DISCUSSION

The chances of a miner making a successful escape
while wearing an SCSR depend on three issues:

1. Training.—Did the miner don the SCSR properly?

2. SCSR integrity.—Did the SCSR function, or did the
miner decide to abandon it?

3. Oxygen consumption.—Did the SCSR provide enough
oxygen?

A computer simulation that takes these issues into account
was developed to estimate survival odds for a prototypical
escape and was used to show that these odds change when
SCSR training improves. The computer simulation was
applied to four mines that were part of an SCSR donning
proficiency field study. The results show that relative
survival odds for different mines can vary by as much as

30% and that this difference is due to SCSR donning
proficiency. The results also confirm the common sense
view that using an SCSR is the best survival strategy and
the only one that is tenable over long distances. The real
limitation on escape distance is that SCSR’s make available
only a finite quantity of usable oxygen. This must be taken
into account in planning for mine emergencies.

Because theoretical issues are clearly segregated and
the mathematical structure of the model is open to modifi-
cation, it seems likely that the computer simulation can
be naturally extended to cover other factors affecting sur-
vival odds: (1) the location of SCSR caches along escape
routes, (2) decisionmaking under uncertainty, with regard
to choice of escape routes, and (3) group dynamics in mine
emergencies. These will be topics for future research.


CONTENTS
Page

Abstract «oc oss 3:6 55 Se His Hs $4 SE Ee Seer ea ae
Introduction . . ; . .
Mine escape model . .
Prototypical escape .
Training ‘
Self-contained self-rescuer integrity . . .
Oxygen consumption
Calculating survival odds
Results Pay
Discussion . 3% .
Appendix A.—Simulation algorithm . :
Appendix B.—Worksheet representation . .
Appendix C.—Cell-by-cell worksheet listing

FSCmIANUHNNNne

Be

Donning proficiency profiles
Probability of successfully escaping unbreathable atmosphere using SCSR
Survival strategy regions

Serr
a AA

SCSR donning trial performance
SCSR donning probabilities
Oxygen consumption parameters ...

a a
AUnUw


U.S. Department of the Interior
Bureau of Mines

2401 E Street, N.W., MS #9800
Washington, D.C. 20241

OFFICIAL BUSINESS
PENALTY FOR PRIVATE USE-$300

AN EQUAL OPPORTUNITY EMPLOYER


Figure 1.-Donning proficiency profiles.

¢ The miner adjusted the neck strap after looping, but
never secured the waist strap. The mouthpiece was taken
out to look for nose clips and put back in once the nose
clips were found, Initially, the goggles were hung around
the neck. The mouthpiece and nose clips had to be re-
moved to put the goggles on. After donning the goggles,
the mouthpiece and nose clips were replaced.

Adequate:

¢ The miner adjusted the neck strap before activating
the oxygen.

¢ The miner adjusted the neck strap before donning
the goggles. After the hat was put on, the waist strap was
fastened and snugged.

¢ The miner looped the neck strap over the hat and
lamp cord.

Perfect:
¢ The miner performed a perfect 3+3 sequence.’

¢ The miner did a perfect 3+3 sequence, except that
the waist strap should have been slightly tighter.

As can be seen, failing here merely applies to an individ-
ual’s omission of one or another of the steps necessary to
isolate the lungs. In point of fact, miners in both the
failing and poor categories would be considered less than
proficient with the apparatus. Individuals in the adequate
and perfect categories, on the other hand, would be con-
sidered proficient.

Vaught, C., M. J. Brnich, and H. J. Kellner. Instructional Mode
and Its Effect on Initial Self-Contained Self-Rescuer Donning Attempts
During Training. BuMines RI 9208, 1988, 11 pp.


PROBABILITY OF MAKING A SUCCESSFUL MINE ESCAPE
WHILE WEARING A SELF-CONTAINED SELF-RESCUER-
A COMPUTER SIMULATION

By John G. Kovac,’ Charles Vaught, ? and Michael J. Brnich, Jr.?

ABSTRACT

A computer simulation has been developed by the U.S. Bureau of Mines to estimate the chances of
a miner making a successful escape while wearing a self-contained self-rescuer (SCSR). The model
takes into account (1) training in the use of SCSR’s, (2) apparatus integrity, and (3) oxygen cost of a
mine escape. This report examines survival odds for a prototypical escape, and illustrates how these
odds change when SCSR training is improved.

Supervisory physical scientist.

{Research sociologist.

3Mining engineer.

Pittsburgh Research Center, U.S. Bureau of Mines, Pittsburgh, PA.


UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT
kg kilogram m meter
kg-m kilogram meter min minute

L liter mL milliliter



TRAINING

Attrition occurs at the start of a prototypical escape
because some miners cannot don their SCSR’s. The first
component of the mine escape model, therefore, is
training. Training involves two related factors:

1. Proficiency.—At any given mine, each worker can be
classified according to how well he or she is able to don
and activate the SCSR. For the purposes of this model,
donning proficiency is defined by a five-level classification
scheme (failing, poor, marginal, adequate, and perfect).
2. Outcome.—The second factor, donning outcome, focuses
on the actual results when SCSR donning is attempted. A
miner either completes the donning sequence perfectly, or
he or she falls short. The chance that any particular miner
can don the apparatus correctly is influenced by the gen-
eral level of SCSR donning skill at the worker’s minesite.

The two training factors, then, are related by the as-

sumption that the higher the general skill level at a mine,
the greater the odds are that a representative miner will
be able to don an SCSR in an emergency.

Donning proficiency is modeled as a discrete function.

It is represented as a five-state "look-up" table presented
below. Some preliminary definitions are needed:

Skill Level = i;i = 1,23,4,5.

Pr(Skill Level = i) = Probability that a miner drawn
from the work force at a given
mine can don an SCSR at that
skill level.

= Fraction of work force at that
skill level.

Fraction of work force
at that skill level

(Skill level

Donning proficiency:
Failing= 1 .... Fi

Poor = 2. F2
Marginal = 3 F3
Adequate . Fa
Perfect=5 .... FS

Because the skill levels are exclusive and exhaustive, the
following relationship always holds:

Fl + F2 + F3 + F4+ FS =1.

This relationship also guarantees that the skill level proba-
bilities are normalized.

SCSR donning outcome depends on skill level, and it is

represented as a two-state discrete function, defined below:

Skill Level = i;i = 1,2,3,4,5.

Pr(Success,i) Probability that a miner will
successfully don the SCSR,
given his or her donning
proficiency.

1 - Pr(Success,i).

Probability

Pr(Success,i)

Pr(Failure,i) =
State

Successfully dons
SCSR = true
Miner fails to
don SCSR = false

Outcome(i) =

Pr(Failure,i)

Values (F1, F2, F3, F4, F5) for this model have been
obtained from four mines that were part of an empirical
assessment of SCSR donning proficiency at sites in the
Eastern United States. At every mine, 30 volunteers were
selected for testing in the workplace. Each worker was
instructed to don the SCSR just as he or she would if it
were necessary to escape the mine and to do the entire
procedure. While one researcher videotaped the miner’s
performance, another researcher evaluated and timed the
trial. The results have been closely scrutinized and are
an accurate representation of the proficiency levels found
at the four mines. The aggregate data are presented in
figure 1.

In the final analysis, whether a miner fails or succeeds
in the real world would be determined by the miner’s abil-
ity to use the SCSR well enough to survive an attempt to
evacuate through an unbreathable atmosphere. Individual
actions that characterize each category in the classification
scheme, taken from selected donning evaluations, are
profiled below.

Failing:

° The mouthpiece flange was outside the miner’s lips
and the straps were not adjusted.

e The miner put the SCSR on backwards. The
mouthpiece and nose clips were pulled out. The mouth-
piece was put back in, but the miner forgot the nose clips.
The waist or neck straps were not adjusted.

e The miner failed to activate the oxygen and forgot
to put on the nose clips.

Poor.

«© The miner stood up to put the SCSR on. The
mouthpiece and nose clips were pulled out because the
trainee failed to adjust the neck strap. The miner ap-
peared to be very confused during the entire donning
sequence.

« The miner didn’t loop the neck strap. Instead, the
waist strap was put around the neck. The miner also put
the goggles on over the glasses and forgot to put the
hardhat back on.

© The miner failed to adjust the neck strap; as a result,
there was noticeable tension on the breathing hose.

Marginal:

« The miner twisted the neck strap around the breath-
ing hose.

© The miner didn’t put on the goggles and failed to
fasten the waist strap. The nose clips slipped off, but the
miner put them back on.


REPORT OF INVESTIGATIONS/1990.

Probability of Making a Successful Mine
Escape While Wearing a Self-Contained
Self-Rescuer—A Computer Simulation

By John G. Kovac, Charles Vaught, and Michael J. Brnich, Jr.

BUREAU OF MINES

UNITED STATES DEPARTMENT OF THE INTERIOR



short distance, the oxygen consumption ratio (or Holds
Breath Ratio) = Oxygen Consumption/Residual | Oxygen
available in the lungs. For a miner using the SCSR, the
oxygen consumption ratio (or SCSR-Ratio) = Oxygen_
Consumption /Oxygen_Supplied by the SCSR.

In both of the survival scenarios mentioned above, the
oxygen consumption ratios will always be positive. If a
calculated ratio is less than 1, then that particular escape
strategy supplied the miner with enough oxygen to permit
a successful escape. If the ratio calculated is greater than
1, however, a successful escape from the hostile mine at-
mosphere would be considered impossible, since the miner
would not have enough oxygen available under that escape
strategy. The choices for oxygen consumption parameters
are given in table 3.

Table 3.-Oxygen consumption

parameters
Mean
Body weight 197
Oxygen, L (STPI
SCSR .. 100
Residual 05

‘Standard deviation, 10 kg.

CALCULATING SURVIVAL ODDS

When all the models are put together, the computer
simulation calculates survival odds for a specified escape
scenario using a generate-and-test algorithm. Before the
odds can be calculated, however, the user must provide
some initial values for parameters in the simulation. The
parameter set defines a particular prototypical escape. The
user must also specify the escape distance, which is the
independent variable.

Once all user input is specified and the simulation is
activated, the computer simulation will randomly generate
a combination of training, SCSR integrity, and oxygen
consumption. This combination describes (1) whether or
not the miner was able to don the SCSR successfully, (2)
whether the miner possesses a functional SCSR, or an ap-
paratus that he or she will abandon immediately after
donning, and (3) how much oxygen the miner must con-
sume in order to complete the escape. The simulation
then tests whether the combination results in a successful
escape for the miner. In other words, the simulation
checks which of the two survival strategies, if either, lets
the miner travel the escape distance. The simulation is
then repeated a large number of times to accumulate sta-
tistics on the number of successful escapes, using the
following logic:

Pr(Escape) Probability of a successful mine
escape.
= Number of successful escapes divided
by number of trials.

Mathematically, escape probability is calculated by in-
troducing a special function called Is _A_Success that tests
for a successful escape. Js_A_Success has the following
properties:

Is_A_Success= 1, if the miner made a successful escape.
= 0, if the escape attempt fails.
The Js A Success function takes two logical variables:
Uses_SCSR and Holds Breath as arguments.

Uses_SCSR = True, if [(outcome = true) and
(SCSR_integrity = true) and
(SCSRTM Ratio <1)}.
= False, otherwise.
Holds Breath = True, if (Holds_Breath_Ratio <1).

False, otherwise.
The variables are logical analogues of the two survival
strategies. In terms of the logical variables, Is_A_Success
can be rewritten as
Is_A Success = 1, if [(Uses_SCSR) or (Holds_
Breath) = True].
= 0, otherwise.
Let’s look at what happens if Is _A_Success is evaluated for
a large number of trials and the results are accumulated
according to the following program:

Step I: Let j be an index, representing each trial: j =
1 to N Trials. Pick N Trials = 1,000 for a valid
simulation.

Step 2: Randomly generate values for Holds_Breath(j)
and Uses SCSR(j) for the jth trial and evaluate Is_A_
Success.

Is_A_Success(j) = 1, if the jth trial was a success.
= 0, otherwise.

Step 3: Calculate an expected value for Is_A_Success,
E(Is_A_Success). The expected value is the successful es-
cape probability:

Sum(Is_A_Success) = Number of successful escapes in
N_Trals.

E(Is_A_Success) = Sum(Is_A_Success) divided by
N_Tnals.

= Number of successful escapes
divided by N_Trials.
Pr(Escape) = E(Is_A_Success).

By varying the escape distance and repeating the prob-
ability calculation, the user can map out the functional
dependence of survival odds based on escape distance and
parameter choices. A complete listing of computer pseu-
docode for the simulation algorithm is in appendix A.
Because the mine escape model was written in Lotus 1-2-
3, appendix B is an example of a worksheet template and
appendix C is a cell-by-cell listing of the worksheet.


In order to arrive at a conservative but fair interpreta-
tion of what performance at a particular skill level might
mean in the real world, rescarchers analyzed evaluations
of 1,264 donning trials, To illustrate use of this analysis,
consider how failures were treated. It was found that
32.8% of all critical steps (those necessary to isolate one’s
lungs) omitted initially were subsequently corrected during
the trials. While a miner’s inability to get the lungs
isolated would result in death, there are 3 chances in 10
that the miner might convert the failure into a partial
success. For this reason, failing was not assigned a zero
chance of survival, but set instead at 30%. The same
reasoning was used to apportion weights to the other
categories. Estimates of successful donning probabilities
for all skill levels are given in tables 1 and 2.

Table 1.-SCSR donning trial performance’

Critical Secondary
Missed steps 525 780
Corrected steps . 172 336
Missed steps subsequently
corrected ........... +. 328 43.41
"1,264 trials.
Table 2.-SCSR donning
Probabilities
‘Skill level Probability, %
30
50
70
90
100

SELF-CONTAINED SELF-RESCUER INTEGRITY

SCSR integrity is the second component of the mine
escape model. This issue was defined by asking what the
chances are that a miner will abandon the SCSR after don-
ning it. The Bureau and the U.S. Mine Safety and Health
Administration have conducted field audits of SCSR’s, and
both agencies have investigated actual mine escapes involv-
ing the apparatus.* The results of this research have
yielded a 10% use-failure rate for the devices and suggest
two reasons why an SCSR might be abandoned. First, the
apparatus fails to provide life support because of a manu-
facturing defect or because of damage caused by the
in-mine environment. Second, the device might be aban-
doned because the miner is unfamiliar with how an SCSR
works and decides that the apparatus is not functioning
properly.

SCSR integrity is modeled as a discrete distribution. It
can also be represented by the two-state look-up table pre-
sented here:

®Kyriazi, N., J. G. Kovac, J. Shubilla, W. Duerr, and J. Kravitz, Self-
Contained Self-Rescuer Field Evaluation: First-Year Results of 5-Year
Study, BuMines RI 9051, 1986, 12 pp.

State Probability
SCSR integrity = Miner keeps Pr (Keeps SCSR)
SCSR = true
Miner abandons Pr (Abandons SCSR)=
SCSR = false 1 - Pr (Keeps SCSR)

OXYGEN CONSUMPTION

The third component in the mine escape model is oxy-
gen consumption. Attrition occurs if a miner is not sup-
plied with enough oxygen to make a successful escape. The
amount of oxygen that a miner consumes while making an
escape depends on three factors: (1) body weight, which
simply refers to how much the escaping miner weighs,
modeled as a normal distribution, (2) escape distance, that
is, the length of the escape route, and (3) oxygen cost of
a mine escape. Oxygen cost, given in terms of standard
temperature and pressure with dry bulb (STPD), is a pa-
rameter that depends on travel mode: walking upright,
walking in a bent posture (duck walking), or crawling. The
oxygen cost values for each of the three modes of travel
during escape are as follows:

0, (STPD), mL. /kg:m
Walking upright 0.3

Bent posture
Crawling

5
7

In other words, a miner consumes twice as much oxygen
while crawling during the attempt to escape as would be
consumed if he or she could walk upright. The formula
for oxygen consumption would be Oxygen_{ Consumption =
Oxygen_cost * Body weight * Escape_distance?

The linear model makes three assumptions. First,
oxygen consumption at rest is insignificant when compared
with consumption while moving. Second, once a miner
starts along the escape route, he or she is always trying to
make forward progress and never stops to rest. Third, in
the computer simulation, the miner walks in a bent posture
the entire length of the escape route.

Another feature of the linear oxygen consumption
model is that by keeping oxygen cost and body weight
fixed, oxygen consumption is a homogeneous function of
degree 1 in escape distance. In other words, when the es-
cape distance is doubled, oxygen consumption is doubled.

A miner who must escape a fatal hostile environment
has two survival strategies available. If the miner cannot
don the SCSR, or the apparatus fails to function, the miner
can simply hold his or her breath, consuming the residual
oxygen in his or her lungs, and make a short-distance
escape attempt. This is a worst-case strategy. The best
course of action and the only one that would be tenable
over a long distance, however, is to use the SCSR while
escaping.

Oxygen consumption for both survival strategies can
be measured in terms of ratios. For a miner who holds his
or her breath and attempts to reach fresh air within a

*ttalic print indicates mathematical variables used in appendix A.


INTRODUCTION

When a mine disaster occurs, the basic survival tech-
nique for a miner is to escape from the mine. After a
mine fire or explosion, the atmosphere inside the mine
may become oxygen deficient or filled with smoke and
toxic gases. Under these circumstances, escape is virtually
impossible unless a miner is equipped with a self-rescue
device that supplies oxygen while isolating his or her lungs
from the ambient atmosphere.

Federal regulations require that every person who goes
into an underground coal mine in the United States be
supplied with an SCSR and trained in its use.“ An SCSR
is a closed-circuit breathing apparatus designed for the
purpose of mine escape. The SCSR must be capable of
providing at least a 60-min supply of oxygen, regardless of
the condition of the mine atmosphere.

The chances of a miner making a successful escape
while wearing an SCSR depend on three issues:

1. Training—Did the miner don the SCSR properly?

2. SCSR integrity.—Did the SCSR function, or did the
miner decide to abandon it?

3. Oxygen consumption.—Did the SCSR provide enough
oxygen?

A computer simulation that takes these issues into account
has been developed to estimate survival odds for a proto-
typical escape. This report examines how these odds
change when SCSR training is improved. This work is in
support of the U.S. Bureau of Mines mission to increase
the chances of all miners surviving a mine disaster.

MINE ESCAPE MODEL

Although mine disasters seem to occur with great regu-
larity, they are still rare events. Since SCSR’s are a rel-
atively new technology, there are very few case studies of
escape attempts involving miners wearing the apparatus.
As a consequence, there is not enough historical data to
assess the impact of the device. Unfortunately, experi-
ments in this area are impractical, if not impossible. It
would be very costly to reconstruct a mine disaster or
escape situation as a controlled experiment. Moreover, it
would be unethical to expose human subjects to risk just
for the sake of collecting experimental data validating
SCSR technology or training. Yet, there are compelling
reasons for evaluating an individual’s chances of escaping
an unbreathable mine atmosphere. The researchers there-
fore decided to develop a model of a mine escape in order
to estimate survival odds under certain conditions.

Models may actually offer some advantages over real-
world scenarios. The first advantage is parsimony. The
Bureau’s model provides a theoretical framework for ex-
plaining or predicting the outcome of an escape attempt
in terms of training, SCSR integrity, and oxygen consump-
tion issues. The underlying logic and formulas are visible,
and the issues are clearly focused and segregated. A
second advantage is that, because the model is computer
generated, a user can make choices or decisions on initial
conditions or parameter sets. This means that the mine
escape model can be used to make "what-if" calculations to
explore alternatives, or to test the effects of marginal
changes in parameters on survival odds.

In essence, for the present task, the probability of a
successful mine escape is arrived at through simulation.
The model can be considered a programmed structure, be-
cause it is a logical progression of "if-then-else" decisions.
In particular, it is a worksheet template using the Lotus
1-2-3° computer software with the @Risk add-on.® The
model has an empirical basis because it uses the experi-
mental results of training studies, SCSR field audits, and
oxygen cost experiments to calculate survival odds.

PROTOTYPICAL ESCAPE

Prototypical escape means that in a hypothetical situa-
tion in which a disaster has occurred, in order to survive,
a miner must evacuate to safety. Certain conditions are
stipulated as follows:

1, The miner is still in fresh air, but the only escape
route is a straight-line path through a fatally hostile
environment.

2. At the start of the escape, the miner tries to don an
SCSR. If the miner can actually don and activate the
device and if the apparatus is functional, the worker begins
moving along the escape route.

3. Once the miner starts along the escape route, he or
she is always trying to make forward progress, never
stopping to rest. The miner continues moving until all of
the oxygen supplied by the SCSR is consumed.

4. At the end of the escape route, there is fresh air and
safety.

4U.S. Code of Federal Regulations. Title 30-Mineral Resources;
Chapter I-Mine Safety and Health Administration, Department of
Labor, Subchapter O-Coal Mine Safety and Health; Part 75-Mandatory
Safety Standards-Underground Coal Mines, sec. 75.1714; July 1, 1988.

*Reference to specific products does not imply endorsement by the
U.S, Bureau of Mines.

Palisade Corp. (Newfield, NY). At Risk: Risk Analysis and Mod-
cling for the P.C. Computer software, 1988.


Library of Congress Cataloging in Publication Data:

Kovac, John.

Probability of making a successful mine escape while wearing a self-contained self-
rescuer: a computer simulation / by John G. Kovac, Charles Vaught, and Michael
J. Bmich, Jr.

p. cm. ~ (Report of investig>*:s; 9310)

Includes bibliographical references (p. ).

Supt. of Docs. no.: I 28.23:9310.

1. Mine rescue work-Computer simulation. 2. Self-contained self-rescuer (Mine
rescue equipment) I. Vaught, C. Il. Brnich, M. J. Ill. Title. IV. Series: Report
of investigations (United States. Bureau of Mines); 9310.

TN23.U43 [TN297} 90-1918
CIP



APPENDIX A.-SIMULATION ALGORITHM

Computer pseudocode for the mine escape model is
listed below. Variable names in the program are con-
catenated for the sake of clarity. Commands or reserved
words in the pseudolanguage are shown in bold type.

REMARK Stipulate parameter set

REMARK Donning Skill Level
ENTER F1,F2,F3,F4,F5

REMARK Donning Probability
ENTER P1,P2,P3,P4,P5

REMARK Create Look Up Table
LET LOOK _UP_TABLE(1) :=P1
LET LOOK_UP_TABLE(2) :=P2
LET LOOK_UP_TABLE(3) :=P3
LET LOOK_UP_TABLE(4) :=P4
LET LOOK" UP. TABLE(5) : =PS

REMARK SCSR Integrity
ENTER Pr(Abandons SCSR)
Pr(Keeps SCSR) := 1 - Pr(Abandons SCSR)

REMARK Oxygen Consumption
ENTER Mean, Std Dev
ENTER SCSR_Oxygen
ENTER Residual_Oxygen

REMARK Choose a value for escape distance
ENTER Escape_Distance

REMARK Choose a value for the number of trials
ENTER N trials

REMARK Initialize variables used as counters or
accumulators
LET j:=0
LET Sum(Is_A_Success) := 0

REMARK Begin while loop
WHILE j <= N_trials

REMARK Training
REMARK Randomly assign a skill level to an escaping
miner

GENERATE Donning Proficiency :
DISCRETE(1,F1;2,F2;3,F3;4, P4555)

REMARK Randomly assign a training outcome
(Failure = FALSE, Success = TRUE)

REMARK Use Look_Up_Table to get successful donning
probabilities

Pr(Success) := LOOK_UP_TABLE
(Donning Proficiency)

Pr(Failure) := 1 - Pr(Success)

GENERATE Outcome := DISCRETE(FALSE,
Pr(Failure); TRUE,
Pr(Success))

REMARK: Generate SCSR Integrity
GENERATE SCSR Integrity := DISCRETE(FALSE,

Pr(Abandons SCSR);

TRUE, Pr(Keeps

SCSR))

REMARK: Calculate Oxygen Consumption

GENERATE Body Weight := NORMAL(Mean,
Std_Dev)

Oxygen_Consumption := Oxygen_Cost * Body_Weight
* Escape_Distance

SCSR_Ratio := Oxygen_Consumption/SCSR_Oxygen

Holds_Breath_Ratio := Oxygen_ Consumption/

Residual_Oxygen
REMARK Calculate Uses_SCSR and Holds Breath
IF [(Outcome = TRUE) AND (SCSR

_Integrity = TRUE) AND (SCSR Ratio
<=1)] THEN TRUE, ELSE FALSE

Uses_SCSR :=

Holds_Breath:= IF (Holds Breath Ratio <=1) THEN
TRUE, ELSE FALSE

REMARK Calculate Is_A_Success

Is_A_Success := IF (Uses SCSR OR Holds Breath =
TRUE) THEN 1, ELSE 0~

REMARK Accumulate Statistics

Sum(Is_A_Success) := Sum(Is_A_Success) +
Is_A_ Success

END WHILE
REMARK Calculate Survival Odds

Pr(Escape) := Sum(Is_A_Success)/N_Trials


ll

APPENDIX C.~CELL-BY-CELL WORKSHEET LISTING

A cell-by-cell listing, showing how to reconstruct the
worksheet template, is presented below.

Al: (FO) ’Probability of Mine Escape
A3: (FO) "Independent Variable
‘Ad: (FO) \-

B4: (FO) \-

AS: (FO) "Distance

BS: (FO) 1000

CS: (FO) ’m

AT: (FO) ’Survival Strategies
A8: (FO) \-

B8: (FO) \-

A9: (FO) ’O2 Available SCSR
C9: (FO) 100

D9: ’L

‘A10: (FO) "Residual O2 lungs
C10: (Fl) 0.5

D10: "L

A12: Physiological Parameters
Al3: \-

B13: \-

C13: \-

Al14: 02 Cost

B14: (FI) 0.5

C14; ’mL/Kg-m

Al6: Body Weight

C16: "Avg

D16: (FO) 87

E16: Kg

C17: ’Std Dev

D117: (FO) 8

E17:

AS: ’Site Specific Training Results
A20: \-

B20: \-

C20: \-

D20: \-

A21: “Rating

C21: "Percentage

A22: ’Fail

22. (P1) 0.069

A23: ‘Poor

C23: (P1) 0.069

A24: "Marginal

C24: (P1) 0.069

A25: ‘Adequate

C25: (P1) 0.448

A26: "Perfect

C26: (P1) 0.345

Q7: \=

A28: Total

C28: (P0) @SUM(C22..C26)
A31: ’Look-up Table for Training Outcome
A32: \-

B32: \-

32: \-

D32: \-

A33: Rating

C33: “Grade

D33: “Outcome

A34: ’Fail

C34: (FO) 0

D34: (FO) @DISCRETE(0,0.7,1,0.3,2)

A3S: Poor

C35: (FO) 1

D35: (FO) @DISCRETE(0,0.5,1,0.5,2)

A36: "Marginal

C36: (FO) 2

D36: (FO) @DISCRETE(0,0.3,1,0.7,2)

A37: "Adequate

C37: (FO) 3

D37: (FO) @DISCRETE(0,0.1,1,0.9,2)

A38: "Perfect

C38: (FO) 4

D38: (FO) 1

A40: "Outcome (0 = fail, 1 = success)

A41: "Integrity (0 = fail, 1 = success)

A44: "Body Weight

C44: ’02 Used

E44: ’SCSR Ratio

G44: ’Holds Breath Ratio

A4S: \-

B45; \-

C45: \-

D45: \-

E45: \-

F45: \-

G45: \-

H45: \-

A46: (FO) @NORMAL(D16,D17)

C46: (F2) +B14*A46*B5/1000

E46: (F2) +C46/C9

G46: (F2) +C46/C10

A48: ’Training

C48: "Outcome

E48: "Integrity

A49: \-

B49: \-

C49: \-

D49: \-

E49: \-

ASO: (FO)
@DISCRETE(0,C22,1,C23,2,C24,3,C25,4,C26,5)

C50: (FO) @VLOOKUP(AS0,C34..D38,1)

E50: (F0) @DISCRETE(0,0.1,1,0.9,2)

A52: (FO) "Is-A-Success

AS3: (FO) \-

B53: (FO) \-

AS4: (FO)
@IF((G46< =1)#OR#((E46< = 1)#AND#(CS0=1)
#AND#(E50= 1)),1,0)

INT.BU.OF MINES,PGH.,PA 29179


Report of Investigations 9310

Probability of Making a Successful Mine
Escape While Wearing a Self-Contained
Self-Rescuer—A Computer Simulation

By John G. Kovac, Charles Vaught, and Michael J. Brnich, Jr.

UNITED STATES DEPARTMENT OF THE INTERIOR
Manuel Lujan, Jr., Secretary

BUREAU OF MINES
T S Ary, Director


Mission: As the Nation’s principal conservation
agency, the Department of the Interior has respon-
sibility for most of our nationally-owned public
lands and natural and cultural resources. This
includes fostering wise use of our lJandand water
resources, protecting our fish and wildlife, pre-
serving the environmental and cultural values of
our national parks and historical places, and pro-
viding for the enjoyment of life through outdoor
recreation. The Department assesses our energy
and mineral resources and works to assure that
their development is in the best interests of all
our people. The Department also promotes the
goals of the Take Pride in America campaign by
encouraging stewardship and citizen responsibil-
ity for the public lands and promoting citizen par-
ticipation in their care. The Department also has
a major responsibility for American Indian reser-
vation communities and for people who live in
Island Territories under U.S. Administration.



RESULTS

The computer simulation was applied to the four mines
that were part of the SCSR donning proficiency field study.
In each case, survival probability was plotted as a function
of escape distance. The resulting family of curves is shown
in figure 2. To make a fair comparison, it was assumed
that all of the miners faced the same prototypical escape,
but each mine had the distribution of SCSR donning skills
shown in figure 1. In other words, the family of survival
probability curves was generated by changing SCSR don-
ning outcomes according to empirical data derived from
field studies.

Overall, workers at mine D have the best chances of
making a successful mine escape, while those at mine C
have the lowest survival odds. The difference amounts
to nearly 30% and is due to relative SCSR donning
proficiency. The lesson seems clear: Survival odds change
for the better when SCSR training improves. The disper-
sion of ability levels may be quite different between two
sites without affecting overall outcomes. For instance, the
survival probability curves for mines A and B almost
overlap, although the pie charts in figure 1 are not divided
the same way. This is because the expected number of

PROBABILITY

b---O---5- -- OF --Q4
4b =
Re
KEY
seme Mine A
2b >: Mine B
~~~ Mine C
—* Mine D
1 L L L
fe) 500 1,000 1,500 2,000 2500 3,000 3,500

DISTANCE, m

Figure 2.-Probabllity of successfully escaping unbreathable
atmosphere using SCSR.

workers at each mine who would actually succeed in using
SCSR’s proficiently is nearly equal. So, at least for a
prototypical escape, the actual details of donning skill
distribution are not so important. What does matter is
that the average level of donning proficiency is as high as
it can be.

The survival probability curve can be divided into three
regions along the escape distance axis, according to which
survival strategy, if any, dominates (shown in figure 3).
Region 1 covers short distances, from 0 to approximately
20 m. Over this range, the miner can simply hold his or
her breath, consuming the residual oxygen in his or her
lungs, and make a quick escape. For short distances, the
worst-case strategy dominates, because a miner avoids the
risk of attrition due to improper donning or SCSR integrity
failure. If we look at escape distances in region 2, from
about 20 to nearly 2,000 m, using the SCSR while escaping
is the best course of action. Finally, no survival strategy
dominates when escape distance greatly exceeds 2,000 m,
which is the case in region 3, because a miner would not
have enough oxygen available under either strategy.

PROBABILITY
cS

ie} 500 1,000 1,500 2,000 2,500 3,000 3,500
DISTANCE, m

Figure 3.-Survival strategy regions. (Patterns from left to right
Indicate regions 1, 2, and 3 as described in text.)


10

APPENDIX B._WORKSHEET REPRESENTATION

An example of a worksheet template for the mine
escape model, using the Lotus 1-2-3 computer software

Outcome

with the @Risk add-on, is listed below. Rating Grade Outcome
Fail 0 0
Probability of Mine Escape Poor 1 0
Independent Variable Marginal 2 i.
y Adequate 3 a
Distance 1000 m Perfect s! 1
Outcome (0 = fail, 1 = success)
Survival Strategies Integrity (0 = fail, 1 = success)
O2 Available SCSR_ 100 L i 2
Residual O2 lungs = 0.S L Body Werght rae ° 2 Used
87 43.50

Physiological Parameters

62Gox 0.5 mL/Kg-m cee Holds Breath ae

0.44 87.00

Body Weight Avg 87 Kg
Std Dev 8 Kg

Training Outcome Integrity
Site Specific Training Results

Rating Percentage
Fail 6.9%
Poor 6.9%
Marginal 69%
Adequate 44.8%
Perfect 34.5%

Total 100%