[Federal Register Volume 63, Number 22 (Tuesday, February 3, 1998)]
[Notices]
[Pages 5687-5712]
From the Federal Register Online via the Government Publishing Office [www.gpo.gov]
[FR Doc No: 97-33937]


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DEPARTMENT OF LABOR

Mine Safety and Health Administration


Coal Mine Respirable Dust Standard Noncompliance Determinations

Correction and Republication

    Note: For the convenience of the user, notice document 97-33937 
is being reprinted in its entirety because of numerous errors in the 
document originally appearing at 62 FR 68395-68420, December 31, 
1997. Those wishing to see a listing of corrections, please call 
Patricia Silvey, Mine Safety and Health Administration, 703-235-
1910.

AGENCY: Mine Safety and Health Administration, Labor.

ACTION: Notice; final policy.

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SUMMARY: This notice announces the Mine Safety and Health 
Administration's (MSHA) final policy concerning the use of single, 
full-shift respirable dust measurements to determine noncompliance and 
issue citations, based on samples collected by MSHA, when the 
applicable respirable dust standard is exceeded. This notice should be 
read in conjunction with the notice published elsewhere in today's 
Federal Register jointly by the Department of Labor and the Department 
of Health and Human Services.

EFFECTIVE DATE: This policy is effective March 2, 1998.

FOR FURTHER INFORMATION CONTACT: Ronald Schell, Chief, Division of 
Health, Coal Mine Safety and Health; MSHA; 703-235-1358.

SUPPLEMENTARY INFORMATION:

I. About This Notice

    This notice provides information about MSHA's new enforcement 
policy for the use of single, full-shift respirable dust measurements 
obtained by inspectors to determine noncompliance with the respirable 
dust standard (applicable standard) under the MSHA coal mine respirable 
dust program. A question and answer format has been used to explain the 
background for the enforcement policy, the reasons for the policy 
change, and the specific elements of the new policy. In addition, 
several appendices are attached to and incorporated with this final 
notice which address technical issues concerning the new enforcement 
policy.

II. Background Information

A. How Has MSHA Sampled Coal Mines for Noncompliance in the Past?

    Prior to October 1975, noncompliance determinations were based on 
the average of full-shift measurements collected from individual 
occupations on multiple shifts. MSHA interprets a full shift for 
underground coal mines to mean the entire shift worked or 8 hours in 
duration or whichever time period is less (30 CFR 70.201(b)). The need 
to reduce the Agency's administrative burden attributable to inspector 
sampling prompted MSHA to revise its underground health inspection 
procedures and redirect the Agency's enforcement resources away from 
sampling and toward assessing the effectiveness of mine operators' 
respirable dust control programs.
    Since October 1975, MSHA has determined noncompliance with the 
applicable standard based on the average of measurements obtained for 
different occupations during the same shift of a mechanized mining unit 
(MMU), or on the average of measurements obtained for the same 
occupation on successive days. The term MMU is defined in 30 CFR 
70.2(h) to mean a unit of mining equipment, including hand loading 
equipment, used for the production of material. MSHA inspectors 
routinely sample multiple occupations to determine compliance with the 
applicable standard, assess the effectiveness of mine operators' dust 
control programs, determine whether excessive levels of quartz dust are 
present, and verify the designation of the ``high risk occupation'' 
(now referred to as the ``designated occupation'' or ``D.O.''--the 
occupation on a working section exposed to the highest respirable dust 
concentration) to be sampled by mine operators.
    Under the sampling procedures in place between 1975 and 1991, MSHA 
inspectors would collect full-shift measurements from the working 
environment of the ``D.O.'' and four other occupations, if available, 
on the first day of sampling each MMU. The mine operator was cited if 
the average of all measurements obtained during the same shift exceeded 
the applicable standard by at least 0.1 milligram of respirable dust 
per cubic meter of air (mg/m<SUP>3</SUP>). If one or more measurements 
exceeded the applicable standard but the average did not, the Agency's 
practice was to continue sampling for up to four additional production 
shifts or days. If the inspector continued sampling after the first day 
because a previous measurement exceeded the applicable standard, 
noncompliance determinations were based on either the average of all 
measurements taken or on the average of measurements taken on any one 
occupation. Thus, if the average of measurements taken over more than 
one day on all occupations was less than or equal to the applicable 
standard, but the average of measurements taken on any one occupation 
exceeded the value set by MSHA (based on the cumulative concentration 
for two or more measurements exceeding 10.4 mg/m<SUP>3</SUP>, which is 
equivalent to a 5-measurement average exceeding 2.0 mg/m<SUP>3</SUP>), 
the operator was cited for exceeding the applicable standard.
    In some instances, MSHA inspectors sampled for a maximum of five 
production shifts or days before making a noncompliance determination. 
However, most citations issued prior to 1991 were based on the average 
of multiple measurements on different occupations collected during a 
single shift. To illustrate, MSHA conducted a computer simulation using 
data from 3,600 MMU inspections conducted between October 1989 and June 
1991. This simulation showed that a total of 293 MMUs would have met 
the criteria to be found in noncompliance with the applicable standard 
based solely on the average of multiple measurements. Two hundred 
forty-two of those noncompliance determinations, or 83 percent, met the 
citation criteria based on sampling results from the first day of MSHA 
sampling, rather than from multi-day sampling. Only 51 MMUs, or 17 
percent, were citable based on the average of measurements collected 
over multiple shifts or days. These statistics clearly show that the 
citation criteria were met based not only on the average of 
measurements taken during several shifts, but also on the average of

[[Page 5688]]

multiple measurements obtained during the same shift.

B. Why Did MSHA Establish the Coal Mine Respirable Dust Task Group and 
Initiate the Spot Inspection Program?

    In 1991 concerns were raised about the adequacy of MSHA's program 
to control respirable coal mine dust in underground coal mines. In 
response to these issues, MSHA established the Coal Mine Respirable 
Dust Task Group (Task Group) to comprehensively evaluate the 
effectiveness of the Agency's respirable dust program.
    The Task Group was directed to consider all aspects of the current 
program, including the role of the individual miner in the sampling 
program; the feasibility of MSHA conducting all sampling; and the 
development of new and improved monitoring technology, including 
technology to continuously monitor the mine environment. Among the 
issues addressed by the Task Group was the actual dust concentration to 
which miners are exposed. As a result, the Agency initiated a special 
respirable dust ``spot inspection program'' (SIP), designed to provide 
the Agency with more accurate information on the dust levels to which 
miners were exposed, through sampling, in the underground coal mine 
environment.

C. How Was Sampling Accomplished During the SIP?

    Because of the large number of mines and MMUs involved and the need 
to obtain data within a short time frame, sampling during the SIP was 
limited to a single shift or day, a departure from MSHA's normal 
sampling procedures. As a result, the Agency determined that if the 
average of multiple occupation measurements taken on an MMU during any 
one-day inspection did not exceed the applicable standard, the 
inspector would review the result of each sample individually. If any 
individual measurement exceeded the applicable standard by an amount 
specified by MSHA, a citation would be issued for noncompliance, 
requiring the mine operator to take immediate corrective action to 
lower the average dust concentration.
    The sampling practice under the SIP was similar to the practice of 
the Metal/Nonmetal Health Division of MSHA, and the Occupational Safety 
and Health Administration (OSHA), which use a single, full-shift 
measurement for noncompliance determinations, and provides for a margin 
of error to account for uncertainty in the measurement process 
(sampling and analytical error). This resulted in the issuance of 
citations using a single, full-shift measurement only when there was a 
high level of confidence that the applicable standard was actually 
exceeded.
    Thus, during the SIP inspections, MSHA inspectors cited violations 
of the current 2.0 mg/m\3\ standard if either the average of five 
measurements taken on a single shift was greater than or equal to 2.1 
mg/m\3\, or any single, full-shift measurement was greater than or 
equal to 2.5 mg/m\3\. Similar adjustments were made when the 2.0 mg/
m\3\ standard was reduced due to the presence of quartz (crystalline 
silica) dust in the mine environment.

D. What Did the SIP Show About MSHA's Sampling Policy?

    MSHA's review of the SIP inspections showed that 28 percent of 718 
MMUs sampled exceeded the applicable standard and would have been 
citable based on a single, full-shift measurement, but only 12 percent 
would have been citable using the average of all measurements for the 
MMU.
    Based on the data from the SIP inspections, the Task Group 
concluded that the Agency practice of determining noncompliance based 
solely on the average of multiple measurements did not always reveal 
situations in which miners were overexposed. For example, if the 
measurements obtained for five different occupations within the same 
MMU were 4.1, 1.0, 1.0, 2.5, and 1.4 mg/m\3\, the average concentration 
would be 2.0 mg/m\3\ and no enforcement action would be taken, even 
though the dust measurements for two of these occupations significantly 
exceeded the applicable standard. While such individual measurements 
were not cited prior to the SIP, they would clearly demonstrate that 
some miners were overexposed. MSHA policy prior to the SIP however, 
required the inspector to return to the mine on the next production day 
and resume sampling, rather than issue a citation at the time the 
overexposures were discovered.

E. Why Did MSHA Decide To Permanently Adopt the SIP Procedures?

    The SIP inspections revealed instances of overexposure that were 
masked by the averaging of results across different occupations. This 
showed that miners would not be adequately protected if noncompliance 
determinations were based solely on the average of multiple 
measurements. The process of averaging dilutes a high measurement made 
at one location with lower measurements made elsewhere. Similarly, 
averaging a number of full-shift measurements can obscure cases of 
overexposure.
    Additionally, the Task Group recognized that the initial full-shift 
samples collected by an inspector are likely to show higher dust 
concentrations than succeeding samples collected on subsequent shifts 
during the same inspection. MSHA's data showed that the average 
concentration of all samples taken on the same occupation on the first 
day of an inspection was almost twice as high as the average 
concentration of those taken on the second day. MSHA recognized that 
sampling on successive days after an inspector first appears could 
result in measurements that are not representative of dust conditions 
to which miners are typically exposed. Unrepresentative measurements 
would arise if mine operators anticipated the continuation of inspector 
sampling and made adjustments in dust control parameters or production 
rates to reduce dust levels during the subsequent monitoring. None of 
this is specifically prohibited by MSHA regulations. As a result of 
these findings, which indicated that miners were at risk of being 
overexposed, MSHA decided to permanently adopt use of the single, full-
shift measurement inspection policy initiated during the SIP. These 
procedures were used by MSHA until the issuance of the decision by the 
Federal Mine Safety and Health Review Commission in the case of 
Keystone Coal v. Sec. of Labor, 16 FMSHRC 6 (Jan. 4, 1994). Since that 
decision, MSHA has reverted to its previous practice of basing 
noncompliance determinations on the average of multiple, full-shift 
measurements. (Please see the notice of joint finding by the Secretary 
of Labor and the Secretary of Health and Human Services (HHS) published 
elsewhere in today's Federal Register for an explanation of this 
decision.)

III. Why MSHA Is Revising Its Enforcement Policy

A. What Has Changed To Warrant Revising the Existing Enforcement 
Policy?

    During the public hearings held on the proposed joint finding that 
a single, full-shift sample is an accurate measurement, during the 
public meetings held on this enforcement policy notice, and in other 
comments submitted to the Agency, several commenters questioned why the 
current program should be altered. The commenters asserted that MSHA's 
practice of issuing citations based on the average of multiple 
measurements has

[[Page 5689]]

been in effect since the 1970s, that technology and equipment 
associated with sampling remain essentially the same, and that 
substantial progress had been made in lowering respirable dust levels 
at U.S. coal mines.
    As stated in the final notice of joint finding published elsewhere 
in today's Federal Register, significant improvements have in fact been 
made in the dust sampling process. Although MSHA agrees that progress 
has been made in reducing average dust concentrations, the SIP 
inspections clearly showed instances of excessive dust concentrations 
that would have been masked by the procedure of averaging measurements. 
Specifically, of the 718 SIP MMUs with valid single, full-shift 
measurements, 203 MMUs had at least one single, full-shift measurement 
that was citable, while only 88 MMUs met or exceeded the citation 
threshold based on the average of multiple measurements. This clearly 
shows that under the procedure of averaging measurements miners would 
be at risk of being overexposed and MSHA would be unable to require 
operators to take corrective actions to protect them.
    MSHA believes that a single, full-shift measurement is more likely 
to detect excessive dust concentrations and thus protect miners than a 
measurement average across multiple occupations on a single shift or 
across multiple shifts for a single occupation. MSHA's computer 
simulation which analyzed data from over 3600 MMU inspections conducted 
between October 1989 and June 1991, showed that 814 MMUs had citable 
overexposures based on individual samples, but only 298 of these 
overexposures were citable on the average of measurements made within 
the MMU. Subsequent to the SIP, between January 1992 and December 1993, 
MSHA continued making noncompliance determinations on a single, full-
shift measurement, and 74 percent or 488 of the 658 MMUs cited by 
inspectors as having overexposures were found to be out of compliance 
based on a single, full-shift measurement, requiring mine operators to 
take appropriate corrective action. This experience clearly 
demonstrates that citing on a single, full-shift measurement, as 
opposed to citing on the average of measurements taken over multiple 
shifts, impacts miners directly, because it requires mine operators to 
take more prompt corrective action once an overexposure has been 
identified. This reduces the risk to miners of continued exposure to 
dust concentrations above the applicable standard on subsequent shifts.
    Furthermore, both NIOSH, in its recently issued criteria document, 
and the Secretary of Labor's Advisory Committee on the Elimination of 
Pneumoconiosis Among Coal Mine Workers recommended the use of single, 
full-shift measurements for determining compliance. According to the 
Committee report, issued in October 1996, the MSHA practice of not 
issuing citations based on single, full-shift samples ``is not 
protective of miner health, moreover, it is inconsistent with the 
stated intent of the Coal Act and the Mine Act, which require that 
exposure be at or below the exposure limit for each shift.''

B. Why Will MSHA No Longer Rely On Averaged Measurements of Dust 
Concentrations To Determine Noncompliance?

    MSHA's current enforcement strategy does not provide the optimal 
level of possible health protection. Basing noncompliance 
determinations on the average of different occupational measurements 
dilutes a measurement of high dust exposure with a lower measurement 
made at a different occupational location. Likewise, averaging 
measurements obtained for the same occupation over different shifts 
does not ensure that the concentration of respirable dust is maintained 
at or below the applicable standard during each shift. Section 
202(b)(2) of the Mine Act clearly requires that dust concentrations be 
maintained at or below the applicable standard ``* * * during each 
shift to which each miner in the active workings'' is exposed.
    Some commenters proposed that MSHA continue to average at least 
five separate measurements prior to making a noncompliance 
determination. They stated that abandoning this practice would reduce 
the accuracy of noncompliance determinations. Specifically, these 
commenters maintain that the average of dust measurements obtained at 
the same occupational location on different shifts more accurately 
represents dust exposure to a miner than a single, full-shift 
measurement. These commenters favored the retention of existing MSHA 
policy on the grounds that not averaging measurement results would 
reduce accuracy to unacceptable levels. Other commenters agreed with 
MSHA that the averaging of multiple samples dilutes measurements of 
dust concentration and masks specific instances of overexposure. Some 
of these commenters stated that averaging distorts not only the 
estimate of dust concentration applicable to individual shifts, but 
also biases the estimate of exposure levels over a longer term. 
According to these commenters, this is because dust control measures 
and work practices affecting dust concentrations are frequently 
modified in response to the presence of an MSHA inspector over more 
than a single shift. These commenters argued that the presence of the 
MSHA inspector causes the mine operator to be more attentive to dust 
control than normal.
    Section 202(b) of the Mine Act requires each mine operator to 
``continuously maintain the average concentration of respirable dust in 
the mine atmosphere during each shift to which each miner is exposed'' 
at or below the applicable standard. The greater the variation in 
mining conditions from shift to shift, the less likely it is that a 
multi-shift average will reflect the average dust concentration on any 
individual shift. For example, during one shift, production may be high 
and dust concentrations may also be correspondingly high. However, the 
next shift may experience lower production levels because of equipment 
breakdowns or because of unusual mining conditions. In addition, when a 
mine operator knows that the MSHA inspector is present, more attention 
may be given to ensuring that dust control measures operate 
effectively, and this may also affect the concentrations of respirable 
coal mine dust found on that shift. Because of such factors, multi-
shift averaging does not improve the accuracy of a noncompliance 
determination for the sampled shift. Therefore, MSHA is discontinuing 
its policy of relying on averaged dust concentrations. A more technical 
discussion of how averaging measurements affects accuracy is given in 
Appendix A.

C. Why Has MSHA Decided To Base Noncompliance Determinations Solely on 
a Single, Full-Shift Measurement?

    One commenter suggested that the new enforcement strategy proposed 
in MSHA's February 1994 notice, involving noncompliance determinations 
based on either a single sample or on the average of multiple samples, 
placed operators in ``double jeopardy'' of being cited--that is, it 
provided for two separate evaluations of whether the applicable 
standard has been exceeded. This commenter pointed out that this 
enforcement strategy would reduce the confidence level at which a 
noncompliance determination could be made.
    Under the MSHA policy proposed in the February 1994 notice, 
measurements made by an MSHA inspector for

[[Page 5690]]

different occupational locations would have been averaged together, not 
in order to estimate a hypothetical average concentration, but rather 
to ascertain whether dust concentration was excessive at any of the 
sampled locations. If the average of measurements across sampling 
locations exceeded the applicable standard, then at least one of the 
sampling locations would almost certainly have been out of compliance 
on the sampled shift. Therefore, the commenter was correct in asserting 
that noncompliance at each sampling location would have been evaluated 
twice: once using the single measurement specific to that location; 
and, if that test did not result in a citation, once again using the 
average of all available measurements.
    MSHA had determined that this strategy was necessary to provide the 
level of health protection to miners required by the Mine Act, and 
included this strategy in the proposed policy notice to protect against 
cases of evident noncompliance that would otherwise go uncited. For 
example, if five occupational measurements of 2.08, 2.28, 2.31, 2.25, 
and 2.17 mg/m<SUP>3</SUP> were obtained for an MMU on a 2.0 mg/
m<SUP>3</SUP> standard, no enforcement action would be taken if 
noncompliance is determined solely based on a single, full-shift 
measurement because no individual measurement meets or exceeds the 
Citation Threshold Value (CTV), defined in section IV.B. of this 
notice. On the other hand, averaging the measurements results in an 
average concentration of 2.22 mg/m<SUP>3</SUP>, indicating, with high 
confidence, that the applicable standard was exceeded.
    Although MSHA originally proposed using a combination of both 
strategies for determining noncompliance, various bodies of data show 
that such hypothetical occurrences are extremely improbable in 
practice. For example, MSHA's computer simulation discussed earlier in 
this notice showed that, between October 1, 1989, and June 30, 1991, 
298 MMUs would have been found in noncompliance with the applicable 
standard based on averaging multiple measurements. All 298 MMUs would 
also have been found in noncompliance using the single, full-shift 
measurement citation criteria. According to the data from the SIP, only 
one noncompliance determination would have been missed if all averaging 
had been discontinued. Similarly, analysis of more recent inspector 
sampling data for 1995 indicates that miners' health will not be 
compromised by discontinuing all measurement averaging. In fact, only 
one additional case of noncompliance would have been identified using 
averaging in addition to citing on a single, full-shift measurement. 
Therefore, MSHA will not continue to use this combination of 
strategies.
    As explained in the final notice of joint finding published 
elsewhere in today's Federal Register, MSHA's improved sampling and 
analytical method performs in accordance with the NIOSH Accuracy 
Criterion whenever a single, full-shift measurement is at or above 0.36 
mg/m<SUP>3</SUP>. The Agency believes that, in accordance with section 
202(f) of the Mine Act, this enables MSHA to base noncompliance 
determinations on a single, full-shift measurement whenever that 
measurement is at or above 0.36 mg/m<SUP>3</SUP>.

IV. The New Enforcement Policy

A. What Is MSHA's New Enforcement Policy?

    MSHA will continue its current dust sampling program as it relates 
to where and how many samples an inspector collects during a sampling 
shift. Specifically, MSHA will continue to collect multiple 
occupational samples for each MMU. The criterion for making 
noncompliance determinations has been revised and, under the new 
enforcement policy, MSHA will use a control filter capsule to adjust 
the resulting weight gain obtained on each exposed filter capsule. 
Noncompliance determinations will be based solely on the results of 
individual, full-shift samples, and MSHA will issue a citation whenever 
noncompliance is demonstrated at a high confidence level. The Agency 
will no longer rely on multi-locational or multi-shift averaging of 
measurements to determine noncompliance.
    The process by which a violation of the applicable standard will be 
abated by a mine operator will also remain unchanged. MSHA will 
consider a violation to be abated when samples collected in accordance 
with 30 CFR 70.201(d) demonstrate that the average dust concentration 
in the working environment of the cited occupation is at or below the 
applicable standard.
    When a measurement exceeds the applicable standard but is less than 
the CTV, noncompliance is not demonstrated at a sufficiently high 
confidence level to warrant a citation. However, MSHA will consider 
whether to target the MMU or environment for additional dust sampling. 
See Appendix B for further discussion of why MSHA believes that such 
measurements indicate probable overexposure.

B. When Will MSHA Issue a Citation for a Violation of the Applicable 
Standard?

    MSHA will issue a citation for noncompliance when a single, full-
shift measurement demonstrates, at a high level of confidence, that the 
applicable standard has been exceeded. Although MSHA will continue to 
collect multiple occupational samples for each MMU, the Agency will 
generally issue only one citation for exceeding the applicable standard 
on a single shift on any one MMU. However, additional citations may be 
issued when excessive dust concentrations are detected for occupations 
exposed to different dust generating sources.
    To ensure that citations are issued only when there is a high level 
of confidence that the applicable standard has been exceeded, MSHA has 
developed the Citation Threshold Values (CTV) below. Each CTV listed is 
calculated so that citations are issued only when the single, full-
shift measurement demonstrates noncompliance with at least 95 percent 
confidence. Citing in accordance with the CTV table does not constitute 
a raising of the applicable standard. Instead, it reflects the need for 
MSHA to ensure a sufficiently high level of confidence in its 
noncompliance determinations. Mine operators are still required to 
implement appropriate controls that will maintain the average 
concentration of respirable dust at or below the applicable standard on 
all shifts.

 Citation Threshold Values (CTV) for Citing Violations Based on Single, 
                         Full-Shift Measurements                        
------------------------------------------------------------------------
             Applicable standard (mg/m<SUP>3)                  CTV (mg/m<SUP>3)   
------------------------------------------------------------------------
2.0.................................................                2.33
1.9.................................................                2.22
1.8.................................................                2.11
1.7.................................................                2.00
1.6.................................................                1.90
1.5.................................................                1.79
1.4.................................................                1.68
1.3.................................................                1.58
1.2.................................................                1.47
1.1.................................................                1.36
1.0.................................................                1.26
0.9.................................................                1.15
0.8.................................................                1.05
0.7.................................................                0.94
0.6.................................................                0.84
0.5.................................................                0.74
0.4.................................................                0.64
0.3.................................................                0.53
0.2.................................................                0.43
------------------------------------------------------------------------

C. How Will the CTV Table Be Applied?

    Each single, full-shift measurement used to determine noncompliance 
will

[[Page 5691]]

be the MRE-equivalent dust concentration as calculated and recorded 
under MSHA's dust data processing system. Every valid measurement will 
be compared with the CTV corresponding to the applicable standard in 
effect. If any measurement meets or exceeds that value, a citation will 
be issued. However, no more than one citation will be issued based on 
single, full-shift measurements from the same MMU, unless separate 
citations are warranted for occupations exposed to different dust 
generating sources. Therefore, when single, full-shift measurements 
from two or more occupations show dust concentrations in violation of 
the applicable standard, as illustrated in the examples below, the 
inspector will determine the dust generation sources and require the 
operator to sample the environment of the occupation most affected by 
these sources which is consistent with current practice. In most cases, 
this will be the working environment of the ``D.O.'' However, if 
noncompliance is indicated based on measurements from two or more 
occupations on the same MMU which are exposed to the same dust 
generating sources, and which do not involve the ``D.O.,'' the 
occupation with the highest dust concentration will be identified in 
the citation as the affected working environment. In any case, when an 
inspector issues a citation for violation of the applicable standard 
under the new policy, the citation narrative will identify the specific 
environment or occupation to be sampled by the operator, as well as any 
other occupation(s) that exceeded the CTV.
    Several commenters requested that the application of the CTV table 
be clarified. The following examples illustrate how inspectors will 
apply the CTV table and make noncompliance determinations. Suppose that 
a measurement of 2.41 mg/m<SUP>3</SUP> is obtained for the ``D.O.'', 
and measurements of 2.34, 1.54, and 1.26 mg/m<SUP>3</SUP>, are obtained 
for three other occupations exposed to the same dust generating sources 
as the ``D.O.'' during a single shift on an MMU required to comply with 
an applicable standard of 2.0 mg/m<SUP>3</SUP>. Because at least one of 
the measurements exceeds the 2.33-mg/m<SUP>3</SUP> CTV (the citation 
value when the applicable standard is 2.0 mg/m<SUP>3</SUP>), a citation 
will be issued for exceeding the applicable standard on the shift 
sampled. Even though two individual measurements (2.41 and 2.34 mg/
m<SUP>3</SUP>) exceeded the CTV, one of which is on the ``D.O.,'' only 
one citation will be issued, specifying the ``D.O.'' as the affected 
working environment because all occupations were exposed to the same 
dust generating sources.
    Suppose now that in the previous example the 2.34-mg/m<SUP>3</SUP> 
measurement was obtained for a roof bolter, and the MMU was ventilated 
using a double-split ventilation system. This means that the roof 
bolter, working on a separate split of air from that of the continuous 
miner, is exposed to a different dust generating source than the 
``D.O.'' and, therefore, may not be adequately protected by dust 
controls implemented for the ``D.O.'' Consequently, two citations would 
be issued.
    As another example, consider an MMU with measurements of 2.14, 
1.92, 1.82, 1.25, and 1.12 mg/m<SUP>3</SUP>. Although none of these 
measurements meet the CTV, there is reason to believe that the MMU is 
out of compliance, since one of the measurements exceeds the applicable 
standard. However, because there is a small chance that the measurement 
exceeded the applicable standard because of measurement error, a 
citation would not be issued. As discussed elsewhere in this notice, 
additional samples would be necessary to verify the adequacy of the 
control measures under current operating conditions. Therefore, MSHA 
would select this MMU for additional sampling. As discussed in Appendix 
B, even if the first measurement were 1.90 mg/m<SUP>3</SUP> instead of 
2.14 mg/m<SUP>3</SUP>, because of measurement error this would not 
demonstrate that the mine atmosphere sampled was in compliance. To 
confirm that control measures are adequate, MSHA would need to take 
additional samples.

D. What Is the Potential for a Citation To Be Issued Due To Measurement 
Error?

    Some commenters expressed concern that noncompliance determinations 
based on single, full-shift measurements would result in an 
unacceptable number of erroneous citations due to measurement error. 
These commenters expected that MSHA's new enforcement policy would 
result in numerous erroneous citations.
    Based on the analysis in Appendix C, MSHA has concluded that, 
because of the large ``margin of error'' separating each CTV from the 
corresponding applicable standard, use of the CTV table provides ample 
protection against erroneous citations. For exceptionally well-
controlled environments (e.g., Case 2 of Appendix C), the probability 
that any given citation is erroneous will be substantially less than 5 
percent. This probability is even smaller in environments which are not 
well controlled (e.g., Case 3 of Appendix C). Therefore, any citation 
issued in accordance with the CTV table will be much more likely the 
result of excessive dust concentration rather than measurement error.

E. What Will Happen When the Evidence Is Insufficient To Warrant a 
Citation?

    If the appropriate CTV is not met or exceeded, MSHA will not issue 
a citation. As discussed earlier, this does not mean that the sampled 
environment is necessarily in compliance. Although in certain cases 
there may be insufficient evidence to demonstrate noncompliance, the 
measurement may nonetheless indicate a possible overexposure. MSHA 
intends to focus on cases of measurements above the applicable standard 
but below the CTV, with special emphasis being directed to working 
environments required to comply with applicable standards below 2.0 mg/
m<SUP>3</SUP>.
    If follow-up measurements do not warrant a citation but suggest 
that the dust control measures in use may be inadequate, MSHA may 
initiate a thorough review of the dust control parameters stipulated in 
the mine operator's approved ventilation or respirable dust control 
plan to determine whether the parameters should be upgraded.

V. Consequences of the Use of the CTVs in Conjunction With the 
Joint MSHA/NIOSH Finding

A. What is the Impact of MSHA's New Enforcement Strategy As Applied 
Under the MSHA/NIOSH Joint Finding?

    The Agency believes that the application of the CTVs in conjunction 
with the MSHA/NIOSH joint notice of finding published elsewhere in 
today's Federal Register to single, full-shift samples collected by 
MSHA inspectors provides for more efficient detection of noncompliance 
by identifying and requiring abatement of individual instances of 
overexposure which meet the CTVs. While this issue is more 
appropriately addressed in the MSHA/NIOSH joint notice, the rationale 
for this conclusion bears repeating here.
    The Mine Act is clear in its intent that no miner should be exposed 
to respirable coal mine dust in excess of the applicable standard on 
any shift. The effect of the joint finding and the new enforcement 
strategy set forth here creates incentives for mine operators to 
control dust exposure on a continuing basis to minimize the chance of 
being found in noncompliance during any MSHA sampling inspection. To 
prevent the possibility of any inspector single,

[[Page 5692]]

full-shift measurement exceeding the CTV and resulting in a violation, 
mine operators will be more likely to keep dust concentrations at or 
below the applicable standard, thereby providing better protection to 
miners from overexposures. This becomes evident upon closer examination 
of the inspector sampling data from the period when noncompliance 
determinations were based on single, full-shift measurements.
    MSHA reviewed inspector MMU sampling results for FY 1992, the first 
full year during which noncompliance determinations were based on 
single, full-shift measurements, and FY 1993, the last year that the 
Agency issued citations based on single, full-shift measurements. This 
review showed a decline in the number of ``D.O.'' and nondesignated 
occupation samples exceeding 2.0 mg/m<SUP>3</SUP>, from 16 percent and 
10 percent in FY 1992 to 13 percent and 7 percent, respectively, in FY 
1993, suggesting that operators were better able to maintain dust 
concentrations below the applicable standard. MSHA also conducted a 
computer simulation using these data which showed that one of every 
four MMU sampling days in FY 1992 would have been found in 
noncompliance based on a single, full-shift measurement, compared to 
one in five MMU sampling days in FY 1993.
    Under the previous enforcement strategy, which utilized averaging, 
inspectors cited violations of the applicable standard on the average 
of multiple measurements taken on a single shift or on different shifts 
or days. Consequently, dust concentrations could be excessive for some 
occupations or work locations, but corrective action would not be 
required so long as the average of the measurements did not exceed the 
applicable standard. For example, averaging occupational measurements 
of 3.2, 2.4, 1.5, 1.3 and 1.0 mg/m<SUP>3</SUP> results in an average 
concentration of 1.8 mg/m<SUP>3</SUP> for the sampled MMU where the 
applicable standard is 2.0 mg/m<SUP>3</SUP>. Despite the fact that two 
of the measurements demonstrate noncompliance with a high degree of 
confidence, corrective action would not have been required because the 
average concentration was below the applicable standard.
    As described in this notice and in conjunction with the MSHA/NIOSH 
joint notice, under the new enforcement policy, whenever an individual 
measurement indicates noncompliance (with a high level of confidence), 
the mine operator will be required to take corrective action to lower 
the concentration of respirable dust to comply with the applicable 
standard.
    Some commenters expressed concern that MSHA would fail to cite some 
instances of noncompliance because of the high level of confidence 
required for a citation. MSHA believes that the new enforcement 
strategy as applied in conjunction with the finding of the MSHA/NIOSH 
joint notice will reduce the chances of failing to cite cases of 
noncompliance as compared to the previous policy of measurement 
averaging, while at the same time ensuring that noncompliance is cited 
only when there is a high degree of confidence that the applicable 
standard has been exceeded. According to the inspector sampling 
inspections conducted in 1995, only 132 MMUs were found to be in 
violation of the applicable standard and cited under the previous 
enforcement policy of measurement averaging, compared to 545 MMUs that 
would have been citable under the new enforcement policy in conjunction 
with the joint notice of finding using single, full-shift measurements. 
This clearly demonstrates that the new enforcement policy, in 
conjunction with the joint notice, will not compromise miners' health 
but would, instead, have identified 413 additional instances of 
overexposure that would have gone unaddressed under the previous policy 
of measurement averaging.
    Some commenters proposed that miners would be even more protected 
if noncompliance was cited whenever any single, full-shift measurement 
exceeded the applicable standard by any amount. That is, it was 
recommended that MSHA not make any allowance for potential measurement 
errors. MSHA has considered this recommendation but has not adopted it 
in the final policy because it could result in citations being issued 
where compliance with the applicable standard is more likely than not. 
If the mine environment is sufficiently well controlled, it is more 
likely that a particular measurement exceeds the applicable standard, 
but not the CTV, due to measurement error rather than due to excessive 
dust concentration. Furthermore, the rationale used by these commenters 
to justify their proposed citation criterion breaks down when, as in 
the case of multiple samples taken during a given shift in the same 
MMU, more than one measurement is made for a single noncompliance 
determination. Appendix D addresses technical details relating to this 
issue.
    Some commenters stated that MSHA's new citation criteria 
implemented in conjunction with the joint notice will not improve 
respirable dust levels in the environment, but will simply result in 
MSHA issuing more citations to mine operators. In these commenters 
view, this will foster a continuation of the adversarial relationship 
that developed between mine operators and MSHA over allegations of 
widespread tampering with respirable dust samples.
    MSHA firmly believes that basing noncompliance determinations on a 
single, full-shift measurement will improve working conditions for 
miners because it will cause mine operators to either implement and 
maintain more effective dust controls to minimize the chance of being 
found in noncompliance by an MSHA inspector, or take corrective action 
sooner to lower dust concentrations that are shown, with high 
confidence, to be in excess of the applicable standard. The effect of 
this new enforcement policy in conjunction with the MSHA/NIOSH joint 
notice will be remedial in nature because it will address instances of 
overexposure that are not addressed under the current policy of 
measurement averaging. For example, between January 1992 and December 
1993, MSHA continued the practice established under the SIP of making 
noncompliance determinations based on single, full-shift measurements 
which demonstrated, with high confidence, that the applicable standard 
was exceeded, and on the average of multiple measurements. During this 
period, MSHA inspectors issued a total of 658 citations at MMUs. The 
majority of these citations (488) were issued based on the result of a 
single, full-shift measurement. Under the existing enforcement policy, 
such individual instances of noncompliance would not be cited and 
corrected, but instead would be factored into an average that could be 
at or below the applicable standard, resulting in no violation and no 
corrective action taken by the mine operator.
    Some commenters also contended that the joint notice of finding, 
and this notice of policy, are solely for the administrative 
convenience of MSHA's mine inspectors. The commenters stated that 
allowing inspectors to make noncompliance determinations on the basis 
of a single, full-shift measurement will eliminate the need for 
inspectors to sample on successive days, as is sometimes required under 
existing policy.
    MSHA recognizes that there are administrative advantages related to 
the adoption of this new enforcement policy and the joint notice of 
finding. By eliminating the need to sample on subsequent days, the 
Agency will be able to utilize its resources more efficiently. That is, 
inspectors will not

[[Page 5693]]

be required to return to a mine to conduct additional dust sampling, 
but the Agency will be able to redirect its resources to other safety 
and health concerns. This result is consistent with the Mine Act's 
objective of protecting miner safety and health. While administrative 
convenience may be a side benefit of this new enforcement policy in 
conjunction with the MSHA/NIOSH joint notice, the primary reason for 
implementing it is to achieve the intent of Congress that no miner 
shall be exposed to dust concentrations above the applicable standard 
on any shift.

B. What is the Impact of the New Policy on Ventilation Plans?

    A number of commenters expressed concern that issuing citations on 
the result of a single, full-shift measurement will cause MSHA to 
require carefully developed ventilation plans to be modified needlessly 
as part of the abatement process. These commenters view such frequent 
revisions as costly, disruptive and unnecessary. They contend that such 
revisions, if required, would be made on the basis of incomplete or 
invalid information, and that they would not necessarily decrease a 
miner's dust exposure. Some commenters believed that some inspectors 
would mandate specific changes without realistically evaluating their 
effectiveness, while other inspectors would not allow operators to make 
their own adjustments to the plans, or provide an opportunity for them 
to evaluate the changes in a rational manner.
    When a citation is issued based on a single measurement, this can 
indicate that the control measures in use may no longer be adequate to 
maintain the environment within the applicable standard. MSHA will 
consequently review the adequacy of the ventilation plan under the 
current operating conditions, and will consider the results of operator 
bimonthly sampling as well as operator compliance with the approved 
ventilation plan parameters. Under this approach MSHA would require 
plan revisions only after an examination of all factors has 
demonstrated that changes are necessary to protect miner health. This 
enforcement strategy should minimize unnecessary changes to plans that 
have been determined to provide adequate controls.
    MSHA believes that the primary focus of the federal dust program is 
to minimize miners' overexposures to respirable dust through the 
application of appropriate environmental controls, which are stipulated 
in the operator's approved mine ventilation plan. After these controls 
are evaluated and shown to be effective under typical mining 
conditions, if properly maintained, they should provide reasonable 
assurance that no miner will be overexposed. Therefore, one of the 
objectives of MSHA's dust sampling is to verify that the controls 
stipulated in ventilation plans continue to adequately control dust 
concentrations under existing operating conditions. In conjunction with 
these sampling and other inspections an inspector checks and measures 
the dust control parameters early in the shift to determine whether the 
approved ventilation plan is being followed. A mine operator's failure 
to follow the parameters stipulated in the plan will result in the 
issuance of a citation, which requires immediate corrective action to 
abate the violation. The type of corrective actions taken to abate plan 
violations can vary from unplugging clogged water sprays to increasing 
the amount of ventilating air delivered to the MMU. However, mere 
correction of these deficiencies to ensure that the ``status quo'' of 
the plan is being maintained may not always be effective in controlling 
miners' exposure to respirable dust. The required plan parameters may 
no longer be effective in maintaining compliance, and may need to be 
upgraded. The determination of how the plan should be revised is 
complicated by the fact that, generally, most approved plans do not 
incorporate all the control measures that were in place when MSHA 
sampled. Consequently, most plan revisions have simply incorporated 
into the plan only those dust controls that were in use when MSHA 
sampled, rather than requiring significant upgrading of the plan. As an 
example, an MSHA inspector might require an increase in the water 
pressure stipulated in the plan from 75 pounds per square inch (psi) to 
125 psi to reflect the 125 psi that the MSHA inspector actually 
measured. If, instead, the operator was required to significantly 
increase the quantity of air being delivered to the MMU, this would be 
considered a major upgrade. MSHA recognizes that a determination of 
noncompliance should not automatically necessitate the revision of a 
plan. Instead, it should result in a thorough review of the plan's 
continued adequacy.
    When an operator of an underground mine is cited for excessive 
dust, 30 CFR 70.201(d) requires the operator to ``take corrective 
action to lower the concentration of respirable dust to within the 
permissible concentration.'' When the citation is based on MSHA 
samples, the inspector may request that the operator describe what type 
of corrective action will be taken. The inspector then determines if 
the corrective action is appropriate. If it is not appropriate in the 
specific situation, the inspector may either suggest or require other 
corrective action or control measures. Operators are provided with the 
opportunity to make adjustments to their dust controls and to evaluate 
their effectiveness in a rational manner during the time for abatement 
set by the inspector, which is based on the complexity of the problem, 
availability of controls, and the types of changes the operator intends 
to make. This abatement time may be extended by the inspector based on 
the operator's performance in reducing the dust concentration in the 
affected area of the mine. Typically, the operator then demonstrates, 
through sampling, that the underlying condition or conditions causing 
the violation have been corrected. Failure to take corrective action 
prior to sampling that shows continuing noncompliance may lead to the 
issuance of a withdrawal order. However, this occurs infrequently.

C. Will the New Enforcement Policy Increase Citations on Individual 
Shifts, Even if the So-Called ``Average Concentration Over the Longer 
Term'' Meets the Standard?

    Some commenters claimed that even when the average dust 
concentration is well below the applicable standard, normal variability 
from shift to shift results in a substantial fraction of shifts for 
which the dust standard is exceeded. According to these commenters, a 
determination of noncompliance is warranted only if the average dust 
concentration to which a miner is exposed exceeds the standard over a 
period of time greater than a single shift, such as a bimonthly 
sampling period, a year, or a miner's working lifetime. Therefore, they 
consider it ``unfair'' to cite operators for exceeding the applicable 
standard on individual shifts, so long as the average over the longer 
term meets the applicable standard. For example, based on historical 
sampling data provided by one commenter, the commenter concluded that, 
``* * * there is at least a 1 in 6 or 17% probability that any single 
sample can show potential overexposure when one does not exist.'' These 
commenters contend that use of the CTV to determine noncompliance, 
based on one sample collected on a single shift, will substantially 
increase the frequency of ``unfair'' citations, compared to existing 
MSHA policy.
    MSHA believes that such comments reflect a misunderstanding of both 
the

[[Page 5694]]

requirements of the Mine Act and MSHA's longstanding policy with 
respect to single, full-shift noncompliance determinations. It should 
be recognized that MSHA has been basing noncompliance determinations on 
the average of multiple occupation measurements obtained on the same 
shift since 1975. In addition, some of the commenters confused the 
average dust concentration over the course of an individual shift with 
the average dust concentration over some longer term. The joint notice 
of finding issued by the Secretaries of Labor and HHS addresses this 
issue. Since the Mine Act requires that dust concentration be kept 
continuously at or below the applicable standard on every shift, it is 
appropriate to cite noncompliance when any single, full-shift 
measurement at a particular location demonstrates, with high 
confidence, that the applicable standard has been exceeded on an 
individual shift.
    Section 201(b) of the Mine Act mandates that MSHA ensure ``to the 
greatest extent possible, that the working conditions in each 
underground coal mine are sufficiently free of respirable dust 
concentrations * * * to permit each miner the opportunity to work 
underground during the entire period of his adult life without 
incurring any disability from pneumoconiosis or any other occupation-
related disease during or at the end of such a period.'' Since neither 
past nor future exposure levels can be assumed for any miner, MSHA's 
enforcement strategy must be to limit the exposure on every shift as 
intended by the Mine Act.

D. Will There Be Any Changes in Operator Bimonthly Sampling?

    Several commenters were unclear about the impact of the joint MSHA/
NIOSH finding and this policy on operator sampling for compliance and 
for abatement of violations. One commenter suggested that 30 CFR 
70.207(a) be revised to allow the operator to submit one single, full-
shift sample, instead of five samples every bimonthly period as 
currently required. Another commenter suggested that MSHA assume 
responsibility for dust sampling from the mine operators.
    MSHA has previously noted that the change in its enforcement policy 
announced through this final notice affects only how it will determine 
noncompliance based on measurements obtained by MSHA inspectors. There 
will be no change in how MSHA evaluates operator-collected respirable 
dust samples for compliance. Under the regulations currently in effect, 
the Agency will continue to average operator samples taken on multiple 
shifts or days to make noncompliance determinations. MSHA is committed 
to revising procedures with respect to operator-collected respirable 
dust samples through the rulemaking process for consistency with this 
final finding.
    Several commenters expressed concerns about the credibility of the 
operator sampling program because of alleged operator tampering with 
respirable dust samples and alleged operator manipulation of mine 
conditions during dust sampling periods. As a result, these commenters 
felt that mine operators should no longer have responsibility for 
sampling because their sampling results are unreliable. Another 
commenter expressed support for the Agency to compel coal mine 
operators to comply with existing dust standards. Another commenter 
voiced concern that a mine operator could be wrongly cited due to the 
loss or mishandling of a single, full-shift sample by MSHA, and claimed 
that such occurrences had happened in the past. Some commenters believe 
that if noncompliance can be determined based on a single, full-shift 
sample, an operator should be allowed to abate a citation with a 
single, full-shift sample, particularly if the operator has recently 
demonstrated compliance through bimonthly samples. Another commenter 
questioned the impact of the proposed program on the operator's 
program, specifically, whether MSHA would require each of the abatement 
samples to meet the single, full-shift sample citation threshold 
values, in addition to meeting the dust standard based on the average 
of five abatement samples.
    Issues concerning operator sampling are not germane to this 
enforcement policy notice, which concerns only the use of samples 
collected by MSHA inspectors. The changes set forth in this final 
notice only address how MSHA will determine noncompliance when sampling 
is conducted by federal mine inspectors. There is no change in how MSHA 
evaluates either operator-collected bimonthly samples or samples taken 
to abate a dust citation. MSHA is committed to revising any procedures 
with respect to the operator program through the rulemaking process for 
consistency with this final finding.
    Concerning the credibility of the operator sampling program, MSHA 
recognizes that there have been instances of abuse under the current 
operator sampling program. The Task Group found that the majority of 
operators do not engage in such conduct. MSHA will continue to monitor 
the operator sampling program, increase the frequency of inspector 
sampling, and target problem mines for additional inspections, as 
appropriate.
    MSHA processes over 80,000 samples annually and it is not 
unrealistic to expect some samples to be either lost in the mail or 
accidentally misplaced. MSHA's experience of processing more than 7 
million dust samples since 1970 indicates that this occurs 
infrequently. In the event a sample is lost, the mine operator is 
afforded ample opportunity to submit a replacement sample. If a 
citation is issued due to the operator's failure to submit the required 
number of samples, the affected operator can present evidence that the 
required number of samples had been submitted and request that MSHA 
vacate the citation.

E. How Can MSHA Base a Noncompliance Determination on a Single, Full-
Shift Sample, When Five Samples Are Required in Operator Bimonthly 
Sampling?

    Once a finding has been made that a single, full-shift measurement 
will accurately represent atmospheric conditions to which a miner is 
exposed during such shift, MSHA is bound by the terms of the Mine Act 
to make noncompliance determinations based on single, full-shift 
measurements. No regulatory action is required to implement this change 
in MSHA's dust sampling program. On the other hand, the present 
regulatory scheme for operator sampling was developed based on 
noncompliance determinations being made by averaging the results of 
multiple samples over five successive shifts or days. In order for MSHA 
to incorporate the single, full-shift sample concept into the operator 
sampling program, the Agency must revise the operator sampling 
regulations through notice and comment rulemaking.

F. Do the New Citation Criteria Have any Impact on Permissible Exposure 
Limits?

    Some commenters contended that a policy of citing in accordance 
with the CTV table, rather than citing whenever a measurement exceeds 
the applicable standard, effectively increases the allowable dust 
concentration limit. Other commenters stated that the enforcement of 
the applicable standard as a limit on each shift, rather than as a 
limit on the average concentration over some longer time period, 
effectively reduces the standard.
    Citing in accordance with the stated CTV neither increases nor 
decreases the dust standard. Operators are required to maintain 
compliance with the

[[Page 5695]]

applicable standard at all times. MSHA's citing of noncompliance only 
when there is high confidence that the applicable standard has been 
exceeded does not increase the permissible concentration limit. Again, 
mine operators must maintain compliance with the applicable standard. 
MSHA requires that dust controls maintain dust concentrations at or 
below the applicable standard on all shifts, not merely at or below the 
CTV. It is also MSHA's intent under this new enforcement policy that if 
a measurement exceeds the applicable standard by an amount insufficient 
to warrant citation--that is, the level does not meet or exceed the 
CTV--MSHA will target that mine or area for additional sampling to 
ensure that dust controls are adequate.
    Those commenters who stated that applying the applicable standard 
to each shift will effectively reduce the respirable dust standard 
overlooked the fact that, since 1975, MSHA has taken enforcement action 
based on average of measurements obtained for different occupations 
during a single shift. This new enforcement policy does not change 
MSHA's interpretation of section 202(b) of the Mine Act that dust 
concentrations be maintained at or below the applicable standard on 
each shift. The new enforcement policy merely reflects a change in the 
technical criteria used to cite violations of the applicable dust 
standard.

Appendix A--The Effects of Averaging Dust Concentration Measurements

    MSHA's measurement objective in collecting a dust sample is to 
determine the average dust concentration at the sampling location on 
the shift sampled. As discussed in the joint notice of finding 
published elsewhere in today's Federal Register, a single, full-shift 
measurement can accurately represent the average full-shift dust 
concentration being measured. Nevertheless, because of sampling and 
analytical errors inherent in even the most accurate measurement 
process, the true value of the average dust concentration on the 
sampled shift can never be known with complete certainty. However 
accurate the representation, a measurement can provide only an estimate 
of the true dust concentration. Some commenters contended that MSHA 
should not rely on single samples for making noncompliance 
determinations, because an average of results from multiple samples 
would estimate the true dust concentration more accurately than any 
single measurement.
    Contrary to the views expressed by these commenters, averaging a 
number of measurements does not necessarily improve the accuracy of an 
estimation procedure. Consider, for example, an archer aiming at 
targets mounted at random and possibly overlapping positions on a long 
partition. Each arrow might be aimed at a different target. Suppose 
that an observer, on the opposite side of the partition from the 
archer, cannot see the targets but must estimate the position of each 
bull's eye by locating protruding arrowheads.
    Each protruding arrowhead provides a measurement of where some 
bull's eye is located. If two arrowheads are found on opposite ends of 
the partition, averaging the positions of these two arrowheads would 
not be a good way of determining where any real target is located. To 
estimate the location of an actual target, it would generally be 
preferable to use the position of a single arrow. The average would 
represent nothing more than a ``phantom'' target somewhere near the 
center, where the archer probably did not aim on either shot and where 
no target may even exist.
    The archery example can be extended to illustrate conditions under 
which averaging dust concentration measurements does or does not 
improve accuracy. If each arrowhead is taken to represent a full-shift 
dust sample, then the true average dust concentration at the sampling 
location on a given shift can be identified with the location of the 
bull's eye at which the corresponding arrow was aimed. The accuracy of 
a measurement refers to how closely the measurement can be expected to 
come to the quantity being measured. Statistically, accuracy is the 
combination of two distinct concepts: precision, which pertains to the 
consistency or variability of replicated measurements of exactly the 
same quantity; and bias, which pertains to the average amount by which 
these replicated measurements deviate from the quantity being measured. 
Bias and precision are equally important components of measurement 
accuracy.
    To illustrate, arrows aimed at the same target might consistently 
hit a sector on the lower right side of the bull's eye. The protruding 
arrowheads would provide more or less precise measurements of where the 
bull's eye was located, depending on how tightly they were clustered; 
but they would all be biased to the lower right. On the other hand, the 
arrows might be distributed randomly around the center of the bull's 
eye, and hence unbiased, but spread far out all over the target. The 
protruding arrowheads would then provide unbiased but relatively 
imprecise measurements.
    More complicated situations can easily be envisioned. Arrows aimed 
at a second target would provide biased measurements relative to the 
first target. Alternatively, if the archer always aims at the same 
target, the first shot in a given session might tend to hit near the 
center, with successive shots tending to fall off further and further 
to the lower right as the archer's arm tires; or shots might 
progressively improve, as the archer adjusts aim in response to prior 
results.
    Averaging reduces the effects of random errors in the archer's aim, 
thereby increasing precision in the estimation procedure. If the archer 
always aims at the same target and is equally adept on every shot 
(i.e., if the arrowheads are all randomly and identically distributed 
around a fixed point), then averaging improves the estimate's precision 
without introducing any bias. Averaging in such cases provides a more 
accurate method of estimating the bull's eye location than reliance on 
any single arrowhead. If, however, the archer intentionally or 
unintentionally switches targets, or if the archer's aim progressively 
deteriorates, then averaging can introduce or increase bias in the 
estimate. If the gain in precision outweighs this increase in bias, 
then averaging several independent measurements may still improve 
accuracy. However, averaging can also introduce a bias large enough to 
offset or even surpass the improvement in precision. In such cases, the 
average position of several arrowheads can be expected to locate the 
bull's eye less accurately than the position of a single arrowhead.
I. Multi-Locational Averaging
    Some commenters opposed MSHA's use of a single, full-shift 
measurement for enforcement purposes, claiming that determinations 
based on such measurements would be less accurate than those made under 
MSHA's existing enforcement policy of averaging multiple measurements 
taken on an MMU. There are two distinctly different types of multi-
locational measurement averages that could theoretically be compiled on 
a given shift: (1) the average might combine measurements taken for 
different occupational locations and (2) the average might combine 
measurements all taken for the same occupational location. For MMUs, 
the averages used in MSHA's sampling program usually involve 
measurements taken for different occupational locations on the same 
shift. These are averages of the first type. MSHA's sampling program 
has never utilized

[[Page 5696]]

averages of the second type. Therefore, those commenters who claimed 
that reliance on a single, full-shift measurement would reduce the 
accuracy of noncompliance determinations, as compared to MSHA's 
existing enforcement policy, are implicitly claiming that accuracy is 
increased by averaging across different occupational locations.
    Averaging measurements obtained from different occupational 
locations on an MMU is like averaging together the positions of arrows 
aimed at different targets. The average of such measurements is an 
artificial, mathematical construct that does not correspond to the dust 
concentration for any actual occupational location. Therefore, this 
type of averaging introduces a bias proportional to the degree of 
variability in actual dust concentration at the various locations 
averaged.
    The gain in precision that results from averaging measurements 
taken at different locations outweighs this bias only if variability 
from location to location is smaller than variability in measurement 
error. However, commenters opposed to MSHA's use of single, full-shift 
measurements for enforcement purposes argued that this is not generally 
the case and even submitted data and statistical analyses in support of 
this position. Commenters in favor of noncompliance determinations 
based on a single, full-shift measurement agreed that variability in 
dust concentration is extensive for different occupational locations 
and argued that MSHA's existing policy of measurement averaging is not 
sufficiently protective of miners working at the dustiest locations.
    Since an average of the first type combines measurement from the 
dustiest location with measurements from less dusty locations, it must 
always fall below the best available estimate of dust concentration at 
the dustiest location. In effect, averaging across different 
occupational locations dilutes the dust concentration observed for the 
most highly exposed occupations or dustiest work positions. Therefore, 
such averaging results in a systematic bias against detecting excessive 
dust concentrations for those miners at greatest risk of overexposure.
    A somewhat better case can be made for the second type of multi-
locational averaging, which combines measurements obtained on the same 
shift from a single occupational location. As some commenters pointed 
out, however, there is ample evidence that spatial variability in dust 
concentration, even within relatively small areas, is frequently much 
larger than variability due to measurement error. Therefore, the same 
kind of bias introduced by averaging across occupational locations 
would also arise, but on a lesser scale, if the average measurement 
within a relatively small radius were used to represent dust 
concentration at every point in the atmosphere to which a miner is 
exposed. A miner is potentially exposed to the atmospheric conditions 
at any valid sampling location. Consistent with the Mine Act and 
implementing regulations, MSHA's enforcement strategy is to limit 
atmospheric dust concentration wherever miners normally work or travel. 
Therefore, the more spatial variability in dust concentration there is 
within the work environment, the less appropriate it is to use 
measurement averaging to enforce the applicable standard by averaging 
measurements obtained at different sampling locations.
    Some of the comments implied that instead of measuring average dust 
concentration at a specific sampling location, MSHA's objective should 
be to estimate the average dust concentration throughout a miner's 
``breathing zone'' or other area near a miner. If estimating average 
dust concentration throughout some zone were really the objective of 
MSHA's enforcement strategy, then averaging measurements made at random 
points within the zone would improve precision of the estimate without 
introducing a bias. This type of averaging, however, has never been 
employed in either the MSHA or operator dust sampling programs. MSHA's 
current policy of averaging measurements obtained from different zones 
does not address spatial variability in the area immediately 
surrounding a sampler unit. Therefore, even if averaging measurements 
from within a zone were somehow beneficial, this would not demonstrate 
that MSHA's existing enforcement policy is more reliable than the new 
policy of basing noncompliance on a single, full-shift measurement.
    Furthermore, if MSHA's objective were really to estimate average 
dust concentration throughout some specified zone on a given shift, 
then it would be necessary to obtain far more than five simultaneous 
measurements within the zone. This is not only because of potentially 
large local differences in dust concentration. In order to use such 
measurements for enforcement purposes, variability in dust 
concentration within the sampled area would have to be estimated along 
with the average dust concentration itself. As some commenters 
correctly pointed out, doing this in a statistically valid way would 
generally require at least twenty to thirty measurements. One of these 
commenters also pointed out that such an estimate, based on even this 
many measurements in the same zone, could be regarded as accurate only 
under certain questionable assumptions about the distribution of dust 
concentrations. This commenter calculated that hundreds of measurements 
would be required in order to avoid these tenuous assumptions. Clearly, 
this shows that the objective of estimating average dust concentration 
throughout a zone is not consistent with any viable enforcement 
strategy to limit dust concentration on each shift in the highly 
heterogeneous and dynamic mining environment. The large number of 
measurements required to accurately characterize dust concentration 
over even a small area merely demonstrates why it is not feasible to 
base enforcement decisions on estimated atmospheric conditions beyond 
the sampling location.
    MSHA recognizes that a single, full-shift measurement will not 
provide an accurate estimate of average dust concentration anywhere 
beyond the sampling location. The Mine Act, however, does not require 
MSHA to estimate average dust concentration at locations that are not 
sampled or to estimate dust concentration averaged over any zone or 
region of the mine, and doing so is not part of MSHA's enforcement 
program. Instead, MSHA's enforcement strategy is to ensure that a miner 
will not be exposed to excessive dust wherever he/she normally works or 
travels. This is accomplished by maintaining the average dust 
concentration at each valid sampling location at or below the 
applicable standard during each shift.
II. Multi-Shift Averaging
    Some commenters maintained that in order to reduce the risk of 
erroneous noncompliance determinations, MSHA should average 
measurements obtained from the same occupation on different shifts. 
These commenters contended that the average of measurements from 
several shifts represents the average dust concentration to which a 
miner is exposed more accurately than a single, full-shift measurement. 
Other commenters, who favored noncompliance determinations based on 
single, full-shift measurements, claimed that conditions are sometimes 
manipulated so as to produce unusually low dust concentrations on some 
of the sampled shifts. These commenters suggested that, due to these

[[Page 5697]]

unrepresentative shifts, multi-shift averaging can yield 
unrealistically low estimates of the dust concentration to which a 
miner is typically exposed. Some of these commenters also argued that 
the Mine Act requires the dust concentration to be regulated on each 
shift, and that multi-shift averaging is inherently misleading in 
detecting excessive dust concentration on an individual shift.
    Those advocating multi-shift averaging generally assumed that a 
noncompliance determination involves estimating a miner's average dust 
exposure over a period longer than an individual shift. This assumption 
is flawed because section 202(b) of the Mine Act specifies that each 
operator shall continuously maintain the average concentration of 
respirable dust in the mine atmosphere during each shift at or below 
the applicable standard. Some of those advocating multi-shift 
averaging, however, suggested that MSHA should average measurements 
obtained on different shifts even if the quantity of interest is dust 
concentration on an individual shift. These commenters argued that 
averaging smooths out the effects of measurement errors, and that 
therefore the average over several shifts would represent dust 
concentration on each shift more accurately than the corresponding 
individual, full-shift measurement.
    The Secretary recognizes that there are circumstances, not 
experienced in mining environments, under which averaging across shifts 
could improve the accuracy of an estimate for an individual shift. Just 
as averaging the positions of arrows aimed at nearly coinciding targets 
might better locate the bull's eye than the position of any individual 
arrow, the gain in precision obtained by averaging dust concentrations 
observed on different shifts could, under analogous circumstances, 
outweigh the bias introduced by using the average to estimate dust 
concentration for an individual shift. This would be the case, however, 
only if variability in dust concentration among shifts were small 
compared to variability due to measurement imprecision. It would do no 
good to average the location of arrows aimed at different targets 
unless the targets were at nearly identical locations.
    To the contrary, several commenters pointed out that variability in 
dust concentration from shift to shift tends to be much larger than 
variability due to measurement error and introduced evidence in support 
of this observation. Measurements on different shifts are like arrows 
aimed at widely divergent targets. The more that conditions vary, for 
any reason, from shift to shift, the more bias is introduced by using a 
multi-shift average to represent dust concentration for any individual 
shift. Under these circumstances, any improvement in precision to be 
gained by simply averaging results is small compared to the bias 
introduced by such averaging. Therefore, the Secretary has concluded 
that MSHA's existing practice of averaging measurements collected on 
different shifts does not improve accuracy in estimating dust 
concentration to which a miner is exposed on any individual shift. To 
paraphrase one commenter, averaging Monday's exposure measurement with 
Tuesday's does not improve the estimate of Monday's average dust 
concentration.
    Some commenters argued that since the risk of pneumoconiosis 
depends on cumulative exposure, MSHA's objective should be to estimate 
the dust concentration to which a miner is typically exposed and to 
identify cases of excessive dust concentration over a longer term than 
a single shift. Other commenters claimed that a multi-shift average 
does not provide a good estimate of either typical dust concentrations 
or exposures over the longer term. These commenters claimed that 
different shifts are not equally representative of the usual 
atmospheric conditions to which miners are exposed, implying that the 
average of measurements made on different shifts of a multi-day MSHA 
inspection tends to systematically underestimate typical dust 
concentrations.
    The Secretary interprets section 202(b) of the Mine Act as 
requiring that dust concentrations be kept at or below the applicable 
standard on each and every shift. Nevertheless, the Secretary 
recognizes that, under certain conditions, the average of measurements 
from multiple shifts can be a better estimate of ``typical'' 
atmospheric conditions than a single measurement. This applies, 
however, only if the sampled shifts comprise a random or representative 
selection of shifts from whatever longer term may be under 
consideration. As shown below, evidence to the contrary exists, 
supporting those commenters who maintained that measurements collected 
over several days of a multi-day MSHA inspections do not meet this 
requirement. Therefore, the Secretary has concluded that averaging such 
measurements is likely to be misleading even for the purpose of 
estimating dust concentrations to which miners are typically exposed.
    Whether the objective is to measure average dust concentration on 
an individual shift or to estimate dust concentration typical of a 
longer term, the arguments presented for averaging across shifts all 
depend on the assumption that every shift sampled during an MSHA 
inspection provides an unbiased representation of dust exposure over 
the time period of interest.<SUP>1</SUP> To check this assumption, MSHA 
performed a statistical analysis of multi-shift MSHA inspections 
carried out prior to the SIP. This analysis, placed into the record in 
September 1994, examined the pattern of dust concentrations measured 
over the course of these multi-shift inspections and compared results 
from the final shift with results from a subsequent single-shift 
sampling inspection [1].
---------------------------------------------------------------------------

    \1\ Technically, the assumption is that dust concentrations on 
all shifts sampled are independently and identically distributed 
around the quantity being estimated.
---------------------------------------------------------------------------

    The analysis found that dust concentrations measured on different 
shifts of the same MSHA inspection were not randomly distributed. The 
later samples tended to show significantly lower results than earlier 
samples, indicating that dust concentrations on later shifts of a 
single inspection may decline in response to the presence of an 
inspector. Furthermore, the analysis provided evidence that the 
reduction in dust concentration tends to be reversed after the 
inspection is terminated. These two results led to the conclusion that 
averaging dust concentrations measured on different shifts of a multi-
day MSHA inspection introduces a bias toward unrealistically low dust 
concentrations.
    One commenter questioned the validity of this analysis, stating 
that ``there is absolutely no basis in the * * * report for the 
assertion that the trend is reversed after the inspection is 
terminated.'' This commenter apparently overlooked Table 3 of the 
report. That table shows a statistically significant reversal at those 
mine entities included in the analysis that were subsequently inspected 
under MSHA's SIP. Dust concentrations measured at these mine entities 
had declined significantly between the first and last days of the 
multi-shift inspection. It was primarily to address the commenter's 
implication that these reductions reflected permanent ``adjustments in 
dust control measures'' that the analysis included a comparison with 
the subsequent SIP inspection. An increase, representing a reversal of 
the previous trend, was observed on the single shift of the subsequent

[[Page 5698]]

inspection, relative to the dust concentration measured on the final 
shift of the previous multi-shift inspec tion. This reversal was found 
to be ``statistically significant at a confidence level of more than 
99.99 percent.''
    The same commenter also stated that MSHA ``* * * fails to address 
the systematic [selection] bias of the study. MSHA only does multiple 
day sampling when the initial results are higher, but not out of 
compliance.'' It is true that in order to be selected for revisitation, 
a mine entity must have shown relatively high concentrations on the 
first shift--though not, in the case of an MMU, so high as to warrant a 
citation on first shift. Since no experimental data were available on 
mine entities randomly selected to receive multi-shift inspections, the 
only cases in which patterns over the course of a multi-shift 
inspection could be examined were cases selected for multi-shift 
inspection under these criteria.
    Although the impact of the selection criteria was not explicitly 
addressed, it was recognized that entities selected for multi-day 
inspections do not constitute a random selection of mine entities. This 
recognition motivated, in part, the report's comparison of the final 
shift measurement to the dust concentration measured during a 
subsequent single-shift inspection. The magnitude of the average 
reversal indicates that most of the reduction observed over the course 
of the multi-shift inspection cannot be attributed to the selection 
criteria. Furthermore, it was not only mine entities with relatively 
low dust concentration measurements that were left out of the study 
group. Mine entities with the highest dust concentration measurements 
were immediately cited based on the average of measurements taken and 
excluded from the group subjected to multi-shift dust inspections. 
Therefore, the effect on the analysis of selecting mine entities with 
relatively high initial dust concentration measurements was largely 
offset by the effect of excluding those entities with even higher 
initial measurements. In any event, the magnitude of the average 
reduction between first and last shifts of a multi-shift inspection was 
significantly greater than what can be explained by selection for 
revisitation due to measurement error on the first shift sampled.
    The assumption that multiple shifts sampled during a single MSHA 
inspection are equally representative is clearly violated if, as some 
commenters alleged, operating conditions are deliberately altered after 
the first shift in response to the continued presence of an MSHA 
inspector and then changed back after the inspector leaves. However, if 
samples are collected on successive or otherwise systematically 
determined shifts or days, the assumption can also be violated by 
changes arising as part of the normal mining cycle. As one commenter 
pointed out, multi-shift averaging within a single MSHA inspection 
potentially introduces biases typical of ``campaign sampling,'' in 
which observations of a dynamic process are clustered together over a 
relatively narrow time span. In order to construct an unbiased, multi-
shift average for each phase of mining activity, it would be necessary 
to collect samples from several shifts operating under essentially the 
same conditions. Alternatively, to construct an unbiased, multi-shift 
estimate of dust concentration over a longer term, it would be 
necessary to collect samples from randomly selected shifts over a 
period great enough to reflect the full range of changing conditions. 
Neither requirement is met by multi-shift MSHA inspections because (1) 
the mine environment is dynamic and no two shifts are alike and (2) 
MSHA inspectors are not there long enough to observe every condition in 
their inspection.
    Based on the analysis presented by Kogut [1] and also on public 
comments received in response to the February 18 and June 6, 1994, 
notices, the Secretary has concluded that it should not be assumed that 
multiple shifts sampled during a single MSHA inspection are equally 
representative of atmospheric conditions to which a miner is typically 
exposed. This conclusion undercuts the rationale for multi-shift 
averaging within a single MSHA inspection, regardless of whether the 
objective is to estimate dust concentration for the individual shifts 
sampled as it is for MSHA inspector sampling or for typical shifts over 
a longer term as implied by some commenters. Measurements collected by 
MSHA on consecutive days or shifts of the same inspection do not 
comprise a random or otherwise representative sample from any larger 
population of shifts that would properly represent a long-term exposure 
or a particular phase of the mining cycle. Therefore, there is no basis 
for assuming that multi-shift averaging improves accuracy or reduces 
the risk of an erroneous enforcement determination.

Appendix B--Citation Threshold Values (CTV)

I. Interpretation of the CTV Table
    Each CTV was calculated to ensure that, if the CTV is met or 
exceeded, noncompliance with the applicable standard can be inferred 
with at least 95-percent confidence. It is assumed that whatever dust 
standard happens to be in effect at the sampling location is binding, 
and that a citation is warranted whenever there is sufficient evidence 
that an established standard has been exceeded. The CTV table does not 
depend on how the applicable standard was established, or on any 
measurement uncertainties in the process of setting the applicable 
standard.
    Some commenters argued that in order to construct a valid table of 
CTVs, MSHA would have to take into account the statistical distribution 
of dust concentrations over many shifts and locations. One commenter 
suggested that stochastic properties of the dust concentrations, which 
describe variability over time in probabilistic terms, should also be 
taken into account. MSHA, however, intends to use single, full-shift 
measurements only in determining noncompliance with the applicable 
standard on a particular shift and at the sampling location consistent 
with the measurement objective described in the MSHA and NIOSH joint 
finding published elsewhere in today's Federal Register. This is 
analogous to using a single measurement to identify individual 
suitcases that are unacceptable because they weigh more than five 
pounds. The efficacy of using a single measurement to identify 
unacceptable suitcases depends on the accuracy of the scale and the 
skill of the weigher. It does not depend on the statistical 
distribution of weights among suitcases or on any stochastic properties 
of the suitcase production process. These considerations would be 
relevant to estimating average weight for all suitcases produced, but 
they have nothing whatsoever to do with determining the weight of an 
individual suitcase using a sufficiently accurate scale. Averaging the 
weights of several suitcases would be entirely inappropriate and 
extremely misleading, since the object is to identify individual 
suitcases weighing more than five pounds. Although the measured weight 
of an individual suitcase is liable to contain some error (so the 
decision might be uncertain for a suitcase weighing five pounds and one 
ounce), a suitcase weighing seven or eight pounds could be rejected 
with high confidence on the first weighing. Additional weighings (of 
the same suitcase) would be required only for those suitcases whose 
initial measurement was very close to five pounds.
    The CTV table provides criteria for testing a tentative, or 
presumptive,

[[Page 5699]]

hypothesis that the true full-shift average dust concentration did not 
exceed the applicable standard (S) at each of the individual locations 
sampled during a particular shift. For purposes of this test, the mine 
atmosphere at each such location is presumed to be in compliance unless 
the corresponding full-shift measurement provides sufficient evidence 
to the contrary. The ``true full-shift average'' does not refer, in 
this context, to an average across different occupations, locations, or 
shifts. Instead, it refers entirely to the dust concentration at the 
specific location of the sampler unit, averaged over the course of the 
particular shift during which the measurement was obtained. The CTV 
table is not designed to estimate or test the average dust 
concentration across occupational locations, or within any zone or mine 
area, or in the air actually inhaled by any particular miner.
    Some commenters questioned why more than one sample might be 
required, if the first sample collected does not exceed the CTV. One of 
these commenters argued that in such case, ``compliance has already 
been established at a 95% confidence level based on the first single 
shift sample.'' This line of argument confuses confidence in issuing a 
citation with confidence of compliance. It also shows a basic 
misunderstanding of how the citation criteria relate to the requirement 
of continuous compliance under section 202(b) of the Mine Act.
    The CTV table ensures that noncompliance is cited only when there 
is a 95-percent level of confidence that the applicable standard has 
actually been exceeded. If a single measurement does not meet the 
criterion for citation, this does not necessarily imply probable 
compliance with the dust standard--let alone compliance at a 95-percent 
confidence level. For example, a single, full-shift measurement of 2.14 
mg/m<SUP>3</SUP> would not, according to the CTV table, indicate 
noncompliance with sufficient confidence to warrant a citation if S = 
2.0 mg/m<SUP>3</SUP>. This does not imply that the mine atmosphere was 
in compliance on the shift and at the location sampled. On the 
contrary, unless contradictory evidence were available, this 
measurement would indicate that the MMU was probably out of compliance. 
However, because there is a small chance that the measurement exceeded 
the standard only because of measurement error, a citation would not be 
issued. Additional measurements would be necessary to verify the 
apparent lack of adequate control measures. Similarly, a single, full-
shift measurement of 1.92 mg/m<SUP>3</SUP> would not warrant citation; 
but, because of possible measurement error, neither would it warrant 
concluding that the mine atmosphere sampled was in compliance. To 
confirm that control measures are adequate, it would be necessary to 
obtain additional measurements.
    Furthermore, even if a single, full-shift measurement were to 
demonstrate, at a high confidence level, that the mine atmosphere was 
in compliance at the sampling location on a given shift, additional 
measurements would be required to demonstrate compliance on each shift. 
For example, if S = 2.0 mg/m<SUP>3</SUP>, then a valid measurement of 
1.65 mg/m<SUP>3</SUP> would demonstrate compliance on the particular 
shift and at the particular location sampled. It would not, however, 
demonstrate compliance on other shifts or at other locations.
II. Derivation of the CTV Table
    Some commenters requested an explanation of the statistical theory 
underlying the CTV table. To understand how the CTVs are derived and 
justified, it is first necessary to distinguish between variability due 
to measurement error and variability due to actual differences in dust 
concentration. The variability observed among individual measurements 
obtained at different locations (or at different times) combines both: 
dust concentration measurements vary partly because of measurement 
error and partly because of genuine differences in the dust 
concentration being measured. This distinction, between measurement 
error and variation in the true dust concentration, can more easily be 
explained by first carefully defining some notational abbreviations.
    One or more dust samples are collected in the same MMU or other 
mine area on a particular shift. Since it is necessary to distinguish 
between different samples in the same MMU, let X<INF>i</INF> represent 
the MRE-equivalent dust concentration measurement obtained from the 
i<SUP>th</SUP> sample. The quantity being measured is the true, full-
shift average dust concentration at the i<SUP>th</SUP> sampling 
location and is denoted by <greek-m><INF>i</INF>. Because of potential 
measurement errors, <greek-m><INF>i</INF> can never be known with 
complete certainty. A ``sample,'' ``measurement,'' or ``observation'' 
always refers to an instance of X<INF>i</INF> rather than 
<greek-m><INF>i</INF>.
    The overall measurement error associated with an individual 
measurement is nothing more than the difference between the measurement 
(X<INF>i</INF>) and the quantity being measured 
(<greek-m><INF>i</INF>). Therefore, this error can be represented as

<greek-e><INF>i</INF> = X<INF>i</INF>-<greek-m><INF>i</INF>.

Equivalently, any measurement can be regarded as the true concentration 
in the atmosphere sampled, with a measurement error added on:

X<INF>i</INF> = <greek-m><INF>i</INF> + <greek-e><INF>i</INF>.

For two different measurements (X<INF>1</INF> and X<INF>2</INF>), it 
follows that X<INF>1</INF> may differ from X<INF>2</INF> not only 
because of the combined effects of <greek-e><INF>1</INF> and 
<greek-e><INF>2</INF>, but also because <greek-m><INF>1</INF> differs 
from <greek-m><INF>2</INF>.
    The probability distribution of X<INF>i</INF> around 
<greek-m><INF>i</INF> depends only on the probability distribution of 
<greek-e><INF>i</INF> and should not be confused with the statistical 
distribution of <greek-m><INF>i</INF> itself, which arises from spatial 
and/or temporal variability in dust concentration. This variability 
[i.e., among <greek-m><INF>i</INF> for different values of I] is not 
associated with inadequacies of the measurement system, but real 
variation in exposures due to the fact that contaminant generation 
rates vary greatly in time and contaminants are heterogeneously 
distributed in workplace air.
    Since noncompliance determinations are made relative to individual 
sampling locations on individual shifts, derivation of the CTV table 
requires no assumptions or inferences about the spatial or temporal 
pattern of atmospheric dust concentrations--i.e., the statistical 
distribution of <greek-m><INF>i</INF>. MSHA is not evaluating dust 
concentrations averaged across the various sampler locations. 
Therefore, the degree and pattern of variability observed among 
different measurements obtained during an MSHA inspection are not used 
in establishing any CTV. Instead, the CTV for each applicable standard 
(S) is based entirely on the distribution of measurement errors 
(<greek-e><INF>i</INF>) expected for the maximum dust concentration in 
compliance with that standard--i.e., a concentration equal to S itself.
    If control filters are used to eliminate potential biases, then 
each <greek-e><INF>i</INF> arises from a combination of four weighing 
errors (pre-and post-exposure for both the control and exposed filter 
capsule) and a continuous summation of instantaneous measurement errors 
accumulated over the course of an eight-hour sample. Since the eight-
hour period can be subdivided into an arbitrarily large number of sub-
intervals, and some fraction of <greek-e><INF>i</INF> is associated 
with each sub-interval, <greek-e><INF>i</INF> can be represented as 
comprising the sum of an arbitrarily large number of sub-interval 
errors. By the Central Limit Theorem, such a summation tends to be 
normally distributed, regardless of the distribution of subinterval 
errors. This does not depend on the distribution of

[[Page 5700]]

<greek-m><INF>i</INF>, which is generally represented as being 
lognormal.
    Furthermore, each measurement made by an MSHA inspector is based on 
the difference between pre- and post-exposure weights of a dust sample, 
as determined in the same laboratory, and adjusted by the weight gain 
or loss of the control filter capsule. Any systematic error or bias in 
the weighing process attributable to the laboratory is mathematically 
canceled out by subtraction. Furthermore, any bias that may be 
associated with day-to-day changes in laboratory conditions or 
introduced during storage and handling of the filter capsules is also 
mathematically canceled out. Elimination of the sources of systematic 
errors identified above, together with the fact that the concentration 
of respirable dust is defined by section 202(e) of the Mine Act to mean 
the average concentration of respirable dust measured by an approved 
sampler unit, implies that the measurements are unbiased. This means 
that <greek-e><INF>i</INF> is equally likely to be positive or negative 
and, on average, equal to zero.
    Therefore, each <greek-e><INF>i</INF> is assumed to be normally 
distributed, with a mean value of zero and a degree of variability 
represented by its standard deviation
[GRAPHIC] [TIFF OMITTED] TN31DE97.012

Since X<INF>i</INF> = <greek-m><INF>i</INF> + <greek-e><INF>i</INF>, it 
follows that for a given value of <greek-m><INF>i</INF>, X<INF>i</INF> 
is normally distributed with expected value equal to 
<greek-m><INF>i</INF> and standard deviation equal to 
<greek-s><INF>i</INF>. CV<INF>total</INF>, described in the MSHA and 
NIOSH joint finding published elsewhere in today's Federal Register, is 
the coefficient of variation in measurements corresponding to a given 
value of <greek-m><INF>i</INF>. CV<INF>total</INF> relates entirely to 
variability due to measurement errors and not at all to variability in 
actual dust concentrations.
    MSHA's procedure for citing noncompliance based on the CTV table 
consists of formally testing a presumption of compliance at every 
location sampled. Compliance with the applicable standard at the 
i<SUP>th</SUP> sampling location is expressed by the relation 
<greek-m><INF>i</INF> <ls-thn-eq> S. Max{<greek-m><INF>i</INF>} denotes 
the maximum dust concentration, among all of the sampling locations 
within an MMU. Therefore, if Max{<greek-m><INF>i</INF>} <ls-thn-eq> S, 
none of the sampler units in the MMU were exposed to excessive dust 
concentration. Since the burden of proof is on MSHA to demonstrate 
noncompliance, the hypothesis being tested (called the null hypothesis, 
or H<INF>0</INF>,) is that the concentration at every location sampled 
is in compliance with the applicable standard. Equivalently, for an MMU 
the null hypothesis (H<INF>0</INF>) is that max{<greek-m><INF>i</INF>} 
<ls-thn-eq> S. In other areas, where only one, full-shift measurement 
is made, the null hypothesis is simply that <greek-m><INF>i</INF> 
<ls-thn-eq> S.
    The test consists of evaluating the likelihood of measurements 
obtained during an MSHA inspection, under the assumption that 
H<INF>0</INF> is true. Since X<INF>i</INF> = <greek-m><INF>i</INF> + 
<greek-e><INF>i</INF>, X<INF>i</INF> (or max{X<INF>i</INF>} in the case 
of an MMU) can exceed S even under that assumption. However, based on 
the normal distribution of measurement errors, it is possible to 
calculate the probability that a measurement error would be large 
enough to fully account for the measurement's exceeding the standard. 
The greater the amount by which X<INF>i</INF> exceeds S, the less 
likely it is that this would be due to measurement error alone. If, 
under H<INF>0</INF>, this probability is less than five percent, then 
H<INF>0</INF> can be rejected at a 95-percent confidence level and a 
citation is warranted. For an MMU, rejecting H<INF>0</INF> (and 
therefore issuing a citation) is equivalent to determining that 
<greek-m><INF>i</INF> <SUP><ls-thn-eq></SUP> S for at least one value 
of I.
    Each CTV listed was calculated to ensure that citations will be 
issued at a confidence level of at least 95 percent. As described in 
MSHA's February 1994 notice and explained further by Kogut [2], the 
tabled CTV corresponding to each S was calculated on the assumption 
that, at each sampling location:
[GRAPHIC] [TIFF OMITTED] TN31DE97.013

The MSHA and NIOSH joint finding establishes that for valid 
measurements made with an approved sampler unit, CV<INF>total</INF> is 
in fact less than CV<INF>CTV</INF> at all dust concentrations 
(<greek-m><SUP>i</SUP>).
    The situation in which measurement error is most likely to cause an 
erroneous noncompliance determination is the hypothetical case of 
<greek-m><INF>i</INF> = S for either a single, full-shift measurement 
or for all of the measurements made in the same MMU. In that borderline 
situation--i.e., the worst case consistent with H<INF>o</INF>--the 
standard deviation is identical for all measurement errors. Therefore, 
the value of s used in constructing the CTV table is the product of S 
and CV<INF>CTV</INF> evaluated for a dust concentration equal to S:
[GRAPHIC] [TIFF OMITTED] TN31DE97.014

    Assuming a normal distribution of measurement errors as explained 
above, it follows that the probability a single measurement would equal 
or exceed the critical value
[GRAPHIC] [TIFF OMITTED] TN31DE97.015

is five percent under H<INF>o</INF> when CV<INF>total</INF> = 
CV<INF>CTV</INF>. The tabled CTV corresponding to S is derived by 
simply raising the critical value c up to the next exact multiple of 
0.01 mg/m<SUP>3</SUP>.
    For example, at a dust concentration (<greek-m><INF>i</INF>) just 
meeting the applicable standard of S = 2 mg/m<SUP>3</SUP>, 
CV<INF>CTV</INF> is 9.95 percent. Therefore, the calculated value of c 
is 2.326 and the CTV is 2.33 mg/m\3\. Any valid single, full-shift 
measurement at or above this CTV is unlikely to be this large simply 
because of measurement error. Therefore, any such measurement warrants 
a noncompliance citation.
    The probability that a measurement exceeds the CTV is even smaller 
if <greek-m><INF>i</INF>>S for any I. Furthermore, to the extent that 
CV<INF>total</INF> is actually less than CV<INF>CTV</INF>, <greek-s> is 
actually less than S<bullet>CV<INF>CTV</INF>. This results in an even 
lower probability that the critical value would be exceeded under the 
null hypothesis. Consequently, if any single, full-shift measurement 
equals or exceeds c, then H<INF>o</INF> can be rejected at confidence 
level of at least 95-percent. Since rejection of H<INF>o</INF> implies 
that <greek-m><INF>i</INF> <ls-thn-eq> S for at least one value of I, 
this warrants a noncompliance citation.
    It should be noted that when each of several measurements is 
separately compared to the CTV table, the probability that at least one 
<greek-e><INF>i</INF> will be large enough to force X<INF>i</INF> 
<gr-thn-eq> CTV when <greek-m><INF><greek-i></INF> <ls-thn-eq> S is 
greater than the probability when only a single comparison is made. For 
example (still assuming S = 2 mg/m<SUP>3</SUP>), if CV<INF>total</INF> 
is actually 6.6%, then the standard deviation of 
<greek-e><INF><greek-i></INF> is 6.6% of 2.0 mg/m<SUP>3</SUP>, or 0.132 
mg/m<SUP>3</SUP>, when <greek-m><INF><greek-i></INF> = S. Using 
properties of the normal distribution, the probability that any single 
measurement would exceed the CTV in this borderline situation is 
calculated to be 0.0062. However, the

[[Page 5701]]

probability that at least one of five such measurements results in a 
citation is 1--(0.9938)<SUP>5</SUP> = 3.1 percent. Therefore, the 
confidence level at which a citation can be issued, based on the 
maximum of five measurements made in the same MMU on a given shift, is 
97%.
    The constant 1.64 used in calculating the CTV is a 1-tailed 95-
percent confidence coefficient and is derived from the standard normal 
probability distribution. At least one commenter expressed confusion 
about whether the CTV table is based on a 1-tailed or a 2-tailed 
confidence coefficient. This commenter claimed that MSHA's use of a 
confidence coefficient equal to 1.64 ``clearly establishes a 90% 
confidence level'' rather than 95%. The commenter apparently confused 
the CTV for rejecting a 1-tailed hypothesis 
(<greek-m><INF><greek-i></INF> <ls-thn-eq> S) with the pair of critical 
values for rejecting a 2-tailed hypothesis 
(<greek-m><INF><greek-i></INF> = S) and inferring that 
<greek-m><INF>i</INF> simply differs from S in either direction. The 
criterion for rejecting the latter hypothesis would be a measurement 
either sufficiently above the applicable standard or sufficiently below 
it. In testing for a difference of arbitrary direction, 1.64 would 
indeed yield a pair of 90-percent confidence limits, with a 5-percent 
chance of erring on either side. The purpose of the CTV table, however, 
is to provide criteria for determining that the true dust concentration 
strictly exceeds the applicable standard. Since such a determination 
can occur only when a single, full-shift measurement is sufficiently 
high, there is exactly zero probability of erroneously citing 
noncompliance when a measurement falls below the lower confidence 
limit. Consequently, the total probability of erroneously citing 
noncompliance equals the probability that a standard normal random 
variable exceeds 1.64, which is 5 percent.
    One commenter alluded to testimony in the Keystone case (Keystone 
v. Secretary of Labor, 16 FMSHRC 6 (Jan. 4, 1994)), suggesting that 
application of the CTV to a single measurement involves an invalid 
comparison of two distributions or comparison of two means. Contrary to 
much of the testimony presented in that case, a determination of 
noncompliance using the CTV table is based on the decision procedure 
described above. It does not involve any comparison of probability 
distributions or means. Nor does it involve any statistical 
distribution of dust concentrations. It involves only the comparison of 
an individual full-shift measurement to the applicable standard. There 
is only one probability distribution involved in this comparison: 
namely, the distribution of random measurement errors by which each 
full-shift measurement deviates from the true dust concentration to 
which the sampler unit is exposed.
    Some commenters apparently misunderstood the effect of potential 
weighing errors on the formula for calculating the CTV corresponding to 
different applicable standards. Weight gain is estimated from the 
difference between two weighings of an exposed filter capsule, adjusted 
by subtracting the difference between two weighings of a control filter 
capsule. Since weight gains are small compared to the total weight of 
capsules being weighed, any dependence of weighing error on the 
magnitude of the mass being weighed is canceled in the process of 
calculating the difference. Since the standard deviation of the error 
in weight gain is, therefore, essentially constant, the ratio of that 
standard deviation to the dust concentration being measured decreases 
with increasing dust concentration. This causes CV<INF>CTV</INF> to 
decrease as the dust concentration increases. As explained above, the 
CTV corresponding to S is calculated using the value of 
CV<INF>CTV</INF> for dust concentrations exactly equal to S. 
Consequently, the CTV corresponding to a standard of 2.0 mg/
m<SUP>3</SUP> is based on a smaller value of CV<INF>CTV</INF> than the 
CTV corresponding to a standard of 0.2 mg/m<SUP>3</SUP>.
    One commenter implied that use of the CTV table relies on an 
assumption that CV<INF>total</INF> declines at concentrations greater 
than 2.0 mg/m<SUP>3</SUP> (or S in general). As explained previously, 
the CTV corresponding to different applicable standards is designed to 
test the null hypothesis that S is not exceeded. For each applicable 
standard, entries are based on the probability distribution of 
observations expected under that presumption. Consequently, the 
magnitude of CV<INF>total</INF> assumed in establishing or applying any 
CTV does not decrease below the value of CV<INF>total</INF> calculated 
for a concentration of 2.0 mg/m<SUP>3</SUP>, since that is the maximum 
applicable standard being tested. Because the probability of wrongly 
citing noncompliance is zero when S is exceeded, measurement 
uncertainty at concentrations greater than S is not relevant to 
noncompliance determinations. (It would, however, be relevant to 
inferring compliance at a specified confidence level--i.e., to a test 
of the alternative hypothesis that S is not exceeded.)
III. Validity of the CTV table
    Some commenters questioned the validity of the CTV table and 
challenged the formula used to calculate each CTV listed. Some objected 
to the use of a normal distribution and claimed that a lognormal 
distribution or nonparametric assumptions would be more appropriate. 
Other commenters objected specifically to the use of a confidence 
coefficient based on a standard normal probability distribution, rather 
than a t-distribution. The validity of using <radical>n, rather than 
<radical>(n-1), in the formula used to calculate citation threshold 
values in MSHA's February 1994 notice, was also questioned. At least 
one commenter contended that the formula used to generate the CTV table 
is not valid for use with only one measurement.
    Such comments would have some validity if the CTV table were 
intended to test or estimate average concentration over some spatially 
distributed region of a mine or some period greater than the single 
shift during which each measurement is taken. In either case, it might 
be necessary and appropriate to estimate variation in concentration 
directly from the measurement samples obtained. Such an estimate could 
conceivably be used in establishing a site-specific threshold value for 
citation. This would, indeed, require a theoretical minimum of two 
samples, or far more for valid practical applications. Estimating 
variability from the samples collected would also require additional 
assumptions or nonparametric methods to reflect the pattern of 
variation in dust concentration between locations or shifts.
    The objections raised, however, apply to a very different task from 
the one for which the CTV table is designed. As explained previously, 
the CTV table is not meant to test dust concentration averaged over any 
period greater than the shift during which measurements were taken. Nor 
is it meant to test dust concentration averaged across different 
occupational locations or throughout any spatially distributed region 
of the mine. Instead, the CTV table provides criteria for determining 
noncompliance at individual sampling locations on individual shifts. 
Neither the spatial nor temporal distribution of the dust 
concentrations is germane to the intended citation criteria. Although 
several measurements may be taken during a single inspection, MSHA 
regards each of these measurements as relating to the dust 
concentration uniquely associated on a given shift with a separate 
sampling location. Each such dust concentration (<greek-m><INF>i</INF>) 
is the average for the atmosphere at the sampling location, accumulated 
over the course of the single, full shift sampled. Since the 
enforcement objective is to determine whether <greek-m><INF>i</INF> > S 
for any individual I, it is not necessary to estimate or assume 
anything about the

[[Page 5702]]

degree to which <greek-m><INF>i</INF> varies from location to location 
or from shift to shift. Nor is it necessary to assume anything about 
the spatial or temporal statistical distribution of 
<greek-m><INF>i</INF>. No such assumptions are built into the CTV 
table. A normal distribution is imputed only to 
<greek-e><INF><greek-i></INF>, the difference between X<INF>i</INF> and 
<greek-m><INF>i</INF>. Since the mean across various 
<greek-m><INF>i</INF> is not being estimated or tested, it is not 
necessary to estimate variability among the <greek-m><INF>i</INF> from 
measurements taken during the inspection. MSHA emphatically agrees with 
those commenters who stressed the impossibility of doing so with a 
single measurement.
    Those commenters who objected to MSHA's use of a normal 
distribution, claiming that a lognormal distribution or nonparametric 
assumptions would be more appropriate, apparently confused the 
distribution of dust concentrations over time and between locations 
with the distribution of errors that arise when measuring dust 
concentration at a specific time and location. In other words, they 
confused the distribution of <greek-m><INF>i</INF> with the 
distribution of <greek-e><INF><greek-i></INF>. The concerns about non-
normality stem from confusion about what quantity is being estimated.
    MSHA does not dispute the fact that lognormal or nonparametric 
methods are often appropriate for modeling variability in occupational 
dust concentrations. MSHA, however, is explicitly not claiming to 
estimate any quantity beyond the average dust concentration at a 
particular sampling location on a single shift. MSHA does not claim 
that dust concentrations are normally distributed from shift to shift, 
from occupation to occupation, or from location to location; nor is any 
such assumption built into the CTV table. Since the object is not to 
estimate average concentration over a range of different locations or 
shifts, the statistical distribution of <greek-m><INF>i</INF> is 
irrelevant, and application of lognormal or nonparametric techniques in 
constructing citation criteria is both unnecessary and inappropriate.
    In constructing the CTV table, MSHA used a normal probability 
distribution solely to represent a potential measurement error, 
<greek-e><INF><greek-i></INF>. This measurement error causes a 
measurement X<INF>i</INF> to deviate from <greek-m><INF>i</INF>, the 
actual dust concentration at a specific time and place. As 
distinguished from the statistical distribution of dust concentrations, 
it is generally accepted that the distribution of measurement errors 
around a given concentration is normal [3]. This was explicitly 
acknowledged by members of the industry panel in their Morgantown 
testimony.
    Similarly, criticism directed against MSHA's use of a confidence 
coefficient derived from the standard normal distribution instead of 
the t-distribution arises from a basic misunder standing of what is or 
is not being estimated in the decision procedure. Contrary to the 
remark of one commenter, use of the t-distribution is not justified as 
a ``compromise'' between normal-theoretic and nonparametric 
assumptions. The
t-distribution arises in statistical theory when a normally distributed 
random variable is divided by an estimate of its standard deviation. 
Typically it is applied to situations in which the mean and standard 
deviation are estimated from the same normally distributed data, 
consisting of fewer than about thirty or forty random data points. If 
the estimate of standard deviation is based on more data, then the 
confidence coefficient derived from the t-distribution is approximately 
equal to the corresponding value derived from the standard normal 
distribution. Use of the t-distribution is appropriate, for example, 
when a group of normally distributed observations is ``standardized'' 
by subtracting the group mean from each observation and dividing the 
result by the group standard deviation.
    Those commenters advocating a confidence coefficient based on the
t-distribution failed to recognize that CV<INF>CTV</INF> was not 
derived from the measurements that MSHA inspectors will use to test for 
compliance with S. Use of the t-distribution is not appropriate when an 
independently known or stipulated standard deviation is used in 
comparing observations to a standard [3]. The standard deviation of 
measurement errors used in constructing the CTV table is derived from 
prior knowledge, rather than estimated from a few measurements taken 
during an inspection. Experimental analysis has shown that 
CV<INF>total</INF> is less than CV<INF>CTV</INF>. So long as this is 
true, use of a confidence coefficient derived from the standard normal 
distribution is entirely appropriate.
    Contrary to the claims of some commenters, there is no valid basis 
for including a so-called [n/(n-1)]<SUP>1/2</SUP> ``correction factor'' 
in the formula for establishing a CTV. (The ``n'' in this expression 
would refer to the number of measurements, if a noncompliance 
determination were based on the average of several measurements.) The 
theory behind such a factor does not apply when, as in the case of the 
CTV table, a predetermined or maximum tolerated variability in 
measurement error is used in comparing observations to a standard [3]. 
It would apply only if variability in measurements observed during each 
inspection were somehow used to construct a CTV specific to that 
inspection. The variability observed among multiple samples collected 
during an MSHA inspection has little to do with the accuracy of an 
individual measurement and is not used at all in constructing the CTV 
table.
    Although no explicit reason was given for the claim by some 
commenters that the formula used to generate the CTV table is not valid 
for use with a single measurement, this would follow if either: (1) the 
appropriate basis for the confidence coefficient were a
t-distribution rather than a standard normal distribution; or (2) it 
were necessary to multiply the CTV by [n/(n-1)]<SUP>1/2</SUP>, where n 
is the number of measurements on which a noncompliance determination is 
based. In the former case, the standard normal distribution would not 
adequately approximate the t-distribution; and in the latter case, n = 
1 would cause the so-called correction factor, and hence the CTV, to be 
mathematically indeterminate for determinations based on a single 
sample. It has already been explained, however, that neither of these 
considerations are applicable to the CTV table.
    Some commenters stated that a single measurement cannot accurately 
be used to detect excessive dust concentrations, even if the 
noncompliance determination applies only to a specific shift and 
location. These commenters implied that due to random, temporary 
fluctuations in dust concentration, a single measurement is inherently 
unstable and misleading. Such arguments fail to differentiate a full-
shift sample from a ``grab sample,'' which is typically a sample 
collected over only a few minutes or seconds and used to estimate 
average conditions over an entire shift. In contrast to a grab sample, 
each full-shift dust sample is collected continuously over the full 
period to which the measurement applies. An 8-hour dust sample consists 
of 480 1-minute grab samples, or an arbitrarily large number of even 
shorter grab samples. A full-shift dust sample can be viewed as 
measuring average concentration over the entire shift by averaging 
together all of these shorter subsamples. Although short-term 
fluctuations in dust concentration, as well as random changes in flow 
rate and collection efficiency, may cause many of the subsamples to 
poorly represent average concentration over the entire shift, random 
short-term aberrations tend to cancel one another when the subsamples 
are combined. Therefore, a

[[Page 5703]]

full-shift dust sample does not suffer from lack of sample size.

Appendix C--Risk of Erroneous Enforcement Determinations

I. What Constitutes Compliance or Noncompliance?
    To simplify the following discussion, let <greek-m> denote the 
average dust concentration to which a sampler unit is exposed on a 
given shift, let S denote the applicable standard, and let X denote a 
valid, full-shift measurement of <greek-m>. Also, let c be the CTV in 
the table corresponding to S so that a citation is issued when X 
<gr-thn-eq> c. Section 202(b)(2) of the Mine Act requires that the 
average dust concentration during each shift be maintained at or below 
the applicable standard wherever miners normally work or travel. This 
means that, on any given shift, the average dust concentration 
(<greek-m>) at any valid sampling location must not exceed the 
applicable standard (S).
    Since the CTVs listed always exceed S it can happen that a full-
shift measurement (X) falls between S and c. In such instances, MSHA 
will not issue a citation. This does not, however, imply that MSHA 
considers the mine atmosphere sampled to have been in compliance with 
the Mine Act or that cases of marginal noncompliance are tolerable. 
MSHA's use of the CTVs is not motivated by any tacit acceptance of 
marginal noncompliance. Rather, it is motivated by the necessity to 
avoid unsustainable violations. When X falls between S and c, this 
provides some evidence that <greek-m> > S; but the evidence is 
insufficient to warrant a citation.
    Although <greek-m> > S constitutes a violation, X greater than S 
but less than the CTV does not provide compelling evidence that 
<greek-m> > S. This is because, in a sufficiently well-controlled 
mining environment, X is more likely to slightly exceed S due to 
measurement error than due to <greek-m> > S. In fact, as demonstrated 
in Appendix D, citing when X > S but X < c could result in citations 
when the probability of compliance (<greek-m> <ls-thn-eq> S) on the 
shift and location sampled is greater than 50 percent. Use of the CTV 
table is necessary in order to avoid citing in such cases.
    There are two sorts of conclusions that might be drawn from the 
results of a single MSHA inspection: those relating to the individual 
shift sampled and those relating to some longer time period, such as 
the full interval between MSHA inspections. Therefore, in evaluating 
the probability of erroneous enforcement determinations, it is 
essential to distinguish between (1) compliance or noncompliance with 
the applicable standard on the shift sampled and (2) compliance or 
noncompliance with the full requirement of the Mine Act as it applies 
to every shift over a longer term, such as the period between MSHA 
inspections.
    If <greek-m> > S on some proportion of shifts, say P < 1, then the 
mine does not comply with the applicable standard on some individual 
shifts and, therefore, does not comply with the Mine Act over the 
longer term. At the same time, the mine is in compliance with the 
applicable standard (at the location sampled) on a complementary 
proportion, equal to 1--P, of individual shifts. If an MSHA inspection 
happens to fall on one of those shifts that is out of compliance, then 
a correct determination with respect to the individual shift would also 
be correct with respect to the longer term. If, on the other hand, the 
MSHA inspection happens to fall on a shift that is in compliance, then 
it would be a mistake to assume compliance on subsequent shifts and 
vice versa. Although MSHA interprets the Mine Act as requiring 
<greek-m> <ls-thn-eq> S on each shift and at each sampling location to 
which miners in the active workings are exposed, the immediate 
objective of an MSHA dust inspection can only be to determine 
compliance or noncompliance for the shift and location sampled. 
Therefore, MSHA does not consider a compliance or noncompliance 
determination to be erroneous if it is correct with respect to the 
individual shift and location but incorrect with respect to other 
shifts or locations.
II. Uncertainty in the Standard-Setting Process
    In response to the March, 12, 1996 MSHA/NIOSH Federal Register 
notice, a commenter claimed that a noncompliance determination based on 
a single, full-shift measurement could be erroneous if the applicable 
standard was improperly established due to measurement errors 
associated with silica analysis. It was, therefore, suggested that 
uncertainty in the standard-setting process should be factored into the 
risk of erroneous enforcement decisions. MSHA agrees that, like any 
measurement process, the sampling and analytical method used to 
quantify the silica content of a respirable dust sample in order to set 
the applicable standard is subject to potential measurement errors. 
Therefore, MSHA uses an analytical procedure that meets the requirement 
of a NIOSH Class B analytical method. Applicable standards are set 
based on results of silica analysis using the most up-to-date 
laboratory equipment.
    The Secretary, however, considers the accuracy of the standard-
setting process to be a separate issue from the accuracy of 
noncompliance determinations based on a single-full-shift measurement, 
once the applicable standard has been set. The present notice relates 
only to the enforcement of the applicable standard in effect at time of 
the sampling inspection. Therefore, the following discussion treats any 
applicable standard in effect at the time of sampling as binding and 
evaluates the risk of erroneous determinations relative to that 
standard.
III. Measurement Uncertainty and Dust Concentration Variability
    Variability in dust concentration refers to the differing values of 
<greek-m> on different shifts or at different locations. For a given 
value of <greek-m>, measurement uncertainty refers to the differing 
measurement results that could arise because of different potential 
measurement errors. If <greek-m> <ls-thn-eq> S, measurement error can 
cause an erroneous citation. Similarly, if <greek-m> > S, then 
measurement error can cause an erroneous failure to cite.
    The ``margin of error'' separating each CTV from the corresponding 
applicable standard does not eliminate the possibility of erroneous 
enforcement determinations due to uncertainty in the measurement 
process. A determination based on comparing X to the CTV could be 
erroneous in either of two ways with respect to the individual shift 
sampled: (1) the comparison could erroneously indicate noncompliance on 
the shift (i.e, X <gr-thn-eq> c but <greek-m> <ls-thn-eq> S) or (2) the 
comparison could erroneously fail to indicate noncompliance on the 
shift (i.e, X < c but <greek-m> > S). The margin of error built into 
the CTV table reduces the probability of erroneous citations but 
increases the probability of erroneous failures to cite.
    MSHA recognizes that in determining how large the margin of error 
should be, there is a tradeoff between the probabilities of these two 
mistakes--i.e., if the chance of erroneously failing to cite is 
reduced, then the chance of erroneously citing is increased, and vice 
versa. MSHA has constructed the CTV. table so as to ensure that 
citations will be issued only when they can be issued at a high level 
of confidence. As will be shown below, doing this provides assurance 
that for any given citation, <greek-m> is more likely than not to 
actually exceed S. In contrast, if there were no margin of error, 
citations more likely than not to be erroneous could occasionally be 
issued. Examples of this are given in Appendix D.

[[Page 5704]]

    In the discussion below, the risk of erroneous citations and 
erroneous failures to cite is quantified for noncompliance 
determinations based on the CTV table. To illustrate points in the 
theoretical discussion, three different mining environments will be 
used as examples. These environments exemplify different degrees of 
dust concentration variability and dust control effectiveness. The 
first example (Case 1) is based on historical mine data provided by 
commenters in connection with these proceedings. The second and third 
examples (Case 2 and Case 3) are hypothetical and are designed to 
reflect extremely well-controlled and poorly controlled mining 
environments, respectively. In these three examples, it will be assumed 
that <greek-m> is lognormally distributed from shift to shift. This is 
a standard assumption for airborne contaminants in an occupational 
setting [3]. The three cases considered are characterized as follows:

----------------------------------------------------------------------------------------------------------------
                                                                   Dust concentration (mg/m<SUP>3)                   
                                               -----------------------------------------------------------------
                     Case                        Arithmetic     Arithmetic                          Prb {<greek-
                                                    mean,       Std. Dev.,   Geometric  Geometric      m>>S}    
                                                E{<greek-m>}  SD{<greek-m>}     mean    Std. Dev.    (percent)  
----------------------------------------------------------------------------------------------------------------
1.............................................       1.66           0.70         1.53       1.50         25.4   
2.............................................       1.20           0.24         1.18       1.22          0.4   
3.............................................       2.20           1.32         1.89       1.74         45.8   
----------------------------------------------------------------------------------------------------------------

    In addition to the variability in dust concentrations described by 
the arithmetic and geometric standard deviations of <greek-m>, full-
shift measurements contain a degree of uncertainty described by 
CV<INF>total</INF>, the coefficient of variation for measurements of 
the same dust concentration. In calculating the probability of 
erroneous determinations for the three example cases, it will also be 
assumed that the applicable standard is S = 2.0 mg/m<SUP>3</SUP> and 
that the coefficient of variation in full-shift measurements taken at a 
given value of <greek-m> is:
[GRAPHIC] [TIFF OMITTED] TN31DE97.016

Where <greek-s><INF>e</INF> = 9.12 <greek-m>g is the standard deviation 
of error in weight gain, as determined from MSHA's 1995 field 
investigation of measurement precision [4]; 1.38 is the MRE-equivalent 
conversion factor for measurements made with an approved sampler unit; 
the first quantity being squared is CV<INF>weight</INF>; 
CV<INF>pump</INF> = 4.2% and CV<INF>sampler</INF> = 5%, as explained in 
Appendix B.II of the joint MSHA and NIOSH notice of finding published 
elsewhere in today's Federal Register.
    It should be noted that the ``total'' in CV<INF>total</INF> refers 
to total measurement uncertainty and is not meant to include the 
effects of variability in dust concentration.
    Because it employs a higher value for CV<INF>sampler</INF> 
(reflecting variability amongst used rather than new 10-mm nylon 
cyclones), this composite estimate of CV<INF>total</INF> is slightly 
greater and perhaps slightly more realistic than that obtained directly 
from MSHA's 1995 field investigation. It declines from 11.3% at dust 
concentrations of 0.2 mg/m<SUP>3</SUP> to no more than 6.6% at 
concentrations of 2.0 mg/m<SUP>3</SUP> or greater. At all dust 
concentrations within this range, it falls well below the 12.8% maximum 
value permitted for a method meeting the NIOSH Accuracy Criterion [5]. 
It is also smaller than the value, CV<INF>CTV</INF>, used to construct 
the CTV table. As explained in Appendix B, this ensures that any 
citation issued will be warranted at a confidence level of at least 95 
percent.
    To simplify the discussion below on risk of erroneous citations and 
erroneous failures to cite, it is necessary to introduce some 
additional notation and to focus on just one measurement collected 
during each inspection.<SUP>2</SUP> This could be the ``D.O.'' sample 
in a MMU, or the measurement collected for a designated area. Let 
<greek-e> = X-<greek-m> represent the measurement error in a valid 
measurement. For reasons explained in Appendix B, <greek-e> is assumed 
to be normally distributed with zero mean and standard deviation equal 
to <greek-s> = <greek-m><SUP><bullet></SUP>CV<INF>total</INF>. 
Consequently, X is normally distributed with mean equal to <greek-m> 
and standard deviation equal to <greek-s>. This normal distribution of 
X around <greek-m> reflects uncertainty in the measurement of a given 
dust concentration. On any given shift, the probability distribution of 
X is determined by the value of <greek-m> for that shift and sampling 
location. Therefore, the probability of citation on a given shift is 
conditional on <greek-m> and is denoted by Prb{X<gr-thn-eq>c | 
<greek-m> .}<SUP>3</SUP>
---------------------------------------------------------------------------

    \2\ Appendix D addresses cases in which a noncompliance 
determination is based on the maximum of several measurements.
    \3\ A vertical bar is used to denote conditional probability. 
Prb {A | B} denotes the conditional probability of event A, given 
the occurrence of event B. For any events A and B,
    Prb{A|B}=Prb{A and B}/Prb {B}=Prb{B|A}<bullet>Prb {A}/Prb{B}
---------------------------------------------------------------------------

    Since <greek-m> varies from shift to shift, variability in dust 
concentration is represented by the probability distribution of 
<greek-m>. Let E {<greek-m>} denote the expected (i.e., arithmetic 
mean) dust concentration over some longer term of interest, such as the 
interval between MSHA inspections; and let SD{<greek-m>} denote the 
standard deviation of <greek-m> over the same period. Although the 
value of <greek-m> on any individual shift is unknown, 
Prb{X<gr-thn-eq>c} can be calculated using the probability distribution 
of <greek-m>. In particular, if the probability is known that <greek-m> 
fulfills a specified condition, such as <greek-m> <ls-thn-eq> S or 
<greek-m> > S, then

    Prb{X<gr-thn-eq>c} = Prb{X<gr-thn-eq>c | <greek-m> <ls-thn-eq>S}
    <SUP><divide></SUP>Prb{<greek-m><ls-thn-eq>S}+Prb{X<gr-thn-eq>c | 
<greek-m> >S}
    <SUP><divide></SUP>Prb{<greek-m>>S}.

    Over a sufficiently long term, with respect to any particular 
sampling

[[Page 5705]]

location, Prb{<greek-m>>S} and Prb{<greek-m><ls-thn-eq>S} can be 
identified, respectively, with the proportion of noncompliant shifts, 
P, and the proportion of compliant shifts, 1-P. P is sometimes called 
the noncompliance fraction and more or less defines the likelihood that 
the applicable standard is or is not exceeded on the particular shift 
inspected.<SUP>4</SUP>
---------------------------------------------------------------------------

    \4\ P defines this likelihood exactly only if shifts are 
randomly selected for MSHA inspection and there is no adjustment of 
conditions in response to the inspection.
---------------------------------------------------------------------------

    If the statistical distribution of <greek-m> can be adequately 
represented by a probability density function, denoted f(<greek-m>), 
then Prb{<greek-m>>S} and Prb{<greek-m><ls-thn-eq>S} can also be 
calculated by integrating f(<greek-m>) over the desired range. The 
probability that <greek-m> falls in any interval, say between a and b, 
is given by:
[GRAPHIC] [TIFF OMITTED] TN31DE97.017

    It follows that:
    [GRAPHIC] [TIFF OMITTED] TN31DE97.018
    
IV. Risk of Erroneous Citation
    Some commenters argued that a citation for noncompliance is 
warranted only if the average dust concentration to which a miner is 
exposed exceeds the applicable standard over a period of time greater 
than a single shift, such as a bimonthly sampling period, a year, or a 
miner's lifetime. Therefore, these commenters called it ``unfair'' to 
cite individual shifts on which the applicable standard is exceeded, so 
long as the average over this longer term meets the applicable 
standard. For example, based on the historical sampling data provided 
by a commenter and employed here as Case 1, one commenter concluded 
that ``* * * there is at least a 1 in 6 or 17% probability that any 
single sample can show potential overexposure [using the CTV table] 
when one does not exist.'' Further, these commenters maintained that 
basing citations on a single, full-shift measurement would 
substantially increase the frequency of unfair citations, compared to 
existing MSHA policy.
    Using the notation introduced above, these commenters have confused 
<greek-m> with E(<greek-m>) and confounded the noncompliance fraction P 
with the probability of erroneous citation. For example, the 17-percent 
figure mentioned above includes all cases in which X <gr-thn-eq> c, 
regardless of whether <greek-m> > S on the shift sampled. In the 
discussion accompanying the data, commenters argue that since 
E(<greek-m>) is approximately 1.66 mg/m\3\, or less than 1.85 mg/m\3\ 
at a high confidence level, ``* * * [cases of X <gr-thn-eq> c] show 
potential overexposure when one does not exist.'' This statement 
depends on the unwarranted assumption that miners exposed to these 
conditions have been exposed to similarly distributed dust 
concentrations in the past and that they will be exposed to similarly 
distributed concentrations in the future. These commenters' own 
analysis indicates that the dust concentration has not been kept below 
the standard on each shift. Therefore, a citation is warranted under 
the Mine Act.
    To more fully explore what is going on in Case 1, suppose, as these 
commenters suggest, that dust concentrations over the period observed 
are lognormally distributed from shift to shift, with E{<greek-m>} = 
1.66 mg/m<SUP>3</SUP> and a geometric standard deviation of about 1.5 
mg/m<SUP>3</SUP>. Under this assumption, <greek-m> > 2.0 mg/
m<SUP>3</SUP> on more than 25 percent of all shifts, and <greek-m> > 
2.33 mg/m<SUP>3</SUP> on 15 percent. These percentages pertain to 
actual dust concentrations and have nothing to do with measurement 
error or accuracy of an individual measurement. Therefore, a 2.0 mg/
m<SUP>3</SUP> dust standard would be violated on 25 percent of all 
production shifts. The applicable standard would be violated by an 
amount greater than 0.33 mg/m<SUP>3</SUP> on 15 percent. Since 2.33 is 
the CTV for a single measurement, this 15 percent actually represents 
shifts sufficiently far out of compliance that they would probably be 
cited if inspected. Nevertheless, the commenters' analysis includes 
such shifts in the 17 percent claimed as cases subject to erroneous or 
unfair citation.
    The expected value of the noncompliance fraction (P) in Case 1 is 
25 percent. Therefore, close to 25 percent of all single shift 
measurements made under the conditions of Case 1 would be expected to 
exceed the standard. Only 17 percent of the single full-shift 
measurements taken, however, exceeded the CTV and would have warranted 
citations. Using the estimate of CV<INF>total</INF> described above, 15 
percent of all single shift measurements would be expected to do so. 
Therefore, contrary to the commenters' conclusion, Case 1 does not 
demonstrate a high probability of erroneously identifying 
overexposures. Instead, it illustrates an effect of the high confidence 
level required for citation: the margin of error built into the CTV 
reduces the probability of citing whatever shift happens to be selected 
for inspection from about 25 percent to 15 percent. Although the 
applicable standard is violated on 25 percent of the shifts, there is 
only a 15 percent chance that any particular measurement meets the 
citation criterion.
    To correctly and unambiguously quantify the risk of ``unfair'' 
citations, it is necessary to identify three distinct ways of 
interpreting the risk of erroneous noncompliance determinations. This 
risk can be defined alternatively as:
    (1) the probability of citing when the mine atmosphere sampled is 
actually in compliance, Prb{X<gr-thn-eq>c|<greek-m><ls-thn-eq>S};
    (2) the probability that the mine atmosphere on a shift randomly 
selected for inspection is in compliance but is nevertheless cited, 
Prb{<greek-m><ls-thn-eq>S and X<gr-thn-eq>c}; or
    (3) the probability that a given citation is erroneous,
    Prb{<greek-m><ls-thn-eq>S|X<gr-thn-eq>c}.
    These three different probabilities apply to three different base 
populations. Although the different interpretations of risk give rise 
to quantitatively different probabilities, the expected total number of 
erroneous citations, denoted N<greek-a>, remains constant if each 
probability is multiplied by the size of the population to which it 
applies. To obtain N<greek-a>, the first probability must be multiplied 
by the number of valid measurements made when <greek-m> <ls-thn-eq> S, 
the second by the total number of valid measurements, and the third by 
the total number of citations issued--i.e., valid measurements for 
which X <gr-thn-eq> c.
    The CTV table limits the probability of erroneously citing defined 
by the first two interpretations to a maximum of less than five 
percent. However, in a

[[Page 5706]]

well-controlled mining environment, where citations are rarely 
warranted, the third probability can be larger than the first two. 
Since the burden of proof rests with MSHA to demonstrate noncompliance, 
it is essential that <greek-a> deg. be kept well below 50 percent. As 
will be shown by example, the use of the CTV table accomplishes this 
goal.
    Each of the three different probabilities related to erroneous 
noncompliance determinations will now be explained in detail. 
Calculations for all examples are performed under the assumptions (1) 
that <greek-m> is lognormally distributed and (2) that <greek-e> is 
normally distributed with mean equal to zero and standard deviation 
equal to <greek-m><bullet>CV<INF>total</INF>.
1. <greek-a> = Prb{X<gr-thn-eq>c|<greek-m><ls-thn-eq>S}
    The first risk to be considered is the probability of citing 
noncompliance when the mine atmosphere sampled is actually in 
compliance. This probability represents the proportion of those 
measurements made when <greek-m> <ls-thn-eq> S that result in X 
<gr-thn-eq> c. In other words, 
<greek-a>=Prb{X<gr-thn-eq>c|<greek-m><ls-thn-eq>S} is the probability 
that, due to measurement error, a citation is issued under the 
condition that <greek-m> <ls-thn-eq> S. This is the probability 
associated with what is commonly designated Type I error for testing 
the null hypothesis: <greek-m> <ls-thn-eq> S on the shift sampled.
    Essentially, <greek-a> is the expected (i.e., mean) probability of 
citation over all those shifts sampled that are at or below the 
applicable standard. The relative frequency distribution of <greek-m> 
over those shifts is described by its probability density function, 
f(<greek-m>). Therefore, <greek-a> can be calculated as follows:
[GRAPHIC] [TIFF OMITTED] TN31DE97.019

    If <greek-m> did not vary, then <greek-a> would be directly related 
to the confidence level at which the null hypothesis could be rejected 
when X <gr-thn-eq> c. That confidence level, which applies to citations 
issued in accordance with the CTV table, is defined as the minimum 
possible value of 1-Prb{X<gr-thn-eq>c|<greek-m>}, subject to the 
restriction that <greek-m> <ls-thn-eq> S. There is a subtle but 
extremely important distinction between this and 1-<greek-a>. Among all 
those shifts on which <greek-m> <ls-thn-eq> S, 
Prb{X<gr-thn-eq>c|<greek-m>} is maximized when <greek-m> = S. 
Therefore, the minimum possible value of 1-<greek-a>, arises when 
<greek-m> = S on every shift. The resulting confidence level for 
concluding <greek-m> > S when X <gr-thn-eq> c is equal to 
1-Prb{X<gr-thn-eq>c|<greek-m>=S}. For the value of CV<INF>total</INF> 
described above (i.e., 6.6% when <greek-m> = S = 2.0 mg/m<SUP>3</SUP>), 
this works out to a confidence level of 0.99, or 99%.
    Although MSHA interprets the Mine Act as requiring <greek-m> 
<ls-thn-eq> S on each shift at any location to which a miner in the 
active workings is exposed, citations for noncompliance are intended to 
apply only to the shift and location sampled. Therefore, MSHA makes no 
assumption regarding the relative frequency distribution of <greek-m> 
from shift to shift. This is consistent with the concept of defining 
the confidence level according to the scenario most susceptible to an 
erroneous determination under the null hypothesis. However, the 
resulting confidence level for citing when X <gr-thn-eq> c really 
applies only to the hypothetical case most susceptible to erroneous 
citation.
    In reality, so long as <greek-m> falls below S on some shifts, 
<greek-a> will be smaller than 0.01. The further <greek-m> falls below 
the applicable standard, and the more shifts on which this occurs, the 
less likely it becomes that measurement error alone (<greek-e>) will be 
great enough to cause X <gr-thn-eq> c on a shift randomly selected for 
inspection. For example, if S = 2.0 mg/m<SUP>3</SUP>, then c = 2.33 mg/
m \3\.
    Therefore, if <greek-m> = 1.8 mg/m<SUP>3</SUP>, a citation would be 
issued only if <greek-e> <gr-thn-eq> c-<greek-m>. An <greek-e> 
<gr-thn-eq> 0.53 mg/m<SUP>3</SUP> (resulting in X <gr-thn-eq> 2.33 mg/
m<SUP>3</SUP>) amounts to a measurement error greater than 29 percent 
of the true dust concentration. If the sample is valid, then the 
probability of such an occurrence (given that CV<INF>total</INF> = 6.6% 
at <greek-m> = 1.8 mg/m<SUP>3</SUP>) is less than 4 per million. This 
illustrates the general point that Prb{X<gr-thn-eq>c|<greek-m>} can be 
far less than 0.01 when <greek-m> < S.
    Since Prb{X<gr-thn-eq>c|<greek-m>} is smaller the further <greek-m> 
falls below S, Prb{X<gr-thn-eq>c|<greek-m><ls-thn-eq>S} depends on the 
probability distribution of <greek-m>. This probability distribution is 
expressed by the relative frequency with which <greek-m> assumes each 
possible dust concentration at or below S. If <greek-m> falls 
substantially below the applicable standard on many shifts, then many 
of the corresponding values of Prb{X>c|<greek-m>} averaged into the 
calculation of <greek-a> should be much smaller than 0.01, as shown by 
the foregoing example. Consequently, in a mining environment where the 
dust concentration is usually well below the applicable standard, 
<greek-a> can reasonably be expected to fall substantially below its 
maximum possible value.
    The number of erroneous citations expected (N<greek-a>), is 
obtained by first multiplying the total number of production shifts 
during the period of interest by the expected proportion of these 
shifts for which <greek-m> <ls-thn-eq> S. This proportion is 1 - P. The 
result is the number of production shifts expected to be in compliance 
at the sampling location. This must then be multiplied by <greek-a> to 
calculate N<greek-a>.
    In Case 1, which is based on real sampling data (submitted by 
commenters), E{<greek-m>} is 1.66 mg/m \3\ and SD{<greek-m>} is 0.70 
mg/m \3\. As mentioned earlier, P is expected to be 0.25 in this case. 
This distribution results in a negligible probability of citing when 
the mine atmosphere sampled is in compliance: <greek-a> = 0.00012. If 
10,000 production shifts are sampled in this type of environment, 7500 
of these would be expected to be in compliance at the sampling 
location. Approximately one of these 7500 samples (i.e., 
7500<SUP><divide></SUP><greek-a>) would be erroneously cited.
    In Case 2, which is meant to represent a more controlled mining 
environment, less than one percent of the shifts are expected to exceed 
the standard: P = 0.0037. Furthermore, <greek-m> can be expected to 
fall below the geometric mean of 1.18 mg/m \3\ on about half of the 
shifts. Therefore, <greek-a> is even smaller than in the first case: 
<greek-a> = 0.0000079. Out of 10,000 sampled shifts, 9963 would be 
expected to be in compliance. Since 9963 <SUP><divide></SUP><greek-a> 
is less than 0.1, it is unlikely that any of these shifts would be 
cited erroneously.
    Case 3 is meant to represent a poorly controlled mining 
environment, in which E{<greek-m>} exceeds the applicable standard and 
the coefficient of variation in shift-to-shift dust concentrations is a 
relatively high 60% (i.e., 1.32 <divide> 2.20). The geometric mean, 
however, falls slightly below the applicable standard, so <greek-m> is 
expected to fall below the applicable standard on more than 50% of the 
shifts. The noncompliance fraction is expected to be P = 0.46. Also, 
because of the high shift-to-shift variability, <greek-m> is not very 
close to its geometric mean on most shifts, and a fairly large 
percentage of shifts can be expected to experience <greek-m> well below 
the standard. The probability of citing when the mine atmosphere is in 
compliance is: <greek-a> = 0.00015. If 10,000 of shifts in this 
environment are sampled, then 5400 of these shifts would be expected to 
comply with the applicable standard at the sampling location. As in 
Case 1, an erroneous citation would be expected on about one of these 
shifts.
2. <greek-a>* = Prb{<greek-m><ls-thn-eq>S and X<gr-thn-eq>c}
    The probability of erroneous citation can also be defined 
unconditionally. The second way of interpreting this risk represents 
the proportion of all measurements expected to result in an erroneous 
citation. Let <greek-a>* = Prb{<greek-m><ls-thn-eq>S and X<gr-thn-eq>c} 
be the probability that a shift and/or mine atmosphere randomly 
selected for inspection is in compliance but, because of measurement 
error, is nevertheless cited. For an erroneous

[[Page 5707]]

citation to occur, two events must take place: first, the atmosphere 
sampled must be in compliance (<greek-m><ls-thn-eq> S); second, a 
measurement error must occur of sufficient magnitude that a citation is 
issued (X <gr-thn-eq> c). The probability that a randomly selected 
shift will be in compliance is Prb{<greek-m><ls-thn-eq>S} = 1-P. The 
probability of citation, given compliance on the sampled shift, has 
already been quantified above as 
Prb{X<gr-thn-eq>c|<greek-m><ls-thn-eq>S} = <greek-a>. The probability 
that both events occur is the product of these two probabilities--i.e.,

Prb{<greek-m><ls-thn-eq>S and X<gr-thn-eq>c} = 
Prb{<greek-m><ls-thn-eq>S} <SUP><divide></SUP> 
Prb{X<gr-thn-eq>c|<greek-m><ls-thn-eq>S}

    Therefore, <greek-a>*=(1-P) <SUP><divide></SUP><greek-a>.
    If the applicable standard is exceeded on all shifts, it is 
exceeded on the shift sampled, so there is no chance of erroneously 
citing that shift: i.e., P = 1, so <greek-a>*=(1-1)<bullet><greek-a>=0. 
At the opposite limit, if the applicable standard is never exceeded, 
then P = 0 and <greek-a>* = <greek-a>. Between these two extremes, 
<greek-a>* decreases as the noncompliance fraction P increases, so that 
<greek-a>* is always less than <greek-a>. To get the number of 
erroneous citations, <greek-a>* is simply multiplied by the number of 
shifts sampled. This always gives an identical result for N<greek-a> as 
that obtained from multiplying the number of compliant shifts by 
<greek-a>.
    In Case 1, P = 0.25. Therefore, the probability of erroneously 
citing a randomly selected shift is <greek-a>* = 
0.75<SUP><divide></SUP><greek-a> = 0.00009, or about nine in 100,000. 
If 10,000 shifts are sampled, then 10,000 <SUP><divide></SUP><greek-a>* 
gives the same number of erroneous citations as <greek-a> multiplied by 
the 7500 compliant shifts expected in this case.
    In the relatively well-controlled environment exemplified by Case 
2, dust concentrations on most shifts generally fall well below the 
standard. Only occasional excursions approaching or (rarely) exceeding 
the standard occur, so P is near zero. Therefore, <greek-a>* is only 
slightly smaller than <greek-a>. Since P = 0.0037, <greek-a>* = 0.9963 
<SUP><divide></SUP><greek-a>. In this environment, the chance of 
erroneously citing a randomly selected shift is less than one in 
100,000.
    In Case 3, the noncompliance fraction is much greater: P = 46%. 
Therefore, <greek-a>* is substantially smaller than <greek-a>. In this 
environment the probability of erroneously citing a randomly selected 
shift is <greek-a>* = 0.00008, or about eight in 100,000.
3. <greek-a> deg. = Prb{<greek-m><ls-thn-eq>S|X<gr-thn-eq>c}
    Finally, the risk of an erroneous citation can be interpreted as 
the probability, given a measurement of sufficient magnitude to warrant 
citation (X <gr-thn-eq> c), that the dust concentration measured 
actually complies with the standard (<greek-m><ls-thn-eq>S). Let 
<greek-a> deg. = Prb{<greek-m><ls-thn-eq>S|X<gr-thn-eq>c} denote this 
probability, which represents the expected proportion of all citations 
issued because of measurement error. If any particular citation, based 
on a valid single, full-shift measurement, is selected for scrutiny, 
then <greek-a> deg. is the probability that this citation is erroneous. 
Using the definition of conditional probability: 
[GRAPHIC] [TIFF OMITTED] TN31DE97.020

    Prb{X<gr-thn-eq>c|<greek-m>>S} represents the power of the citation 
criterion to identify cases of noncompliance when they actually occur. 
This probability is calculated as follows: 
[GRAPHIC] [TIFF OMITTED] TN31DE97.021

    When the distribution of dust concentrations is such that the 
applicable standard is rarely exceeded (i.e., when P is near zero), the 
denominator in the expression for <greek-a> deg. namely 
[GRAPHIC] [TIFF OMITTED] TN31DE97.022

is only slightly greater than the numerator, <greek-a>*. This implies 
that <greek-a> deg. is not constrained to be smaller than <greek-a> or 
<greek-a>*. Since this situation arises in environments where the 
applicable standard is rarely exceeded, such citations will not often 
be issued. However, when one is issued, the probability that it is 
erroneous can exceed <greek-a>.
    For example, in the relatively well-controlled environment 
exemplified by Case 2, <greek-a>* is 0.00000788, P is 0.00370, and 
Prb{X<gr-thn-eq>c|<greek-m>>S} = 0.133. Therefore, in this example, 
<greek-a> deg. = 0.0158, or about 1.6 percent. That is to say, 1.6 
percent of the citations issued under these circumstances will be 
erroneous. This is considerably greater than <greek-a>, which was 
earlier shown to equal only 0.00079 percent. However the expected 
proportion of measurements resulting in citation, given by 
Prb{X<gr-thn-eq>c}, is only 0.000498, or 0.050%. Therefore, out of

[[Page 5708]]

10,000 shifts sampled, it is expected that only five would be cited. 
Since on average only 1.6% of these five citations would be erroneous, 
it is unlikely that the 10,000 samples would result in any erroneous 
citations.
    Case 2 represents an environment in which the noncompliance 
fraction is less than one percent. In contrast, the noncompliance 
fraction in Case 3 is nearly 50%: P = 0.458. For this case, <greek-a> = 
0.000147, <greek-a>* = 0.0000799, and <greek-a> deg. = 0.000227. The 
calculated value of Prb{X<gr-thn-eq>c} is 0.3513, so approximately 35 
percent of all measurements would result in citation. Only about 0.027% 
of these citations, however, would be erroneous. Therefore, out of 
10,000 shifts sampled in such an environment, 3513 citations could be 
expected; and only about one of these citations 
(3513<greek-a><bullet> deg.) would be expected to be erroneous.
    In Case 2, the probability (<greek-a> deg.) that a given citation 
is erroneous is relatively high (though low enough to sustain a 
citation), but the probability of citing noncompliance in such an 
environment is very low. In Case 3, the probability of citation is more 
than 700 times higher, but <greek-a> deg. is commensurately lower than 
in Case 2. Comparison of Cases 2 and 3 illustrates the general 
principle: as the noncompliance fraction  P increases, the probability 
of citation increases but the probability that a given citation is 
erroneous decreases.
    It is important to note that even in the well-controlled 
environment of Case 2, the probability that a given citation is 
erroneous (<greek-a> deg.) remains substantially below five percent and 
far below 50 percent. Although environments even more well controlled 
could give rise to somewhat greater values of <greek-a> deg., the 
probability of citing in such environments would be even smaller than 
the probability in Case 2. If a citation is issued because X > c, then 
the probability that <greek-m> > S is simply 1 - <greek-a> deg.. This 
shows that in any particular instance where a citation based on a 
single, full-shift measurement is reasonably likely to be issued 
according to the CTV table, there would be compelling evidence that 
<greek-m> > S.
V. Risk of Erroneous Failure to Cite
    Use of the CTV implies that citations will be issued only when they 
can be issued with high confidence that the applicable standard has 
actually been exceeded on the shift sampled. On the other hand, failure 
to meet or exceed the CTV does not in itself imply compliance at a 
similarly high confidence level--even on the shift sampled, let alone 
continuously over any longer term. Because of limited resources, MSHA 
inspections are relatively infrequent and serve only to identify 
instances in which the rest of the dust control program has been 
ineffective. They cannot be relied upon to ensure continuous 
compliance.
    It should be remembered, however, that MSHA does not rely 
exclusively on sampling by inspectors to ensure compliance. The MSHA 
inspection is only one element of the Agency's comprehensive health 
protection program, which includes mandatory implementation and 
maintenance by operators of effective dust control methods to control 
dust levels where miners normally work or travel. It also provides for 
periodic evaluation by mine operators of the quality of mine air and of 
the effectiveness of the operator's dust control system through 
operator bimonthly sampling. If they are not detected during an MSHA 
inspection, poorly controlled environments, which are out of compliance 
with the dust standard in a substantial fraction of instances, are 
likely to be detected during some other phase of the MSHA's enforcement 
program.
    It should also be remembered that MSHA's new enforcement policy 
eliminates an important source of sampling bias due to averaging, as 
explained in Appendix A. Under the existing policy, measurements made 
at the dustiest occupational locations or during the dustiest shifts 
sampled are diluted by averaging them with measurements made under less 
dusty conditions. As shown by the SIP data, this practice has 
frequently caused failures to cite clear cases of excessive dust 
concentration.
1. <greek-b> = Prb{X<c|<greek-m>>S}
    The complement of power, the probability of detecting cases of 
noncompliance when they occur, is the probability of erroneously 
failing to detect such cases. Let <greek-b> = Prb{X<c|<greek-m>>S} be 
the probability that a citation will not be issued when the true dust 
concentration being measured exceeds the standard. This is the 
probability of what is commonly called Type II error for testing the 
null hypothesis that <greek-m> <ls-thn-eq> S. Since <greek-b> = 1 - 
Prb{X<gr-thn-eq>c|<greek-m>>S}, the power of the citation criterion, 
formulated earlier as Prb{X<gr-thn-eq>c|<greek-m>>S}, can be used to 
calculate <greek-b>. The expected number of erroneous failures to cite, 
N<greek-b> is obtained by multiplying <greek-b> by the number of shifts 
for which <greek-m> > S.
    It is true that due to the high confidence level required for 
citation, <greek-b> is greater than it would be if a citation were 
issued whenever X > S. In fact, setting the CTV to any value greater 
than S results in Prb{X<c|<greek-m>} potentially greater than 50 
percent when a single dust concentration exceeding the standard is 
being measured. For example, if <greek-m> = 2.12 mg/m<SUP>3</SUP> and S 
= 2.0 mg/m<SUP>3</SUP>, then the CTV is c = 2.33 mg/m<SUP>3</SUP>. 
Since the probability distribution for X is centered on <greek-m>, any 
individual measurement is more likely to fall below the CTV than to 
exceed it. The probability of erroneously failing to cite in this 
instance, based only on a single measurement, would be 
Prb{X<2.33|<greek-m>=2.12} = 93 percent.
    Citing in accordance with the CTV table does not, however, 
necessarily result in <greek-b> > 50%. When more than one measurement 
is made during a single shift in the same general area of a mine, such 
as in the same MMU, the dust concentrations are correlated. This 
increases the chances that if <greek-m> exceeds the standard at one of 
the sampled locations, at least one of the measurements will meet the 
citation criteria. More importantly for the present discussion, 
however, the value of <greek-b> depends on the distribution of 
<greek-m> even when only a single measurement is considered on each 
shift.
    This is because the magnitude of <greek-b> depends on the average 
magnitude of Prb{X<c|<greek-m>} over all those instances in which 
<greek-m> > S. Although Prb{X<c|<greek-m>} exceeds 50 percent when 
<greek-m> < c, it does not exceed 50 percent when <greek-m> > c. Poorly 
controlled environments are likely to experience a significant number 
of shifts during which <greek-m> exceeds not only S but also the CTV. 
If these shifts ``outweigh'' those shifts on which S < <greek-m> 
<ls-thn-eq> c, then this will result in <greek-b> < 50 percent.
    On those shifts for which <greek-m> > S, Prb{X<c|<greek-m>} exceeds 
50% only when <greek-m> falls between S and c. In contrast, the range 
of potential values of <greek-m>>c is essentially unlimited, and 
Prb{X<c|<greek-m>} approaches zero as <greek-m> increases. Therefore, 
<greek-b> is less than 50% whenever the distribution of <greek-m> is 
such that Prb{<greek-m>>c} > Prb{S<<greek-m><ls-thn-eq> c}. In a poorly 
controlled environment, <greek-m> is more likely to exceed the CTV than 
to fall into the relatively narrow interval between S and the CTV.
    For example, in Case 1 the probability that <greek-m> exceeds c = 
2.33 is 14.9 percent, whereas the probability that <greek-m> falls 
between S and c is only P - 14.9 = 10.5 percent. Therefore, in this 
environment, the probability of erroneously failing to cite an instance 
of <greek-m> > S works out to be somewhat less than 50 percent: 
<greek-b> = 1 - Prb{X<gr-thn-eq>c|<greek-m>>S} = 0.404, or 40.4%.
    For worse offenders, <greek-b> is considerably smaller. In Case 3, 
Prb{<greek-m>>c} = 35.2%, whereas Prb{S<<greek-m><ls-thn-eq>c} is 
10.6%. In this case, even though dust concentrations below the 
applicable standard are

[[Page 5709]]

expected on a majority of shifts (as indicated by the geometric mean), 
<greek-b> is calculated to be only 23.3%. Stated another way, if MSHA 
were to select 10,000 shifts in this environment, an expected 4580 of 
those shifts would be out of compliance. It is expected that on 76.7% 
of those 4580 shifts a single measurement would be sufficiently large 
to warrant citation.
    There are inherent tradeoffs, not only between <greek-b> and 
<greek-a>, but also between <greek-b> and the probability that a given 
citation is erroneous, <greek-a> deg. = 
Prb{<greek-m><ls-thn-eq>S|X<gr-thn-eq>c}. Decreasing the CTV in order 
to reduce <greek-b> forces both <greek-a> and <greek-a> deg. to 
increase. Even if <greek-a> remains below 50 percent, the effect on 
<greek-a> deg. can be so great as to render some citations clearly 
unsustainable. In particular, setting the CTV at or near S could result 
in citations more likely than not to be erroneous. Circumstances in 
which this can occur are discussed in Appendix D. Use of the CTV, on 
the other hand, ensures that any given citation based on X <gr-thn-eq> 
c is more likely than not to represent a case of actual noncompliance 
(i.e., <greek-m> > S).
    Failure to issue a citation based on a single, full-shift 
measurement collected during an MSHA inspection does not imply failure 
to detect and correct a noncompliant condition in the context of MSHA's 
entire enforcement program. Those commenters expressing concern over 
the potential magnitude of <greek-b> have largely ignored other means 
MSHA uses to protect miners from excessive dust concentrations relative 
to the longer term. As stated earlier in this notice, MSHA's health 
protection program provides for the implementation and maintenance by 
mine operators of effective methods to control dust concentrations 
where miners normally work or travel, as well as for periodic 
evaluation of the quality of mine air to which miners may be exposed 
and the effectiveness of the operator's dust control program through 
operator bimonthly sampling. Furthermore, MSHA intends to continue its 
long-standing practice of collecting additional measurements when the 
standard is exceeded by an amount insufficient to warrant citation at a 
high confidence level.
VI. Summary and Conclusions
    Use of the CTV table is based on MSHA's need for sufficient 
evidence to issue a citation and show, by a preponderance of the 
evidence, that a violation occurred. The burden rests with MSHA to show 
that the applicable standard has in fact been violated on the 
particular shift cited. Accordingly, the CTV table is designed so that 
the risk of erroneously not citing is subordinated to the risk of 
erroneously issuing a citation. However, the probability of erroneously 
failing to cite a case of noncompliance at a given sampling location is 
less than 50 percent when the applicable standard is exceeded on a 
significant proportion of shifts at that location.
    Three cases were used to illustrate the risk of erroneous 
enforcement determinations over a broad range of environmental 
conditions. The results calculated for each of the three cases 
considered are summarized in the following table.

--------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                        Probability (percent)                                       Average number of   
                                     ------------------------------------------------------------------------------------------ erroneous determinations
                                                                                                                                   (per 10,000 sampled  
                Case                                                                                                                     shifts)        
                                        Prb{X>S}   Prb{X<gr-thn-eq>c}    <greek-a>    <greek-a>*   <greek-a> deg.   <greek-b>  -------------------------
                                                                                                                                 N<greek-a>   N<greek-b>
--------------------------------------------------------------------------------------------------------------------------------------------------------
1...................................        25.51            15.14         0.0121        0.00903          0.060           40.4          0.9        1,026
2...................................         0.53             0.05          .000791       .000788         1.581           86.7           .1           32
3...................................        45.69            35.17          .0147         .00799          0.0227          23.3           .8        1,067
--------------------------------------------------------------------------------------------------------------------------------------------------------

    Based on this analysis, it can be concluded that application of the 
CTV table provides ample protection against erroneous citations. The 
probability (<greek-a>) of issuing a citation when the mine atmosphere 
sampled is actually in compliance is constrained to fall below a 
maximum of five percent. This maximum defines the 95-percent confidence 
level claimed for any citation issued. The expected proportion 
(<greek-a>*) of all valid samples resulting in an erroneous citation is 
constrained not to exceed <greek-a>. In practice, both <greek-a> and 
<greek-a>* are expected to fall far below five percent in a broad range 
of mining environments.
    Furthermore, even in an exceptionally well-controlled environment, 
where <greek-m> is very unlikely to exceed the applicable standard on 
any particular shift, the probability (<greek-a> deg.) that a given 
citation is erroneous will also fall substantially below five percent. 
If a measurement exceeds the CTV, the probability that the standard has 
actually been exceeded is (1-<greek-a> deg.). Therefore, any citation 
issued in accordance with the CTV table will be based on clear and 
compelling evidence that the standard has been exceeded on the 
particular shift sampled.
    Although it is increased by the margin of error built into the CTV 
table, the probability (<greek-b>) of erroneously failing to cite 
noncompliance using a single measurement is expected to be 
significantly less than 50 percent in mining environments where 
<greek-m> > S on a substantial percentage of shifts. For the example 
considered of a poorly controlled mining environment (Case 3), 
<greek-b> was calculated to be about 23 percent. This means that on any 
given shift for which <greek-m> > S, there would be a 77-percent chance 
that X would exceed the CTV, thereby warranting a citation. Despite the 
high confidence level required for single-sample citations, <greek-b> 
is considerably less than 50 percent even in the better-controlled 
environment exemplified by Case 1. Although citing whenever X > S would 
increase the probability of detecting conditions of excessive dust 
concentration, Appendix D shows that doing so instead of using the CTV 
table could result in citations under conditions of probable 
compliance. As shown by the small values of <greek-a> deg. in the table 
above, use of the CTV table makes it very unlikely that this would 
happen.
    Moreover, poorly controlled environments are likely to be detected 
and cited during some other phase of MSHA's enforcement program even if 
they are not immediately cited on a particular MSHA sampling 
inspection. Regardless of the value of <greek-b>, it can safely be 
concluded that the risk of failing to detect excessive dust is lower 
under MSHA's new enforcement policy than under existing procedures, in 
which measurements of high dust concentration are diluted by averaging.

Appendix D--Consequences of Eliminating the Margin of Error

    Several commenters objected to the emphasis placed on avoiding 
erroneous citations and took issue with MSHA's intention to cite 
noncompliance only when indicated at a high confidence level. These 
commenters proposed that it is unfair to limit citations to cases in

[[Page 5710]]

which a measurement (X) meets or exceeds some critical value (c) 
greater than the applicable standard (S). They argued that such an 
approach unfairly exposes miners to a far higher probability of wrongly 
failing to cite than the maximum probability specified for wrongly 
citing. Their recommendation was to divide the burden equally between 
proving noncompliance and ensuring compliance. They maintained that if 
X exceeds S by an arbitrarily small amount, noncompliance is more 
likely than compliance and that under such circumstances a citation 
should be issued.
    Using notation explained in Appendix C, X = <greek-m> +<greek-e>, 
where <greek-e> is a random, normally distributed measurement error 
whose standard deviation is 
<greek-s>=<greek-m><SUP><divide></SUP>CV<INF>total</INF>.CV<INF>total</INF>
 is given by the formula presented in Appendix C. A citation based on a 
single, full-shift measurement applies specifically to the shift and 
location sampled, and hence to a distinct value of <greek-m>. For the 
citation to be upheld, the preponderance of evidence must indicate that 
<greek-m> > S at one or more of the sampling locations on the cited 
shift.
    Those commenters who maintained that a citation should be issued 
whenever X > S all assumed (1) that a citation could withstand legal 
challenge so long as noncompliance is more likely than compliance, even 
if the probability of compliance is nearly 50 percent; and (2) that if 
X > S, then noncompliance is more likely than compliance. Aside from 
the question of the legal validity of the first assumption (which 
equates preponderance of evidence with any probability greater than 50 
percent), the second assumption is not always true. Specifically, the 
second assumption fails to hold in relatively well-controlled 
environments or in cases where more than one measurement is used to 
check for noncompliance. Commenters making this assumption confused 
Prb{X>S|<greek-m><ls-thn-eq>S} with Prb{<greek-m><ls-thn-eq>S|X>S} and 
also failed to consider citations based on the maximum of several 
measurements.
I. Well-controlled Environments
    In a relatively well-controlled environment, where <greek-m> is 
generally below the applicable standard, the probability that X > S due 
to a large value of <greek-e> can exceed the probability that X > S due 
to <greek-m> > S. If X < c and sampling records indicate that the 
environment is relatively well-controlled, the preponderance of 
evidence may support <greek-m> <ls-thn-eq> S on the particular shift 
sampled.
    For example, suppose a citation is based on a single, full-shift 
measurement that barely exceeds S=2.0 mg/m\3\, but dust sampling 
records for the environment indicate a pattern of dust concentrations 
resembling Case 2 in Appendix C. That is to say, the statistical 
distribution of <greek-m> is lognormal, with arithmetic mean and 
standard deviation of 1.2 mg/m\3\ and 0.24 mg/m\3\, respectively. As in 
Appendix C, let f(<greek-m>) denote the lognormal probability density 
function. Then the probability that <greek-m><ls-thn-eq>S, given a 
single full-shift measurement that falls between S and c, is:
[GRAPHIC] [TIFF OMITTED] TN31DE97.023

    In other words, when X falls between S and c in this environment, 
there is a 52-percent chance that the standard has not actually been 
exceeded. It is more likely that X>S due to a large measurement error 
than because <greek-m> itself has exceeded the applicable standard. It 
would be unreasonable to cite noncompliance in such situations. By 
citing when and only when X<gr-thn-eq>c, the probability that 
<greek-m><ls-thn-eq>S is reduced to <greek-a> deg.=1.5%, as shown for 
Case 2 in Appendix C.
II. Multiple Samples
    Proponents of citing whenever X>S based their argument on a premise 
of symmetry: since potential measurement errors (<greek-e>) are 
symmetrically distributed around <greek-m>, they assumed that citing 
when X=S would result in equal probabilities of erroneously citing and 
erroneously failing to cite. From this, they argued that if X>S by an 
arbitrarily small amount, the probability of erroneously failing to 
cite would exceed the probability of erroneously citing.
    The symmetry argument for citing whenever X>S fails to hold if, on 
a single inspection, more than one measurement is compared to the 
standard. In MSHA's dust inspection program, several measurements are 
routinely made on the same shift, within the same MMU. MSHA intends to 
use each of these measurements individually to determine noncompliance 
at the MMU. However, as described in the notice to which this Appendix 
is attached, no more than one citation will be issued based on single, 
full-shift measurements from the same MMU. The commenters advocating 
issuance of a citation whenever X>S all endorsed such single-sample 
determinations. Since any of several measurements could warrant a 
citation against the MMU, the citation will be based, in most cases, on 
the maximum measurement taken in the MMU during the shift. If each of 
several measurements is compared directly to the applicable standard, 
then the symmetry assumed for citing whenever X>S breaks down. The 
mistake of wrongly citing occurs when any one of the measurements 
exceeds the applicable standard because of a sufficiently large 
measurement error, but the mistake of wrongly failing to cite occurs 
only when each and every measurement is at or below the standard. Each 
additional measurement reduces the probability of erroneously failing 
to cite while increasing the probability of erroneously citing.

[[Page 5711]]

    A few examples will be used to demonstrate how the premise of 
symmetric error probabilities breaks down when more than a single 
measurement is taken. These examples demonstrate that noncompliance 
determinations made by comparing so few as two measurements directly to 
the S can result in citations issued at a confidence level 
substantially below 50 percent.
    Using I to index different valid measurements for the same MMU, let 
max{X<INF>i</INF>} denote the maximum measurement, and let 
max{<greek-m><INF>i</INF>} denote the maximum true dust concentration. 
Note that due to potential measurement errors, the maximum dust 
concentration does not necessarily correspond to the maximum 
measurement. For example, max{X<INF>i</INF>} might be X<INF>3</INF> 
even though max{<greek-m><INF>i</INF>}=<greek-m><INF>2</INF>. Since the 
object is to examine the consequences of citing whenever any of several 
measurements exceeds S by any amount, it will be assumed in these 
examples that the citation criterion is max{X<INF>i</INF>}>S rather 
than max{X<INF>i</INF>}>c.
    As in Appendix C, let <greek-a> be the probability of citing under 
conditions of compliance, and let <greek-b> be the probability of 
erroneously failing to cite. Then:
[GRAPHIC] [TIFF OMITTED] TN31DE97.024

    For simplicity, suppose S=2.0 mg/m<SUP>3</SUP>. The following 
quantities will be used in the calculations:

----------------------------------------------------------------------------------------------------------------
                                                                                Prb{X>2.0|  Prb{X<ls-thn-eq>2.0|
       <greek-m> (mg/m<SUP>3)          CV<INF>total    <greek-s>=<greek-m><SUP>bulletCV<INF>total   <greek-m>}        <greek-m>}    
                                 (percent)                (mg/m<SUP>3)               (percent)         (percent)     
----------------------------------------------------------------------------------------------------------------
1.90..........................        6.602                  0.1254                   21.3              78.7    
1.99..........................        6.596                  0.1385                   47.1              52.9    
2.00..........................        6.595                  0.1319                   50.0              50.0    
2.01..........................        6.595                  0.1326                   53.0              47.0    
----------------------------------------------------------------------------------------------------------------

    If exactly one measurement is taken and <greek-m>=1.99 mg/
m<SUP>3</SUP>, then <greek-s>=0.1385 mg/m<SUP>3</SUP>. Using the 
standard normal probability distribution for <greek-e>/<greek-s>,
[GRAPHIC] [TIFF OMITTED] TN31DE97.025

    On the other hand, if <greek-m>=2.01 mg/m\3\, then <greek-s>=.1319 
mg/m\3\; so
[GRAPHIC] [TIFF OMITTED] TN31DE97.026

    It is this approximate equality of <greek-a> and <greek-b>, for 
values of <greek-m> symmetrically falling below or above S=2.0 mg/m\3\ 
that motivates the premise of symmetric error probabilities.
    Suppose now that two measurements are taken, and a citation is 
issued if either X<INF>1</INF> or X<INF>2</INF> exceeds S=2.0. Suppose 
further that <greek-m><INF>1</INF>=1.99 and <greek-m><INF>2</INF>=1.90. 
Then:
[GRAPHIC] [TIFF OMITTED] TN31DE97.027

    Since a citation is justified if <greek-m><INF>i</INF> > S for any 
I, the greatest probability of wrongly not citing in a comparable case 
of noncompliance is obtained when <greek-m><INF>1</INF>=2.01 and 
<greek-m><INF>2</INF> is held at 1.90. In that case:
[GRAPHIC] [TIFF OMITTED] TN31DE97.028

    This example illustrates the point that <greek-a> can exceed 
<greek-b> by a substantial amount when as few as two measurements are 
directly compared to the applicable standard. If <greek-m><INF>2</INF> 
were actually 1.99, then the discrepancy would be even greater: 
<greek-a>=72% and <greek-b>=25%. Notice, furthermore, that in both 
cases, <greek-a> would be greater than 50%. The confidence level at 
which a citation is issued depends on the maximum possible value of 
<greek-a>. Therefore, when one measurement out of two marginally 
exceeds S, the confidence level at which a citation can be issued is 
less than 28% (i.e., 100%-72%). Such a citation would be difficult to 
defend if challenged.

[[Page 5712]]

    If five measurements are made, as is routinely done during MSHA 
inspections of an MMU, then citing whenever max{X<INF>i</INF>}>S is 
even less defensible. The confidence level for a citation based on the 
maximum of five measurements is defined by the value of <greek-a> when 
<greek-m><INF>i</INF>=S for all five values of I. Under these 
circumstances, the probability that at least one of the five 
measurements would exceed the applicable standard is:
[GRAPHIC] [TIFF OMITTED] TN31DE97.029

    Therefore, the confidence level at which a citation could be issued 
is only 3%. At the same time, the probability that none of the five 
measurements will exceed S is <greek-b>=(0.5)<SUP>5</SUP>=3%, so the 
probability that a citation would be issued is 97%.
III. Conclusion
    MSHA, along with other federal agencies, recognizes that in issuing 
citations, the burden rests with the Agency to show that a violation of 
the applicable standard occurred. Use of the CTV table will severely 
limit the risk of an erroneous citation, even when the true dust 
concentration being measured is exactly equal to or slightly below the 
applicable standard. If a single measurement falls between S and the 
CTV, then the measurement does not necessarily provide sufficient 
evidence of <greek-m>>S to support a citation. Consequently, MSHA 
cannot justify issuing a citation whenever a measurement exceeds the 
applicable standard by an arbitrarily small amount. Although citing 
whenever X>S would result in a smaller probability (<greek-b>) of 
erroneously failing to cite, and hence in a greater level of protection 
for the miner, doing so would result in citations that may not 
withstand legal challenge. However, as stated earlier in the notice, if 
the measurement exceeds the applicable standard but not the CTV, MSHA 
intends to target environments for additional sampling to confirm that 
dust control measures in use are adequate. These follow-up inspections, 
in conjunction with operator dust sampling and MSHA monitoring of 
operator compliance with approved dust control parameters, should 
further help to protect miners from excessive dust concentration.

References

    1. Kogut, J. Memorandum of September 6, 1994, from Jon Kogut, 
Mathematical Statistician, Denver Safety and Health Technology 
Center, MSHA, to Ronald J. Schell, Chief, Division of Health, Coal 
Mine Safety and Health, MSHA, Subject: Multi-day MSHA Sampling of 
Respirable Coal Mine Dust.
    2. Kogut, J. Memorandum of September 6, 1994, from Jon Kogut, 
Mathematical Statistician, Denver Safety and Health Technology 
Center, MSHA, to Ronald J. Schell, Chief, Division of Health, Coal 
Mine Safety and Health, MSHA, Subject: Coal Mine Respirable Dust 
Standard Noncompliance Determinations.
    3. Leidel, N.A. and K.A. Busch. Statistical Design and Data 
Analysis Requirements. Patty's Industrial Hygiene and Toxicology, 
Third Edition, Vol. 3, Part A, Chapter 10, 1994.
    4. Kogut, J., T.F. Tomb, P.S. Parobeck, A.J. Gero, and K.L. 
Suppers. Measurement Precision With the Coal Mine Dust Personal 
Sampler. Internal MSHA Report, 1995.
    5. Kennedy, E.R., T.J. Fischbach, R. Song, P.M. Eller, and S.A. 
Shulman. Guidelines for Air Sampling and Analytical Method 
Development and Evaluation. U.S. Department of Health and Human 
Services, Public Health Service, National Institute for Occupational 
Safety and Health, DHHS (NIOSH) Publication No. 95-117.

    Dated: December 19, 1997.
J. Davitt McAteer,
Assistant Secretary for Mine Safety and Health.
    Note: For the convenience of the user, notice document 97-33937 
is being reprinted in its entirety because of numerous errors in the 
document originally appearing at 62 FR 68395-68420, December 31, 
1997. Those wishing to see a listing of corrections, please call 
Patricia Silvey, Mine Safety and Health Administration, 703-235-
1910.
[FR Doc. 97-33937 Filed 12-30-97; 8:45 am]
BILLING CODE 4510-43-P