) and the NBS on February

1, 1977. The agreement has as its technical objective "the quantitative determination of the accuracy and reliability of dust measure- ments when taken with the current equipment by coal miners in

underground mines," and the work is to be conducted in two phases. In

Phase I, NBS is to develop an experimental plan for the determination

of the accuracy and reliability of coal mine dust measurements at

three levels of funding, and submit a report to BOM in accordance with

terms of the agreement. This report was reviewed by BOM, with comments

and suggestions from the Mining Safety and Health Administration (MSHA')

and the National Institute for Occupational Safety and Health (NIOSH)

to serve as a basis for decisions in carrying out the experimental program

in the field and in laboratories. The actual experimental program will

be conducted in Phase II. This document is the final report called for

at the conclusion of the Phase I part of the agreement.

1
In Section 1 of this report, the terms "reliability" and "accuracy"

are clarified and defined for the purpose of this investigation. Certain

pertinent information, collected as results of personal contacts and

study of existing literature, is presented and discussed. In Section 2 an experimental design is suggested to measure the various sources of

variability as relating to the use of approved personal samplers "by

coal miners in underground mines." In Section 3, a dry run is suggested

to test the efficacy of the design. The results of this dry run will be

used to modify the protocol to reflect the effect of increased or diminished monitoring (supervision) , and for the design of experimental

programs at different levels of funding. Pilot experiments on 10 to 12

mines are also recommended to obtain preliminary estimates of variabilities due to different sources. In Section 4 an overall view is

presented and factors that may contribute to the resulting uncertainty

of coal mine dust measurements are discussed in that context. A statistical model and corresponding analysis of variance for the design is

given in Appendix A.

1. Accuracy and Reliability of the Coal Mine Dust Measurements

The terms "reliability" and "accuracy" have been used in many

fields of measurement so much so that clarification of their meanings

for the purpose of this report becomes mandatory. In general, inaccuracy, or uncertainty, refers to the departure of a measured value from

an agreed reference base; reliability refers to the frequency that a system will perform satisfactorily its intended function when used under

stated conditions.

Following these concepts, which we believe are reasonable for the

purpose of this report, we will discuss in more detail the various

factors (sources of systematic errors, and extent of random variability)

that contribute to the uncertainty and unreliability of the results of

dust measurements.

1.1 Accuracy/Uncertainty of the Coal Mine Dust Measurements

By the term "uncertainty" of a reported value we mean the credible

limits to its likely inaccuracy [4] as measured from some agreed basis

of reference. Two components of uncertainty are usually present: the

uncertainty due to systematic error and the uncertainty due to imprecision. The distinction between the two types, however, is by no means

rigid and fixed, and is only meaningful in relation to the frame of

reference.

1.1.1 Reference Base for the Coal Mine Dust Measurements

In the "Federal Coal Mine Health and Safety Act of 1969", the

reference base for the concentration of respirable dust is the average

concentration of respirable dust if measured with the instrument

2
developed by the Mining Research Establishment (MRE) . Measurements made

with any other instrument must be converted to an MRE equivalent for the

purpose of the Act.

The currently used conversion factor for all personal samplers is a multiplicative factor of 1.38 based on comparison data of personal

sampler and MRE collected in 200 coal mines in 1973, and recommended in

MHSA Report of Investigations RI 7772 [5]. The uncertainty of this

value, however, was not given in the report.

The same data were reanalyzed by BOM and essentially the results

supported the value of 1.38 recommended by MESA [6]. Using different

criteria for the selection of "valid" data, and different assumptions on the error structure, the conversion factors calculated for several

levels of concentrations range from 1.19 to 1.84. Laboratory measurements and measurements in return airways gave much higher results. The

reasons for these high values were not known. [6]

Among the many difficulties encountered in the determination of a conversion factor, we note the following major ones:

a. Data editing. In the analysis by MHSA or BOM, nearly

50 percent of the data collected were rejected for reasons

that these sets of data were impossible, inconsistent, or unreliable.

b. Treatment of data at lower range of concentration. At the

lower range of concentration, the relationship between the

two results in this range was difficult to characterize.

From an inspection of the results of BOM’s alysis, it

is not at all certain that one value of conversion

factor could serve adequately throughout the dust concentration range from 0.0 to 5.5, mg/m . BOM, however, indicated

to us that precise measurements at such low concentrations

are not of particular interest.

When the Federal Coal Mine Health and Safety Act was enacted in

1969, it was based on data from Great Britain, using MRE as the standard

instrument for measurements of coal mine dust. The inherent imprecision

of the MRE measurements, however, is about twice that of the personal

samplers, as reported by Eastern Associated Coal Corp. (EACC) in 1976

[7], Other investigators, however, claimed a "consistency" of about ~8',

[18]. The use of the MRE as a reference basis, and hence the conversion

factor contributes a substantial uncertainty to results obtained in the

coal mine dust sampling program.

1.1.2 Possible systematic errors in the Coal Mine Dust Measurement

Program

For the purpose of this report, a systematic error is defined as an error in the measurement process that stays constant in magnitude and

direction for all, or a large part of the resulting data. The conversion

3
factor used to calculate MRE equivalent from results of personal sam- plers certainly would contribute a systematic error, due to the uncertainty of the number 1.38 used for all results of dust concentrations.

However, results of all mines will be treated the same way, and its

presence would have the same effect on all mines in the administration

of the program.

Other sources of systematic errors are less evident, and may in

many cases be uncovered only with improvement of precision of measurements, or with experiments designed specifically to check on particular

sources of systematic errors. For example, the conversion factor of

1.38 was derived using data ranging from 0.5 to 5.5 mg/m , and a straight line relationship is forced through zero by the addition of a large number of zero pairs. It is conceivable that this factor may work

well within this range, but could be improved upon in the range of 0.0-

0.5 mg/m .

A number of sources of systematic errors belong to this category,

where there are no experimental data, or insufficient data, to ascertain

their existence or magnitude. Consequently, we can only discuss those

systematic errors that are conceptually possible.

(i) Possible differences in results as measured by personal

samplers manufactured by different companies.

The existence of a significant difference between the MSA

Bendix personal samplers was alluded to in the 1975 NBS

Report [1], and the difference was attributed to a loss

of tare weight of the Bendix filter capsule. This problem

of weight loss was corrected, but subsequently a weight gain

problem caused Bendix units to be taken off the approved list

again in early 1977. A difference of 20% between average

values of MSA and UNICO was also reported in a 1974 BOM study

[6], Obviously possible systematic error associated with the

design, or material and process in manufacture, must be

closely guarded against.

Recent reports [7,11] that we are aware of did not address

this problem. The difficulty in comparing the results of two or more makes of personal samplers seems to stem from the fact

that variations due to location or positioning of samplers are usually confounded with variations due to differences among

individual personal sampler units. A difference among parallel

samplers set up in the mines could be due to a difference

in unit performance, or due to differing dust concentrations

seen by each sampler in the package. The Pittsburgh

Technical Support Center (PTSC) of MESA routinely checked

only the preweight of cassettes of different manufacturers,

but not the total performance of the units. We are not aware of any routine monitoring program of unit performance

by NIOSH, the agency that approves the use of particular

sampling units, or by the manufacturers of the personal

sampler units.

4
Upon the request of the Administrator of MHSA in

June 1977, an NBS team visited the processing laboratory

of MHSA Pittsburgh Technical Support Center, and reviewed

the quality control program used in the weighing of

respirable dust samples. One of the present recommendations

by NBS deals with the monitoring of the manufacturing

process of each type of filter on a continuing basis to

detect the extent of change of the weight of filters

with time. A report of NBS findings and recommendations

is under preparation [16].

(ii) Treatment of oversized particles in samplers

By the current practice, filters with weight gain of 6 mg or more are examined for oversized particles (greater than

10 micrometers, nonrespirable) either visually or microscopically. The procedure for the determination of oversized

particles is outlined in PTSC Standard Method No. A4 and

Addendum [8]. The justification for using 6 mg as the cut-off

point is demonstrated in a memorandum dated October 28, 1976

from the Chief of Dust Branch, PTSC, to the Assistant Administrator. Essentially, an experiment was performed on 500

samples, with the result that 14 out of 15 samples weighing

more than 6 mg contained an excessive number of oversize

particles, whereas only 7 out of 485 samples weighing less than

6 mg contained excessive oversized particles.

Assuming the above figures are representative, then among

those filters with weight gain less than 6 mg, about 1.5

percent would contain excessive oversized particles. Depending

on the number of oversized particles present on these filters,

the concentration of the respirable dust level as defined

would be biased upward. Although the magnitude of this bias

may be negligible, its presence should continue to be recognized .

(iii) The presence of a disproportionate number of low

concentration of 0.1 mg/m^

Records of "Notice of Compliance" of all occupations of a section in each of two mines, provided to us by MESA, were examined. The Notice listed dust concentrations measured over ten shifts on ten more or less consecutive days. Dust concen- trations of the "Intake Air" for a particular day were also

given, but not always. A sample of these records is shown in

Figure 1.

There were 230 measured values for the mine in Pennsylvania from February 1972 to^January 1977 with a range of

values from 0.1 to 7.6 mg/m . For the mine in Illinois, there

were 344 measured values from November 1970 to December 1976,

5
3 with a range of values from 0.1 to 9.9 mg/m . Frequencies of

dust concentrations from 0.1 to 2.0 mg/m-* are listed in Table

1. We note that among the 20 categories, there are 40 and 41

values of 0.1 mg/m^ out of totals of 175 and 193 values, or about 23 percent and 21 percent respectively. These disproportionately large numbers of 0.1 mg/m^ values raise questions

as to their validity, especially when the dust concentrations

of the intake air were somewhat higher, in the 0.2 and 0.3

range.

At the weighing laboratory in PTSC, we observed the

practice followed in the evaluation of filters which showed a final weight equal to or less than the initial weight that may

account for a portion of large frequency of 0.1 dust concentrations. These filters are set aside and examined visually

or with a microscope. If dust particles are observed the

sample is considered valid and the value 0.1 mg/m is assigned

to the sample. If no dust particles are observed, the sample

is declared invalid and the serial number of the cassette is

forwarded to MHSA Headquarters for investigation of causes leading to the invalid measurement.

3 Whatever the cause of the large number of 0.1 mg/m

measurement values, malfunctioning of the unit or tampering,

the procedure adopted has the effect of biasing the concen- trations downward. It is reasonable to assume that dust

concentration in the coal mine should not be less than that of

the intake air, and to establish a procedure based on this

assumption.

6
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TABLE 1

FREQUENCIES OF DUST CONCENTRATION UNDER 2 mg/m3

Dust Concentration Frequency of occurrence

rn;ig/m

3 Pennsylvania Mine Illinois Mine

0.1 40 41

0.2 9 12

0.3 11 20

0.4 11 12

0.5 16 21

0.6 15 11

0.7 3 8

0.8 15 10

0.9 0 1

1.0 14 7 1.1 8 9

1.2 5 4

1.3 3 6

1.4 1 3

1.5 9 7 1.6 1 9

1.7 5 1

1.8 3 5 1.9 0 2 2.0 6 4

Total 175 193

8
1.1.3 Imprecision of t he Coal Mine Dust Measurements

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Many sources of variability contribute to the imprecision of tb=

laboratory

samplers using

experiments,

a multiple

wesampler

may list

or a sampler packag? pAeArf A

the following poLibU soloes]

(1) weighing

ill

‘^rectness in assembling the cyclone unit to pump

Li

° f a samP ler to repeat a measurement

;«-( differences between samplers of the same make (V differences between samplers of different makes io) possible gradient in dust chamber

For monitored field experiments, additional sources include:

(7) operation under hostile conditions (insufficient

etc!")’

lfflCulty in abstinent, movement of samplers,

(8) presence of over-sized particles

(9) gradients of dust concentration as a result of ventilation arrangement (to replace 6 above)

For unmonitored field experiments, additional possible sources could be

(10)

lack of calibration and checking of air flow rate

9
TABLE 2

Precision of Paired Personal Samplers in the Laboratory,

and in the Field

EACC REPORT [7]

Laboratory Field, monitored

^Field, not monitored

number of pairs 116 593

(b) 101

S 0.14 0.26 0.89

(c)

3

S = standard deviation (in units of mg/m )

a. Bendix, MSA, and Wilson Casella personal samplers, used with a modified Lippman Sampler.

3

b. Dust level ranged from 0 to 5 mg/m ; about 10 percent of paired

data was eliminated because of "oversized material, pump failure

during testing or damaged filters, and differences between pairs

considered improbable."

3 c. 28 pairs showed a difference of 0.7 mg/m or more.

d. We note that the difference between the "monitored" and "not

monitored" field experiments in Table 2 was the presence or absence

of an experienced researcher throughout the work period underground.

The sampler packages (two) were located on the continuous mining

machine or loader. The operators were not involved with the sampler

packages in the course of their work.

10
(11) incorrect placement of samplers

(12) inaccurate reported time period of sampling

(13) vibration and bumping during the use or transit

For the imprecision of personal samplers as used "by coal miners in

underground mines , all the above sources are present with the exception

of one, i.e., the gradient factor (listed as ,9) which may inflate the

imprecision of the sampler package results.- However, the introduction

of an operator will add a new component of variability due to the inter- action of the operator with the personal sampler in the course of his

work. To the best of our knowledge, no attempt has been made to deter- mine the magnitude of this factor.

1 • 2 Reliability of the Coal Mine Dust Measurements

For the personal sampler to perform its intended function satisfactorily , the physical design, construction, and manufacture of the

sampler must be such that a valid dust concentration measurement results

at the conclusion of its use. Pump failure, or other mechanical failure where the sampler failed in a physical sense, may be classified as the first type of unreliability.

A second type of unreliability is inherent in the procedures used

when the identity or the validity of the filter is in question. Cassette mismatched with the mine data card, incorrect data, missing essential

information, etc., cast doubts on the result and it is declared to be invalid.

The third type of unreliability pertains to the measured values

themselves, i.e., whether the measured values represent the respirable

dust concentration at the particular time and place. Presence of

excessive over-sized particles, weight loss or gain of filters, and

incorrect flow rates will yield measured values but do not provide a reliable estimate of the correct respirable dust concentrations.

The physical condition of the personal sampler units, including mechanical breakdowns, improper maintenance, etc., is the responsibility

of the mine operator; procedural problems can be detected by inspection

and dealt with by additional training and educational program under

We note that the difference between the "monitored" and "not

monitored' field experiments in table 2 was the presence or absence

of an experienced researcher throughout the work period underground.

The sampler packages (two) were located on the continuous mining

machine or loader. The operators were not involved with the sampler

packages in the course of their work.

11
Hence, we will be concerned only with the last mentioned component of

unreliability: the presence of excessive oversized particles on filters,

filters showing no weight gain or even showing weight loss after use,

and the flow rates during use.

It is our understanding that the design of the personal samplers

does not preclude the deposit of oversized particles (10 micrometers or larger) on the filters. The decision as to whether an overweight (6 mg

or more) filter sample contains an "excessive" number of oversized

particles is made at the weighing laboratory at PTSC by visual inspection

with a hand magnifier or examination under a microscope. In the latter

case, 10 fields of 0.25 mm are examined. If the total number of over- sized particles is 30 or more in 10 fields, then the sample is voided.

If the total number is 29 or less, the sample is deemed valid. About 80

percent of the overweight samples can be screened for oversized particles

by visual inspection, and 20 percent by the microscope. In the experience of PTSC over a six month period, about 2.7 percent of samples were voided for containing oversized particles (7,380 out of 273,000).

Caplan [15], in studying performance characteristics of the sampler,

noted difficulty encountered in assembling the vortex finder into the

top of the cyclone body. Cracks between the vortex finder and shoulder

due to misalignment in assembly, or occurring after assembly, introduced

high variability between replicate tests. It is possible that the

presence of an excessive number of oversized particles is also due to

leakage between the two components of the sampler. We understand some corrective action has been taken on the MSA sampler since Caplan reported

his findings. The problem is believed to be less severe for the Bendix

samplers

.

3 The evaluation of filters with low dust concentration values (0.1

mg/m or less) was discussed under 1.1.2 (iii), and will not be repeated

here. Possible causes for low weight gain or weight loss are:

a. incorrect initial or final weight

b. filter losing weight over time

c. sampling time overestimated

d. incorrect rate of sampling (air flow rate)

used in computation

Of the four causes, it appears that the estimated sampling time is under

complete control of the miner who reports the number of minutes on the

mine data card. Some elapsed time device on the unit itself, which we understand is being developed, would significantly reduce this source of error and cause dust concentration measurements to be more reliable.

The present protocol calls for a flow of 2.0 liters per minute and

calls for the miner to check the air flow rate after the first hour of

operation. Again there is no assurance that the flow rate is being

checked as required. Recognizing this problem, BOM has initiated contract to design and fabricate an improved personal sampler pump to control the air sampling flowrate automatically.

12
2. Some Unit Designs Appropriate for the Estimation of the

Error Variance of Interest

In arriving at an estimate of the uncertainty of measurements made

with the personal sampler "as used by coal miners in underground mines ,

the most difficult task is, perhaps, the estimation of the imprecision

of the sampler under actual working conditions. A direct estimation

would require burdening the miner with sampling packages, which is

objectionable because of bulk and weight. In any case, the miner would

be aware of the fact that he is performing an experiment and the results

obtained could be biased. Section 2 addresses this problem in particular

and suggests an experimental design where the imprecision of the sampler

under working conditions can be estimated indirectly.

The indirect way of obtaining an estimate of experimental error is

the realistic way in the present context. This estimate would include

subtle changes in the use of the personal sampler. If the causes of

these changes cannot be identified and eliminated, then their effects

must be included as part of the component of imprecision. In addition,

the experimental setup is similar to those checking on the "area" or "fixed point" sampling concept, and the miner need not know that he is

part of the experiment.

The renewed interest toward the study of "Area Sampling" or "Fixed

Point Sampling" to supplement, or even to replace, the personal sampler

[7, 10, 11] is another consideration that motivates the choice of the

unit design described below. Report L-792 of the Bituminous Coal Research,

Inc. [11] suggests that there is a dust level gradient as established

from measurements made with personal samplers mounted on the front cab,

the machine operator, and the rear cab. Comparison of dust concentrations

plotted by the Eastern Associated Coal Corporation [7] for three test

series also showed reasonable correlation between machine operator and

fixed points on the machine. It is expected that data generated from

the unit design can be used to investigate further the advantages of

fixed point sampling methodology as well.

2 . 1 The 5x5 Latin Square Design

This unit design measures the dust concentrations of a section of a mine for five shifts (five days) using five personal samplers. One of

the samplers will be used by the operator of a continuous miner in the

usual manner; the other four samplers will be made into two sampler

packages, to be hung from the front and rear cab posts of the canopy of

the mining machine. Figure 1 on page 7 of BCR report [11] gives a photographic representation of the proposed arrangement.

13
The measurement schedule is given in the diagram below, using the

following notation.

Days : 1, 2, 3, 4, 5

Samplers : A, B, C, D, E

Locations

:

RL - rear cab left

RR - rear cab right

M - miner operator

FL - front cab left

FR - front cab right

'^Location

Days RL RR M FL FR

1 A B C D I d

l

2 B D E C A d

2

3 C E B A D d

3

4 D C A E B d

4

5 E A D B C d

5

L

i

L

2 L3 L

4

L

5

DC

Here the mean dust concentration for a day, d., represents the

average over five samplers at five locations about the operator. The

mean dust concentration for a location, L., represents the average over

five days with five samplers, and the meatl dust concentration as measured

by a sampler, A for example, is averaged over five days and five locations.

DC, of course, represents the grand average of dust concentration over five days as measured at five locations with five samplers. These main

effects of day, location, and sampler may be estimated.

The rotation of the samplers used at a given location assures that

there is no confounding of location effect and sampler effect - a precautionary measure necessary in deciding if adjacent samplers, six to

eight centimeters apart, do or do not measure the same dust concentration.

The main interest of the experiment, however, is not the estimation

and comparison of these main effects. Here we supplement the classical

method in the analysis of a latin square design experiment. After

estimating the main effects from the data by the method of least squares,

the "unexplained" variability is represented by the "residuals" remaining

14
in each of the 25 cells after the differences due to main effects are removed. Standard deviations calculated from these residuals are measures of imprecision of the experiment. The imprecision of the personal sampler as used by the operator in the course of his work would be represented principally by the five residuals under the column M. By accumulating these residuals over a number of unit experiments, the imprecision of the personal sampler for the miner can be estimated and compared with that for the fixed point samplers.

The mathematical model and analysis of this design is given in Appendix A. The assumptions made in the analysis are spelled out and discussed in the Appendix.

2 * 2 Other Unit Designs that may be Considered

Designs other than the class of Latin Squares may be used to avoid the restriction that the number of days, the number of locations and the number of personal samplers are equal to one another. The general principle estimating the imprecision of the personal sampler from the residuals after the main effects are removed — however, remains the same.

Using the same notations, a Youden Square with three locations, seven days, and seven personal samplers is shown below:

Location

Days

Cab Front

Operator

Cab Back

A B C D E F G L

1 BCD E F G A L

2 L

3

d

l

d

2

d

3 d

4

d

5

d

6

d

7 DC

A least squares fit to the data would yield seven residuals for the mining machine operator. The efficiency of this design is not much

from the 5x5 Latin Square, except a unit experiment is

stretched to seven days.

Chapter 11 of Experimental Statistics [12] lists a number of Youden

Square arrangements that may be considered. All of them, however,

involve more personal samplers and longer periods of time.

15
2 .

3

Advantages and Limitations of the Designs

The main advantage of the unit designs given above is that the

imprecision of the personal sampler as used by miners during the course

of their work can be realistically estimated. This estimate, adjusted

for day-to-day dust level variations, would include variability due to

the interaction between the miner and the personal sampler under hostile

conditions — a factor that has not been considered in other experiments

performed to date. Comparison can also be made between supervised and

unsupervised experiments suggested under pilot experiments discussed in

the next section.

On the other hand, the present design is restricted to investigations

for a continuous miner with a cab and canopy. Perhaps it can be adapted

to other "high risk" miners who work in fairly constant position with

respect to a machine; e.g., a roof bolter. During the pilot experiment

stage, we feel that the experiment should apply to the continuous miner

only. Another limitation is that the information obtained for the

main purpose of this experiment is rather low per unit experiment. Even

ten experiments will only give us a barely adequate number of degrees of

freedom for estimating the standard deviation. Other information

collected, however, may be also of value; e.g., to check if two samplers

mounted side by side will yield the same measurements.

2.4

Checking the Performance of the Sampler in the Laboratory

The precision of the personal samplers has been studied in the

laboratory and reported in a number of publications [6,7,13]. The

resulting data, however, usually represented the behavior of these

samplers under "ideal" conditions. How well these samplers work under

"hostile" conditions similar to those encountered in the mines has not

been studied in the laboratory. Do these samplers possess sufficient

"ruggedness" to be used in an environment which they were designed for?

Youden suggested that a procedure used in a collaborative test [14]

must be checked out first by the deliberate introduction of changes of

levels of factors likely to be encountered in actual use. His design,

now called "Youden* s Ruggedness Test", appears to be appropriate in

locating possible sources of trouble in the use of personal samplers in

the mines. A design for checking on seven factors in eight combinations

is shown in Youden' s paper. The factors could be, for example, the

following:

Condition 1

1 . Shock or vibration no

2. Flow rate 2.0 5,/min

3. Rotation in position no

4. Assembly of sampler researcher

5. Oversized particles input none

6. Dust input continuous

7. Position of sampler center

Condition 2 yes

1.5

£/min

yes

other

present

intermittent

side

16
The larger effects of these factors would show up in the analysis of the

resulting data, and a realistic measure of imprecision can be computed

from the seven differences of the averages, each for condition 1 and

condition 2.

3 . Dry Run and the Pilot Experiments

Prior to the conduct of a full scale experiment, it would be prudent

to perform a dry run at two or three mines, to check on:

1. practical aspects of the design presented in section 2, and

2. modifications in procedure and protocol that may be

necessary.

For the dry run, we suggest the use of the unit design (5x5 Latin

Square) on the continuous miner with cab and canopy arrangement. The

first five-day run would be under close supervision of BOM, MSHA, or their contractors. A second five-day run using the same machine would

be repeated by the mine operator, without supervision, within a specif j^d

time period while the mining conditions remain essentially unchanged, —

say, four weeks. (The experiments performed by the mine operators are included to check if the unit experiment is workable without supervision.

Presumably the section foreman, in addition to training as to protocol

to be followed, would also learn from the actual performance of the

monitored experiment.)

The results of the dry run would be analyzed, and the procedure for

further experimentation revised based on the experience gained from the

dry runs. A pilot experiment, involving a minimum number of mines that

would provide a reasonable amount of information on the imprecision of

the personal sampler as used by the miners in the mines, is recommended

following the dry run.

To accumulate 25 to 30 degrees of freedom for the estimate of

imprecision under each of the two conditions, supervised and unsupervised, we need to perform the experiment in 10(12) mines. For convenience,

these mines may be selected in two clusters of 5(6) each; e.g., in West

Virginia and in Pennsylvania. If the information obtained is useful to

NIOSH in their Third Round of National Coal Study, these 10(12) mines

could be selected from the list of mines prepared by NIOSH for their

health study. Since few mines report a dust concentration of 2mg/trf or more, 2(3) mines in each cluster should represent mines that have a high

day-to-day variability, and the remaining a low variability. The

variabilities may be determined from compliance notices given in recent

past. At this stage of the experiment, we feel that all the mine

sections selected should have seams high enough to give best working

conditions for the supervision staff.

2J In the sense that the same miner and same type of cutters are used,

the ventilation system stays about the same condition, etc.

17
Since two types of personal samplers are in general use, the Bendix

and the MSA, two and three of each type could be used for the five

samplers called for in the design for half of the 10(12) experiments,

and reversed for the balance. Differences of samplers of the same type

and those of different types in a sampler package could then be studied.

3 . 1 Treatment of Void Samples

In the EACC Report [7], Harris rejected 11 percent of on-man

samples and 0.6 percent of the fixed point samples "mainly because the

dust filter cassettes were contaminated with oversized material...".

These figures, however, included sampled values in shifts monitored and

not monitored. BCR monitored all shifts in their experiment [11], and

reported a lesser percentage (about 2%) of void samples, most of which

were due to mechanical failure.

Assuming these percentages of void samples are typical in an experiment of this type, we can expect a few missing data in the monitored

experiments due to mechanical failures. If the sampler on the operator

fails, the day’s experiment would have to be repeated on another day

after repair of the sampler. If a sampler in a package fails, a missing

value technique may be applied or an auxiliary sampler may be added to

the package in anticipation of possible failures. In either case, the

interpretation of the results will not be straightforward. We would

prefer to repeat the day’s measurements, provided the period of a unit

experiment is not lengthened enough to be impractical.

Since the purpose of the experiment is to determine the imprecision

of field measurements, the cassettes (with special marking) should be

sent to PTSC for processing in the routine manner. A sample voided

because of contamination of excessive oversized particles may, nevertheless, have to be included in the analysis because the time elapsed

between sampling and weighing would not allow a repeat measurement. If

the weighing can be performed in the field offices of MSHA, it may be

possible to check back and trace the reasons for the malfunction of the

unit.

3 . 2 Protocol for Monitored Experiments

In the following, we assume that six unit experiments are to be

performed at each of two general locations and the samplers are to be

supplied by BOM, MSHA, or NIOSH.

a. For each mining section selected for the experiment, assign

five regular personal samplers to be painted or tagged as A, B, C, D, E. The sixth one is reserved as a spare. For example, A and B could be

Bendix samplers, D and E MSA samplers. C will stand for Bendix or MSA

alternatively in successive experiments.

b. Fixtures on the front and rear post of the cab of the machines

are to be fixed ahead of time for locating the sampler packages. Distances

18
between the operator sampler and the two sampler packages are to be

measured

c. The monitoring personnel, or monitor, will check these samplers

for air flow, pump operation, leakage, cleanliness of cyclone, and other

routine points. He will insert the four samplers in the two packages,

using the design. The days 1 to 5 are to be permuted randomly and the

arrangement of the samplers in the row corresponding to that day are to

be used.

d. The personal sampler for the operator will be carried in and

out of the mine by the operator; the two packages by the monitor. All

samplers are to be turned on and off from portal to portal. Possible

inadvertent abuse of the sampler by the operator in carrying it in and

out of the mine may be noted.

e. The monitor will check the samplers in the package during the

shift, leaving the checking of the on-man personal sampler to the

operator. The monitor may collect other data of interest, e.g., the

shift production, cutting frequency, air flow and brattice location,

etc

f. Upon completion of the shift, the monitor checks conditions of

all samplers, notes leakage of any other irregularities, etc. He will

rearrange the five samplers for the next day.

3.2.1 Unmonitored Experiments

After the completion of a monitored experiment in a mine section,

the foreman or group leader for the section will replace the monitoring

personnel and carry out the latter's duties. Personal samplers

routinely used in the mine will replace those samplers supplied by

government agencies. Some additional explanation or instruction to the

foreman may be necessary to clear up possible misunderstandings.

3 . 3 Estimate of time required for each unit experiment

In view of a number of possible interferences, such as strikes,

work stoppage, insufficient coal production, etc., BOM estimated from

their experience that two calendar weeks should be allowed for each unit

experiment employing one monitor. Therefore, for the 12 mine sections

contemplated in the pilot experiment, about 6 man-months will be required.

We suggest the use of four to six monitors so that the result of the

pilot experiment may be available in about 2 months time.

3.4 Experimental Plans at Different Levels of Funding

Several outcomes are possible at the conclusion of the pilot

experiments. Decisions regarding further experimentation will have to

be conditioned on the results and their interpretation.

19
First, the results of the pilot experiment may be sufficiently

precise for the purpose at hand. In that case no further experimentation

is necessary.

Second, the results may indicate that the information obtained is

useful, but not sufficiently precise or general in nature to allow the

necessary inferences. Then a large-scale experiment will be necessary

to firm up the various estimates of components of variability. The

extent and scope of this experiment will necessarily depend on the

results of the pilot experiments.

Third, if for some reason the pilot experiments do not yield the

needed information, then the design and its execution would have to be

reexamined as to the causes, and further experimentation would be based

on a revised scheme.

4 . 0 General Remarks on the Coal Mine Dust Sampling Program

In evaluating accuracy and reliability of measurements for mandatory

standards and regulatory requirements, it is essential to keep in mind

several criteria:

1. Purpose and intent of the regulation,

2. Measurement capabilities, and

3. Operational procedures and definition of "compliance".

Obviously no one set of criteria will work satisfactorily for all types

of regulatory requirements.

The coal mine dust sampling program is typical of a class of

mandatory regulations which came into being only recently — say in the

past ten years. These regulations generally require measurements of low

concentration health hazards over a long period of time. Air and water

pollution, radiation are other examples. Because the concentrations of

the toxic substances are generally extremely low, measurements made

on them are usually state-of-the-art type, and variability of individual

measurement is in general large enough to obscure the signal. Averaging

over time and space helps, the extent of averaging being dependent on the variability of the measurements. The loss and injury, if any, are over a long term rather than immediate.

The purpose of the coal mine dust sampling program is to determine

that the respirable dust in the mines is at a level sufficiently low to

prevent black lung disease (pneumoconiosis) among the miners. Personal

samplers, carried by the "high risk" miner in a mining section, are used

to collect a quantity of respirable dust. The respirable dust for each

shift collected in a cassette is weighed before and after use. The

regulation specifies that the average of ten shifts should not exceed

2.0 milligrams per cubic meter of air being sampled.

20
The various sources of variabilities that are inherent in the dust

level determinations include:

1. Spatial variability in a section of the mine. At different

locations in a section, the dust levels vary considerably.

The personal sampler is worn by the "high risk" miner, usually

the mining machine operator. But, the "high risk" miner also

moves around in the course of his work.

2. Day to day variability, or shift to shift variability. This

source of variability is estimated by BOM to be about 50-70

percent, mainly because of mining and ventilation conditions.

3. Variability among samplers of the same make, or different

makes. Based on experiments conducted by BOM using samplers

with collectors in parallel and close together, the relative

standard deviation of a measured value is about 5% when

conducted in the laboratory, 5-10% when conducted in mines by

BOM research workers, and as much as 50% when obtained by

miners [17]. Hostile environment no doubt contributes to the

increase, but the magnitudes of components due to various

possible causes are not known. MSHA believes that the "gradient"

in the air flow around the mining equipment may contribute a large portion of the variability.

Given that the above brief description of the various sources of

variabilities is a fair representation of dust concentration measurements

when taken with current equipment by miners in the mine, a model may be

postulated to relate these sources of variabilities and to indicate

appropriate estimates of their magnitudes. The current procedure,

specifying a ten-day average, suggests implicitly that the dust concen- tration of a "high risk" occupation follows some probability distribution,

and the shif t-to-shif t changes are relatively independent. It follows

then that the problem is to estimate the relevant parameters of this

distribution — the mean value, the variance, and possibly the skewness.

These parameters are assumed to remain fairly constant over time, as long as the conditions of mining remain unchanged, to allow estimation

of their numerical values.

A determination of the concentration of respirable dust collected

in one shift then is a sample taken from this distribution, plus collection

and measurement errors. In symbol, we may express the measured weight,

y, as a function of these parameters:

y=U+A + e +e (4.0-1)

where:

y

: the mean value

A : bias that may be inherent in the sampler or in the use of the

sampler,

: collection and measurement error with mean zero and variance

21

e
2 °e ’

e: variability due to distribution of dust levels in a mine

over space and time, with mean zero and variance o^2

.

In the above formulation, A can be reduced by calibration, by

quality control of the manufactured samplers, and by protocol in the use

of samplers through training programs. The "e" term can be reduced by

improving the sampler’s design to reduce chance of tampering, to assure constant flow rate during use, and to improve weighing procedures. The

"e" term, however, will remain with variance a

2 unless the condition in

0

the mine is changed.

It seems reasonable to assume that the purpose of the coal mine

dust sampling program is to assure that the value of "y" in a mine is

less than 2 mg per cubic meter. The difficulty is that even if "A"

and "e" can be reduced to negligible magnitudes, the uncertainty in the

average of ten shifts as an estimate of "y” still depends on the variability of e — a component that is large in comparison with the other

two sources of variability.

A reasonable approach to supplement the ten-day average decision

rule appears to be that of the control chart for each mine section or each mining machine. Decisions based on control charts are useful in

the following sense:

1. Enforcement is based on the long term behavior of measurement

results — based on the distribution of dust level over space

and t ime

.

2. Enforcement can be applied on a graduated series of actions

rather than a violation-compliance decision.

3. Assignable causes for increase and decrease of dust levels can

be investigated, to detect tampering, misuse, and/or to assure

the improvements are real.

4. Almost all data are available, no additional work is involved

except to set up procedures for control charts for averages

and ranges for each mine (or mining machine) , and to study the

results

.

5. A control chart on ranges of, say, measurement results of five

shifts, can be used to compare shif t-to-shif t variability

between different mines. Study of mines which have extremely

large shif t-to-shif t variability may reveal causes of such

erratic behavior, thereby leading to possible improvement in

ventilation and other dust suppression systems.

4 . 1 A Generalized Model

If the assumptions are made that the dust concentrations are time

dependent and that shif t-to-shif t concentrations are correlated, then

the problem becomes much more complicated than that associated with the

model given in subsection 4.0. Some preliminary discussions and suggestions

22
for a respirable dust sampling program under these assumptions can be

found in a thesis by Seppanen [17].

5. Acknowledgement

Current interest in the coal mine dust sampling program can be

demonstrated by the large number of persons whose expertise and willing- ness to help contributed to our understanding of the problem. The list

below is by no means complete. To these and others we owe our thanks.

BOM John A. Breslin

Welby G. Courtney

MSHA Murray Jacobson

Thomas F. Tomb

Paul Parobeck

Mike Lawless

NIOSH Kenneth A. Busch

Nelson A. Leidel

Mike Roder

William Wagoner

Robert Wheeler

BCR R. D. Saltzman

J. A. Kost

Felix duBreuil

EACC H. G. Harris

NBS Cary Gravatt

Edgar S. Etz

George A. Hornbeck

23
REFERENCES

[1] LaFleur, P. D. An Evaluation of the Accuracy of the Coal Mine

Dust Sampling Program Administered by the Department of the

Interior. A final report to the Senate Committee on Labor and

Public Welfare, prepared by staff of the Analytical Chemistry

Division, National Bureau of Standards, December, 1975.

[2] General Accounting Office. Improvements Still Needed in Coal

Mine Dust-Sampling Program and Penalty Assessments and Collections

Report to the Congress by the Comptroller General of the

United States, December 31, 1975.

[3] Contract between U. S. Bureau of Mines and the National Bureau of

Standards, Number J0177013 dated February 1, 1977. Determination

of the Accuracy and Reliability of Coal Mine Dust Measurements.

[4] Eisenhart, C. Expression of the Uncertainties of Final Results.

Science, 160 , Jur^e 14, 1968. pp 1201-1204.

[5] Tomb, T. F. , Treaftis, H. N., Mundell, R. L., and Parobeck, P. S.

Comparison of Respirable Dust Concentrations Measured with MRE

and Modified Personal Gravimetric Sampling Equipment. Report

of Investigations 7772, Bureau of Mines, U. S. Department of

the Interior, 1973.

[6] Breslin, J. A. Precision of Gravimetric Sampling of Respirable

Dust in Coal Mines. Unpublished report, U. S. Bureau of

Mines, 1974.

[7] Harris, H. E. Development of Area Sampling Methodology. Final

Report by the Eastern Associated Coal Corporation under

Contract H0133108 with the U. S. Bureau of Mines. October,

1976, Revised, 1978.

[8] Goldberg, S. A., and Ambrosia, D. Standard Method No. A4,

Dust Group, Technical Support Center, Pittsburgh, Mining

Enforcement and Safety Administration, U. S. Department of

Interior. June, 1972.

[9] Letter from J. A. Kost of Bituminous Coal Research, Inc.,

Pittsburgh, Pa. to W. Courtney, U. S. Bureau of Mines, dated

February 7, 1977.

[10] Tomb, T. F., and Ondrey, R. S. Determining the Feasibility of

Area Sampling to Enforce the Respirable Dust Standard in

Underground Coal Mines. MESA Informational Report 1037, 1976.

24
[ 11 ]

[ 12 ]

[13]

[14]

[15]

[16]

117]

[18]

Kost, J. A. and Saltsman, R. D. Evaluation of the Respirable

Dust Area Sampling Concept as Related to the Continuous Miner

Operator. Report L-792 of the Bituminous Coal Research, Inc.,

Monroeville, Pennsylvania, January 1, 1977.

Natrella, M. G. Experimental Statistics , NBS Handbook 91,

Revised Edition, 1966.

Kaplan, K. J., Doemeny, L. J., and Sorensen, S. Evaluation

of Coal Mine Dust Personal Performance. Final Report to NIOSH

under Contract No. PH CPE-R-70-0036, November 1973.

Youden, W. J. The Collaborative Test, Journal of the Assoc.

Official Agricultural Chemists 4_6, 5562, 1963. (Reprinted as paper 3.4 in NBS Spec. Pub. 300, Vol. 1. Precision Measurement

and Calibration: Statistical Concepts and Procedures , Feb. 1969.)

Caplan, K. J., Doemeny, L. J., and Sorenson, S. D. Performance

Characteristics of the 10 mm Respirable Mass Sampler: Part

II - Coal Dust Studies. American Industrial Hygiene Assoc.

Journal 38^, 162-172, April, 1977.

Parobeck, P., Tomb, T., Ku, H. , and Cameron, J. Measurement Assurance

Program for Weighings of Respirable Coal Mine Dust Samples,

in preparation.

Seppanen, M. S. The Design of an Airborne Respirable Dust

Monitoring System for Underground Coal Mines. A Thesis submitted

to the Faculty of the Graduate School of the University of

Minnesota. December, 1975.

Dunmore, Joan H. , Hamilton, R. J., and Smith, D. S. G. An

Instrument for the sampling of Responsible Dust for Subsequent

Gravimetric Assessment. J. Scientific Instruments, Vol. 41, 1964.

25
APPENDIX A

The purpose of this Appendix is to give a statistical model and

corresponding analysis of variance for the unit design (experiment)

proposed in Section 2.1, and to indicate how data could be combined from

a group of unit experiments

CONTENTS

A.l The Unit Design

A. 2 Statistical Model for Unit Design

A. 2.1 Variants of the Model

A. 2.

2

Discussion of Assumptions

A. 3 Analysis of Variance, Unit Design

A. 3.1 Main Effects

A. 3.2 Comparing Locations

A. 4 Variance Components, Unit Design

A. 5 Combining Results from Several Designs

A. 5.1 Uncertainty of Ten-Day Average

A. 5.2 Over-all Uncertainty

A. 6 A Numerical Example

A. 7 References for Appendix A

26
A. 1 The Unit Design

First, we define notation for the observed values (measured weights)

obtained in carrying out one unit design. In the diagram below, y.

(i=l,2, . .

. , 25) denotes the weight of respirable dust collected at £he

ith day-location-sampler point. The letters A to E identify the five

samplers

Location (1) (2) (3) (4) (5)

Day RL RR M FL FR Sum

1 A/y

1 B/y

z c/y

3 E/y

5 Di

2 B/y

6

D/y

7 £ /y8 c/y9 A/yio

D

2

3 C/yn

E/y

12 B/y13 A/y14 D/y

15 °3

4 D/y

16 C/y17 A/y

18 E/y

19 B/y

20

D

4

5 E/y

21 A/y

22

D/ y

2 3

B/y

24 C/y

25

D

5

Sum L

1

L

2

L

3

L

4

L

5

G

For analysis of the Main effects of days, samplers, and locations, one uses the totals (for the dth day), S

g

(for the s th sampler), and

(for the ftth location) . The day and location totals appear as row

and column sums when measured values are entered in the tabular scheme

above. Sampler totals are calculated as indicated in the diagram,

e.g., for Sampler B, S g = y 2 + y^ + y

13 + y2Q + y^- Finally, G denotes

the grand total, G = y^ + + ... + y

23

*

A. 2 Statistical Model for Unit Design

At the first stage of analysis, for an experiment conducted during

five consecutive operating shifts for one mine section, it is convenient

to assume provisionally that there are fixed (constant) values for

- average dust level,

- day effects,

- location effects,

- sampler effects,

so that the expected value of the observation y^ may be represented by

E(y .) = p+ 0.+Q.+0 where

l d l s

27
y = average dust level,

0 ^ = average effect of day d,

0 ^ = average effect of location £,

0 = average effect of sampler s,

s and the appropriate day, location, and sampler are given in the diagram.

(In the initial analysis, the day, location, and sampler effects are thought of a adjustments to the average dust level and for each set of

effects, we assume + + '** + ^5 = 0 )

In the statistical model for the unit design, the measured values

differ from their expected values because of "error" due to imperfections

of the measuring instruments (samplers) and fluctuations of the dust

level. The model hypothesizes further that there may be additional

variability in the observed dust levels for the "machine operator"

position. The assumptions about errors are expressed as follows: for

observations made at locations where the sampler is fixed on the mining

machine (£=1,2, 4, 5), y. = E(y.) + e„, and for observations made where

the sampler is carried^by the

1machine operator (£=3), y^ = E(y^) + e^ +

nu. We assume that the measurement errors • • • * e

25^ an<* additional

operator-related variations (m„ ,mg, . . . j

11^) are statistically independent

They have zero means by definition, and we define

a

2 = variance of observation error,

e

a

2 = variance due to machine operator.

A. 2.1 Variants of the Model

In practice, it may be necessary to make certain technical modifications of this model. For example, the magnitudes of errors may tend to

be proportional to the level of dust concentration, so that the two

variances a

2 and a2 are not constant from day to day.

e m

One of the purposes of the Dry Run recommended in Section 3 of the

report is to examine whether the additive model appears to be appropriate

for the direct observations or for their logarithms, and whether it is

the variance or the relative variance (coefficient of variation) that

appears to be constant. Depending on the outcome of exploratory analyses

one may rewrite the model as a representation of log(y.), or specify

the use of weights to equalize variances.

If the model should need to be modified, the corresponding modifications in the analyses described below would be straightforward.

28
A . 2 . 2 Discussion of the Assumptions

The question has been raised whether the location effects will be

"fixed” during the five days of the unit experiment. More precisely,

will the differences between front and rear locations be approximately

constant from day to day?

If the unit experiment could be analyzed as a factorial experiment

(i.e., if the five samplers were identical), a departure from the fixedeffect assumption would show up as a Days-by-Locations interaction

effect. An important task in the Dry Run is to investigate the validity

of this assumption. To facilitate this, it would be desirable in the

Dry Run to have samplers as nearly identical as possible, or calibrated

so as to have independent estimates of the differences among them.

Furthermore, the two "left-right" differences between samplers packaged

together could be expected to be relatively negligible.

If the Location effects are not approximately constant, then it may

not be feasible to obtain an indirect estimate of any special variability

(with variance a

2

) due to the mine operator. There are two kinds of

departures from ?he assumption to look for: (1) front-to-rear difference

constant but front-to-operator difference variable or (2) all location

differences variable. In the first case, the estimate of a

2 will be

"inflated", including day-to-day variations of the average concentration

at the mine operator's location in addition to any other variability

introduced by the mine operator's handling of the personal sampler.

Evidence of this kind of variability may be of interest. In the second

case, measurement errors are completely confounded with location- tolocation variability within days.

It is generally agreed that there are large day-to-day changes in

the average dust level, so that the fixed-effect assumption for Days

has not been questioned. The assumption that differences among samplers

are constant is plausible unless some daily calibration activity is

introducing rather than preventing errors.

In this section, no assumption has been made about the shape (normal,

lognormal, or other) of the error distributions. No such assumption is

required for estimating the variances a

2 and a2

, although it will be needed

for performing tests of significance such as F-tests. The Dry Run will

provide initial information about the shape of the error distributions.

A. 3 Analysis of Variance, Unit Design

The analysis of variance has two goals:

(1) to extract information about the magnitudes of the provisionally fixed average dust level and effects of days, locations,

samplers (for use in later analyses where these sources of variability

may be modeled and interpreted in a different way) and

(2) to extract information about the magnitudes of o~ and o^.

29
For the first goal, quantities are calculated according to the established

textbook methods for analysis of Latin Square designs. For the second

goal, we add a special orthogonal decomposition of the "sum of squares

for error". The computations for the analysis of variance are displayed

in Table A-l.

In Table A-l, the total of 25 measurements (25 degrees of freedom)

is allocated to five principal sources of variability. For locations

and for "error", it is indicated that a further orthogonal decomposition

of the sum of squares may be of interest. These (indented) portions of

Table A-l will be discussed later in Sections A. 3. 2 and A. 4. (It is not

customary to show the over-all average as a "source of variability", and

the quantity G^/25 listed as its sum of squares is usually called the

"correction factor". The first row of Table A-l may be ignored during

the discussion of analysis of the unit design.)

A. 3.1 Main Effects

In the textbook analysis of a Latin Square design, the "extra"

variance component Cf2 is not present. The tests for the main effects

of days, samplers and locations are F-tests. For example, the mean

square for Days is the sum of squares divided by the associated degrees

of freedom (d.f.), MSD=SSD/4, the mean square for Error is MSE=SSE/12,

and F=MSD/MSE with 4 and 12 d.f. is the test statistic calculated to assess the significance of day-to-day differences.

Two points must be considered in the interpretation of these F-ratios

under the assumptions of the statistical model stated in Section A. 2.

(1) It must be assumed additionally that the errors e. are normally

distributed—or approximately so.

1

(2) It must be recognized that the F-tests are approximate unless

o

2 =0—or is small in comparison to a

2

, m e Although the statistical tests are approximate, the interpretation

of the F-ratios is guided by the "expected mean squares" which are calculated from the assumptions stated in Section A. 2.

A. 3.2 Comparing Locations

An orthogonal decomposition of the sum of squares for Locations is

indicated in Table A-l. This analysis is of potential interest for

several reasons:

(1) If the Location effects are signficant, it may be possible to

identify meaningful structure such as f ront-to-rear gradient.

(2) Unlike the Day and Sampler effects, the Location effects are "unsymmetrical" with respect to the possible presence of the variance

component associated with the mining machine operator.

30
ANALYSIS

OF

VARIANCE

FOR

THE

UNIT

DESIGN

w

O)p«3

cr 03C

CO3a3po

0)a.*H

COa)P

cO3

cr

C/3 <POe3

C/3

ipO3 E 3 o 3 XI P 3

00 P 3 FP Q

C4-t P O PP 3O

>-i 3 3 •H O P

03 3> IU CM Dl1 cn

c\l 3 2 m

<M 3 i CM 31

-3

C3 to to 1 o D o + + + 1 3 +

CM 0 1 03CM 6

CM 0 2 m

to to to 1 rH | LO G

iH | m P cm 3 cm 3 Pjin rH | in 1 X3P

to to + + + 1 + 11 + +

CM CM XI CM 3 CM o*| 3 CM 0 CM 0

3- CD CD CD | 3 to

D

mW

W CH 1 03 CM in|-cr m|<r m|-cri

p | m l v—/

cn|m illi W l 03 iI 03 1i O 1 II i O 1 i i—i i m i \ i CM i CM -— i /~> j CM i cn i U i O P l lI CM | 1 <r 9i CM 1 1 P < i 03 P 03 p i m m i 03 • 03 03 03 | P P 1 a

03 03 03 | 1 3 1 l + 03

II II II 1 03 1 o O *sf 1 03

n

m

mm i p i—1 P p 1 03p

CM CM CM ! X *-— CM CM 1 + 1 1 3

CM CM CM | ^—V / N P O o O 1 in CM CM CM | Q 1 P P P P 1 03 3 1 1 1 1 03 3 1 1 | + + 03 LO m m m i 1 N-/ CM c—1 P 1 1 | 1

CM -3 CM 3 CM P I P P P P 1 CM P 2

CM

Q 03

p 1 V

W

'— 'w' '—' 1 >o 03 o w w W j111 w

03 P sf 11111 I—1 P p i—1 CM MT 11 i—1 11 f N 1 P ~\ P 1 1 P P 3 1 1 00 P P 1 1 •H 00 P 1 1 pi •H O 1 1 DS P 1 • • j O 1 3 • p 3 1 P i—1 1 > 3 3 > 1 3 3 1 > 3 P > 1 P Pi • j 3 3 1 ip P a i CU rH 1 3 P • O 1 O 1 P 3 3 P 1 P > 3 1 3 3 1 * 3 1 C 3 1 P P P 1 P

X) 3 1 c p

a P 1 P 3 3 1 o 3 o a i O 3 p O 1 P 3 p 3 1 3

00 3 •H 1 P Pi

p 2 2 3 rH 4-1 I 1 P p 3 P 3 1 o 3 >1 0 O 1 p > 3 3 O 1 p < P 03 P 1 w

<n a) Da

03

03I w

0303

00

cO3

03

CO3

DC 3 00 P C 3 O 3 i-i cr p

03 C.6 C 3 3 3 3 3 a 3

31 =

('Sum

of

Squares)

/d.f.

and

the

expected

values

have

been

calculated

under

the

stated

in

Section

A.2
Following are the expected mean squares for the four orthogonal

comparisons among locations that were listed in Table A-l.

Source

Front (Left vs. Right)

Rear (Left vs. Right)

Front vs . Rear

Machine Op. vs. Other

Expected Mean Square

2 (6 FL

0 FR

)2‘K7 e

2 (0 RL

0 RR'

) 2+

°e

5 (e F

-eR)W

(v^y 0 + 0 r,\2 / F + \a 2 + o

2 2 / 5 m e

The subscripts on the 0's correspond to column headings in the diagram

in section A.l, except for the abbreviations 6 - (0 +0 )/2,

r r L r K

0 = (0 +0 )/2. If the location effects do appear to be significant,

R KL KR

notice that some location comparisons should be based on error estimates

that exclude a

2

. On the other hand, if the location effects appear not

to be significant (i.e., 0^=0 for all subscripts, at least approximately),

then the decomposition of the Location Sum of Squares gives additional

estimates of the relative magnitudes of o

2 and a2

. In any case, the two

"right-left" differences should be small fince tfie two samplers at the

front (rear) of the mining machine are packaged together. The sums of

squares for these two comparisons may be compared (possibly pooled) with

SSE.

A. 4 Variance Components, Unit Design

The textbook sum of squares for error (SSE in Table A-l) is an estimate of a

2 +o 2 /5, combining both of the variances that are hypothesised in the statistical model considered here. SSE can, however, be

expressed as the sum of two terms of which one is an estimate of a

2 alone. The general idea is to use the five observations made at

location 3 (Machine operator) to obtain an estimate involving a

2

, and

to estimate a

2 from the other 20 observations. The exact details are

0

a little more complicated because there are only 12 degrees of freedom

for estimation of error.

Table A-l shows a convenient (desk-calculator) formula for

calculating SSE. The result is identical to the result that would

32
be obtained by calculating the sum of 25 squared "residuals’*. The

residual r. associated with the observation y. is the difference between

y, and the value y. calculated using the estimates 0 of the main effects.

E^g., r^ = yy y3

, where y^ is the sum of

V = G/25,

0 d = D

1 /5-y (day one),

0^ = L^/5-y (location three),

0 = S /5—0 (sampler C)

S \j Although there are 25 such residuals, they are not statistically independentthe average y and the three sets of main effects have been estimated and

subtracted from the observed values..

The linear algebra of least squares estimation can produce for each

of the 25 residuals a formula expressing it as a linear combination of

the 25 original observations y.. For example, again using the third

observation, r_ = 1^ [— 3y_ -3y„ + 12y„...]; to complete the formula,

25

a condensed notation is introduced. The 5x5 array below displays the

coefficients of y^,...,y2 3(in the order specified in Section A.l) for

calculation of ry

1

25

-3

2

-3

2

-3

2

2

-3

12

-3

-3

-3

-3

-3

-3

2

2 2

2 2

2 2 -3 2 -3

The set of 25 residuals can be replaced by a set of twelve statistically independent residuals r' , r',...,r' ? in such a way that

£25 r

2 = £12 ,2

^~J ±=1 L ± ^-'j=l j ; the method is indicated in a paper by Cameron [1],

This has been done in such a way that only the first four orthogonal

residuals contain information about the value of a

2

. The first four m

are displayed below in two ways. First, for convenient calculation (if

the residuals are already available from a least squares analysis by

computer)

1

2

5/3 r

6

4 (r3

+ 4r8>

33
4

+ r

8 + 3r n)

+ r

8 + r n + 2r18 )

4 2 The quantity SSM shown in Table A-l may be calculated from SSM = T_._^rj , but it is readily verified that SSM is actually proportional to the sum

of squares of the five residuals in the middle (machine operator) column:

2 SSM - ) . There is no need to show the remaining f

(r

3

2 + r

8

2 + + r 23

8 r

j

, since the last sum of squares, SSR, is obtained by subtraction.

The second display of r^,...,r^ shows them as linear combinations

of original y^, in the condensed notation introduced above, omitting the

display for r^ since it is proportional to r^, whose coefficient array

was shown above:

= 1 /Jo

-1 0

0 1

0 0

0 -1

1 0

0

9

-3

-3

-3

0

0

6

-3

-3

0

0

0

3

-3

1

0

-1

-1

1 3k
Notice first the middle column of each array: there are four orthogonal

comparisons among the observations made at the machine-operator location

The smaller coefficients in other parts of the array are due to correlations among the original residuals, but the row-sums, column-sums, and

sampler-sums of these coefficients are all zero, so it is clear they are

not estimating any of the main effects (under the assumptions of our statistical model)

The ratio of the two mean squares obtained from this decomposition

SSM/4

of SSE provides an F-test which is not approximate, F- g—

y

-g with 4,8

d.f. One such test will not provide a definitive result, but an accumu- lation from several runs of the unit design can increase confidence in

the evaluation.

As a final remark, note that the orthogonal decomposition is not

unique: for example, it could have started with

r" = 5/3 r 23/6

and used the middle-column residuals from the bottom up. But the sum of

squares SSM would always have the same value.

A. 5 Combining Results from Several Designs

The proposals for analysis given in this section are less specific

than those for the unit design, since the approach to analysis depends

on (1) relative magnitudes of main effects and variance components defined for the unit design and (2) the purpose of the analysis.

The two chief purposes that can be served by analysis of a group

of unit designs (say, the group proposed for the pilot experiment) are

(a) to assess the uncertainty of the 10-day (or 5-day) average calculated for checking compliance with the dust level standard under current

regulations and (b) to assess the uncertainty of the dust level determinations made under current regulations when they are considered as measurements to assess the effectiveness of dust control. In the latter

case, the large day-to-day variations of dust level are important and

must be treated in a new way in a statistical model for analysis of the

data.

Analyses for these two purposes will be discussed separately.

Section A. 5.1 is on the uncertainty of a 10-day average and covers the

analyses that would be considered for the pilot experiment, including

those needed to determine whether a large survey would be desirable.

Section A. 5.2 introduces the need for a new model for analysis of the

uncertainty of dust level measurements in the broader context.

A. 5.1 Uncertainty of Ten-Day Average

In the basic statistical model for evaluation of the uncertainty

35
of a ten-day average, it is assumed that there is a fixed dust level

y^ for each of the d=l,2,...,10 days:

E(y

d

) -p

d , where y^ is the observation on the d th day. The quantity of interest

for regulatory action is

y = (y

1+. . .+ y 1Q)/10 ,

and its value is estimated by

y " hV10 •

The observed values y^ differ from their expected values because of

"error" and, since the machine operator's personal sampler is used for

these measurements, the statistical model includes both types of error defined in the statistical model for the unit design. Observation y^ is

represented by

ya = E (y^) + ea +

= y d + ed + m

d

(M-l)

The errors are assumed to be statistically independent and to have

variances a

2

, a^, respectively.

Data obtained in the pilot experiment would be used to estimate

a

2 and a

2 and the variance of y, e m

J

Var(y) = (a 2 + a

2 )/10 , e m

and to assess the precision of the estimate of Var(y). Data obtained in

the pilot experiment would also be used to check the adequacy of the

simple model (M-l) stated above and the assumptions about the errors.

The model (M-l) is closely related to the model adopted for analysis

of the unit design. Here y^ includes the over-all average dust level plus

the effect of the d th day. An equivalent expression would be

p

d = p + e( <6

i + --' + ho * 0)

The effect of location is not included, since all measurements are made

at the machine-operator location. Omission of sampler effects from the

model is discussed below.

The chief analyses of data from the pilot experiment would be

directored to assessing the relative magnitudes of variance components . (1) Each unit experiment provides a test of the hypothesis a

2 = 0

(the F-ratio derived at the end of Section A. 3. 2). (2) Eachm

of the

unit experiments provides an estimate of a

2 based on 8 degrees of freedom.

e 36
These would be tested for equality (e.g., by Bartlett's test, see Dixon and Massey [2], pages 179-180). If they should appear not to

be equal, possible reasons such as (2a) monitored vs. unmonitored

experiments, and (2b) differences between machine operators or mines,

would be tested. Depending on the outcome of analyses for equality of

variance, there could be (3) one or more sets of pooled estimates of

a

2 and a

2

, the latter being estimated only if it appears to be significantly different from zero.

The effect of the sampler (or samplers) used might have to be

included in the statistical model, and does have to be included in the

complete uncertainty analysis. Two cases can be described briefly,

though the actual analysis would probably require additional information:

(1) the machine operator selects "at random" a sampler from the collection

maintained at the mine; (2) the machine operator uses the same sampler on each of the ten days. In the first case, the statistical model might

need to be amplified by adding an additional "error" due to sampling of

samplers. The magnitude of this error could be estimated by laboratory

tests of company samplers; it is possible that it would be small enough

to be neglected (in effect, incorporated into the other errors). In the

second case, there would need to be an estimated limit for any systematic

error that might be present due to the particular sampler used, to be

added to the statistical uncertainty limit for the estimated average

dust level.

Differences among samplers are estimated in the pilot experiment

but the pilot experiment would not provide information about variability

of company samplers if Bureau of Mines samplers were used. Unless there

is strong reason to believe that the accuracy of samplers as maintained

by the company has an effect on the way they are used by the machine

operators, it appears advantageous to estimate the variability due to

differences among samplers in a separate investigation. (A larger

survey following the pilot experiment might include the use of company

samplers if evaluation of this source of variability seemed to require

further investigation).

The summary of analyses of the pilot experiment would indicate

strategies for stratified sampling in the larger population of mines,

and give variance estimates for use in determining sample sizes needed

in a larger survey.

A. 5.

2

Over-all Uncertainty

When the ten-day average dust level is thought of as a sample

estimate of the average dust level in a mine, the daily average dust

level (even if measured without error) is a value obtained on a sample

day. A statistical model appropriate for analysis in this broader

context postulates a long-run average dust level u for a mine and

represents a combination of explanatory and random variables that may

be involved in departures from the long-run average.

Examples of explanatory variables that might be considered are

37
type of coal seam or any other operating conditions that may be

associated with dust level.

The model might be expressed in the following form:

yd

p + I

B k

x

kd + M

a + ewd • k=l

where

y, = observed level on day d,

d

= value on day d of the kth. explanatory variable (e.g., 1 or

0 for presence or absence of some condition)

,

g = regression coefficient for kth explanatory variable,

K. M, = random effect of day d,

de , = within-day error on day d (includes e. and m,)

wd d d

Statistical assumptions about the within-day errors e ^ are derived from

those made above for e^ and m, . The random day-to-day differences M, are assumed to be statistically independent of the other errors, to have

zero expected values, and variance a

2

.

Analysis of the pilot experiment provides estimates of a

2

, since

each unit experiment provides a mean square for days. With the revised

model, the expected mean square for days is given by the expression in

Table A-l with (£0^ 2 /4) replaced by a

2

. The F-ratio comparing SSD/4 to

SSE/12 gives an approximate F-test for the hypothesis a

2 =0. Available

evidence suggests that this statistical test will not be needed —that the

day-to-day variability is vastly larger than within-day variability due

to differences among samplers and machine operators.

The variance of a ten-day average, in terms of the expanded model, is

(a 2 + a

2 + a

2 )/10

d m e A principal outcome of the pilot experiment would be to assess

the need for precise information about the values of a

2 and a

2 r , conin 0 sidering the magnitude of their contribution to the over-all uncertainty.

A caution should be expressed.

In all the suggested analyses of the pilot experiment, it must be

expected that "problems" would arise. If samplers malfunction or if the

rotation scheme for a unit experiment is not followed exactly the

statistical analysis becomes more difficult. The formulas given in

Sections A. 3 and A. 4, and the analyses suggested in this section cannot

be applied mechanically, but should be preceded or accompanied by graphical analyses to check the general assumption that the statistical distributions of errors are reasonably well-behaved. Should such checks

fail, the interpretation of estimated variances would need to be made

with great care.

38
A. 6 A Numerical Example

The following is a numerical example carrying out the computations

required for the analysis of variance exhibited in Table A-l. The

experiment in which these data were obtained did not exactly follow the

unit design, in that the samplers were assigned to fixed locations, but

the numerical computations have been done as if the samplers had been

rotated. Interpretation follows the computations.

Data From Test Shift 1,2, 3, 6, 7, EEAC

Test Series F, A-Shift

(Attached to Letter From Welby Courtney to H. H. Ku, Nov. 7, 1977)

Location

Day

Vv

'N. RL RR M FL FR

1 1.10 1.12 1.42 2.01 2.78 8.43

2 2.44 2.41 2.54 4.57 6.44 18.40

3 0.52 0.64 2.23 1.75 1.68 6.82

4 3.57 3.46 4.19 5.04 6.36 22.62

5 4.43 4.51 9.18 7.89 7.91 33.92

12.06 12.14 19.56 21.26 25.17 90.19

Sampler Totals

Sampler A B C D E

1.10 2.44 0.52 3.57 4.43

4.51 1.12 3.46 2.41 0.64

4.19 2.23 1.42 9.18 2.54

1.75 7.89 4.57 2.01 5.04

6.44 6.36 7.91 1.68 2.78

17.99 20.04 17.88 18.85 15.43

39
Estimates of Main Effects

for the Model: E(y

±

) = y + 6 , + e. + 0 d £ s

y = 90.19 = +3.6076

A 25

V d=l 8.43/5 - 3.6076 = -1.9216

2 (18.40/5) - If = + .0724

j

3 (6.82/5) - II = -2.2436 \ days from

average

4 (22.62/5) -

II = + .9164

5 (33.92/5) - II = +3.1764

AV

it (12.06/5) - II = -1.1956

2 (12.14/5) - If = -1.1796

3 (19.56/5) - II = + .3044

locations from

^ average

4 (21.26/5) - II = + .6444

5 (25.17/5) - II = 1.4264

V s=A (17.99/5) - II = - .0096

B (20.04/5) - II = + .4004

C (17.88/5) - II = - .0316 samplers from

average

D (18.85/5) - II = + .1624

E (15.43/5) - II = - .5216

See pp. 13-32, Experimental Statistics (reference [12] of report).

40
Computation of r'

3 8 13 18 23

V 3.6076 3.6076 3.6076 3.6076 3.6076

T3

<

CD -1.9216 .0724 -2.2436 .9164 3.1764

<

CD .3044 .3044 .3044 .3044 .3044

A

e s - .0316 - .5216 .4004 - .0096 .1624

y 1.9588 3.4628 2.0688 4.8188 7.2508

y 1.42 2.54 2.23 4.19 9.18

r .5388 - .9288 .1612 - .6288 1.9292

r' .7777 -1.5764 - .5154 -2.3351 (undefined)

SSM =|2r ,2 = 8.8084

Residual = 3.9419

SSE 12.7503

Check: SSM = r

^ = 8.8084

41
Analysis

of

Variance

of

Unit

Design

X * -X 3 X X •X 3 X -X X

X

CO r—1

00 CO 00 NO cO »H

m o 3 40 <r <r 00 O 00 cr CM CN CN

cr r^. o CNOO NO o <r

co

mmmO r>*mO CN 3 NO 1—1 t 1 CN o

co cn CN

a) S3

0)3

c03 <r CN CO CO CO 40 i—1 « 1 CN cr

cr CT cr. 00 o 00 cr o 00 rH

co VO o cr. rH CN o o m o

CO CO CM 00

m o r-*

m 00 cr

4-1o LH 00 CN 40 1—1

<3* CN 00 CO

CN CT Csl CN rH e CO 3

co

4-1O So 3 to 3 3 rH <r rH t 1 rH rH CN <r 00

qj a) 1 1 3 3

bO 44 3o

/"“N

4-1 3 S 4-1 -3 4-1 3 CO

•H bO -3 -3 CO f—1 *H bO 4-1 •H 5-t •H O

rQ 3 3

CO • • o

*H CO • 3 3 4-1 /-N 3 > CO 3 > 3 Pi

cO 5-1 > 3 3 CO > O 4J Pi • 3 CO

4-1 44 4-1 34 34 V-/

M-l

O /"“N

p 0) 44 • O

O o cO CO CO 1 1 0) iH

44 CO CO 'Wt 1 > 3 3 3

CO CO VwC- V— 3 3 3

0) 3 /""N 4-1 4-1 •H

w •H 35 o O Q CO 3 3 3 -3 CO -3 •H

5-i *rl CO CO 3 o 3 O

O COO 3 3 4-1 CO 5-i o 3 3 3 3 V 3 3 O a ''w' (1) •rH fH Pi JH S g p3

C/3 3 tH 4-1 3 3 CO a 3 o

5-1 fo S O 3 o cO cO O 3 o Q CO hJ W

42

Significant

at

.05

level
The main purpose of the numerical example is to illustrate the computations required for the analysis of variance of a unit experiment. In

addition, the interpretation of the results may be discussed—with caution.

In the analysis of variance table, notice that the Samplers effect

has a small mean square. This is consistent with the fact that the samplers

were not rotated, and the Samplers mean square (MSS) is actually estimating

the same thing as the Error mean square (MSE) . The "Locations" effect, on the other hand, includes all of any sampler differences that may have

been present.

When the Locations effect is broken down into four parts, it appears

that the left-right differences (samplers packaged together) are small or non-existent, unless there were compensating differences between the

samplers.

The estimate of a

2

, from MSR, is

e

a

2 = 0.4927 , e

*

and the estimate of a

2

, using the formulas for the expected mean squares

shown in Table A-l, is

a

2 = -y (MSM-MSR) m J = 2.8488 .

These numerical results illustrate those that might be expected from

a unit experiment, but the verification of assumptions using a Dry Run is

nevertheless still necessary.

The computations for this numerical example were repeated using

the logarithms of the data, but the results were the same qualitatively

(including the tests of significance) and are not shown.

A. 7 References for Appendix A

[1] J. M. Cameron, An Algorithm for obtaining an orthogonal set of

individual degrees of freedom for error, J. Research NBS - B. Math.

& Math. Physics, Volume 67B (1963), pp. 19-22.

[ 2 ] Dixon, W. J. , and F. J. Massey, Jr., Introduction to Statistical

Analysis , Second Edition, McGraw-Hill, 1957.

43
MD3-I I 4 A (KEV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. 2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

A Suggested Experimental Plan for the Determination of the

Accuracy and Reliability of Coal Mine Dust Measurements

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S) k Harry H. Ku and Joan R. Rosenblatt8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

.mi 77013

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

U. S. Department of the Interior

Bureau of Mines

4800 Forbes Avenue, Pittsburgh, PA 15213

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

\

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

In an agreement between the Bureau of Mines and the National Bureau of Standards

dated February. 1 , 1977 , on the "Determination of the Accuracy and Reliability of

Coal Mine Dust Measurements," NBS is to submit a report to BOM at the conclusion

of the Phase I part of the work. This document is the report called for in the

agreement

In Section I of this report, the terms "reliability" and "accuracy" are clarified

and defined for the purpose of this investigation. Certain pertinent information, collected as results of personal contacts and study of existing literature, is

presented and discussed. In Section 2 an experimental design is suggested to measure

He various sources of variability as relating to the use of approved personal

samplers by coal miners in underground mines." In Section 3, a dry run is suggested

o test the efficacy of the design. Pilot experiments on 10 to 12 mines are also recommended to obtain preliminary estimates of variabilities due to different sources. JL& f+

tl0n k 9X1 ove

f

a11 view is presented as to factors that may contribute to the esultmg uncertainty of coal mine dust measurements.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Coal mine dust; accuracy; reliability; design of experiment; personal sampler;

pneumoconiosis

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