Probability of Making A Successful 

Mine Escape While Wearing 

A Self-Contained Self-Rescuer 

John G. Kouac,1 Charles Vaught,2 and Michael J . Bmich, Jr.3 

lSupervisory Physical Scientist, 2Research Sociologist, 3Mining Engineer 

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

Abstract 

A computer simulation has been developed to estimate the chances of a miner making a successful escape while wearing a SCSR. The model takes into account: (1) training in the use of SCSRs, (2) apparatus integrity, and (3) the oxygen cost of a mine 

escape. This Bureau of Mines report examines survival odds for a prototypical escape, 

and illustrates how these odds change when SCSR training is improved. 

Introduction 

When a mine disaster occurs, the basic survival 

technique 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 gasses. 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 a Self·Contained 

Self·Rescuer (SCSR) and trained in its use (U.S. 

CFR Title 30, 1988). A SCSR is a closed·circuit 

breathing apparatus designed for the purpose of 

mine escape. It must be capable of providing at 

least a 60·minute supply of oxygen, regardless of 

the condition of the mine atmosphere. 

The chances of a miner making a successful 

escape while wearing a 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 cost-Did the SCSR provide 

enough oxygen? 

A computer simulation that takes these issues into 

account has been developed to estimate survival 

odds for a prototypical escape. This report examines how these odds change when SCSR training 

is improved. 

Mine Escape Model 

Although mine disasters seem to occur with 

great regularity, they are still rare events. Since 

SCSRs are a relatively 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 allow us to 

assess the impact of the device. Unfortunately, 

experiments in this area are impractical, ifnot 
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 wishing to evaluate an individual's 

chances of escaping an unbreathable mine atmosphere. We therefore 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 is parsimony. 

Our model provides a theoretical framework for 

explaining or predicting the outcome of an escape 

attempt in terms oftraining, SCSR integrity and 

oxygen consumption issues. The underlying logic 

and formulas are visible, and the issues are clearly 

focused and segregated. A second advantage is 

that, because our 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 

affects 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, because it is a logical progression of ifYthenielse decisions. In particular, it is a 

worksheet template written in Lotus 1-2-3 with 

the @Risk add-on (Palisade Corp, 1988). The 

model has an empirical basis because it uses the 

experimental results of training studies, SCSR 

field audits, and oxygen cost experiments to 

calculate survival odds. 

Prototypical Escape 

Prototypical escape means a hypothetical 

situation in which a disaster has occurred, and, 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 his only 

escape route is a straight-line path through 

a fatally hostile environment. 

2. At the start of his escape, the miner tries 

to don a SCSR. If he 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 is always trying to make forward 

progress, never stopping to rest. He 

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. 

Training 

Attrition occurs at the start of a prototypical 

escape because some miners cannot don their 

SCSRs. 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 is able to don and activate the 

SCSR. For the purposes of this model, 

donning proficiency is defined by a fivelevel 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 falls short. The 

chance that any particular miner can don 

his apparatus correctly is influenced by the 

general level of SCSR donning skill at his 

mine site. 

The two training factors, then, are related by the 

assumption that the higher the general skill level 

at a mine, the greater the odds are that a repre-
sentative miner will be able to don a 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 = 

Pr(Skill Level = i) = 

1,2,3,4,5 

Probability that a miner 

drawn from the 

workforce at a given 

mine can don a SCSR at 

that skillleve!. 

= Fraction of workforce at 

that skillleve!. 

Donning Proficiency 

Skill Level 

Failing = I 

Poor = 2 

Marginal = 3 

Adequate= 4 

Perfect = 5 

Fraction of Workforce 

at that Skill Level 

FI 

F2 

F3 

F4 

F5 

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

FI + F2 + F3 + F4 + F5 = I 

This relationship also guarantees that the skill 

level probabilities are normalized. 

The second factor that the training model 

accounts for is SCSR donning outcome. SCSR 

donning outcome depends on skill level, and it is 

represented as a two-state discrete function, 

defined below: 

1,2,3,4,5 

Values (FI, 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 

SCSRjust as he would ifit were necessary to 

escape the mine, and to do the entire procedure. 

While one researcher videotaped the miner's performance, another evaluated and timed the tria!. 

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 the form of pie charts in Figure 1. 

In the final analysis, whether a miner fails or 

succeeds in the real world would be determined by 

the ability to use his 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 he did not adjust straps. 

The miner put the SCSR on backwards. 

The mouthpiece and nose clips pulled out--

he put the mouthpiece back in but forgot 

the noseclips. He did not adjust the waist 

or neck straps. 

The miner failed to activate the oxygen 

and forgot to put on the noseclips. 

Skill Level = i; 

Pr(Success,i) = Probability that a miner will successfully don his SCSR, given his 

donning proficiency. 

Pr(FaiJure,i) = 

Outcome(i) = 

1 - Pr(Success,i). 

State 

Successfully dons SCSR = True 

Miner fails to don SCSR = False 

Probability 

Pr(Success,i) 

Pr(Failure,i) 
6.3 

pct 

Mine A 

KEY 

_ Failing 

~Poor 

~ Marginal 

Mine B 

f: ! .. 1 Perfect 

Mine C 

Figure 1. Donning proficiency profiles. 

Poor 

• The miner stood up to put the SCSR on. 

The mouthpiece and noseclips pulled out 

because the trainee failed to adjust his 

neckstrap. He appeared to be very confused during the en tire donning sequence. 

• The miner didn't loop the necks trap. 

Instead, he put the waist strap around his 

neck. He also put the goggles on over his 

glasses and forgot to put his hardhat back 

on. 

• The miner failed to adjust the neck strap; 

as a result, there was noticeable tension on 

the breathing hose. 

Mine D 

Marginal 

• The miner twisted the neckstrap around 

the breathing hose. 

• The miner didn't put on the goggles and 

failed to fasten his waist strap. The noseclips slipped off, but he put them back on. 

• The miner adjusted the necks trap after 

looping, but he never secured the waist 

strap. He took the mouthpiece out to look 

for noseclips, and put it back in once he 

found them. He initially hung the goggles 

around his neck. He had to remove the 

mouthpiece and noseclips to put the 
goggles on. After donning the goggles, he 

replaced the mouthpiece and nosec1ips. 

Adequate 

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 

considered proficient. • The miner adjusted the neckstrap before 

activating the oxygen. 

• The miner adjusted the neckstrap before 

donning the goggles. After he put his hat 

on, he fastened and snugged the waist 

strap. 

• The miner looped the neckstrap over his 

hat and lamp cord. 

Perfect 

• The miner performed a perfect 3+3 sequence . 

• The miner did a perfect sequence. The 

waist strap should have been slightly 

tighter. 

As can be seen, "failing" here merely applies to 

an individual's omission of one or another of the 

In order to arrive at a conservative but fair 

interpretation of what performance at a particular 

skill level might mean in the real world, researchers analyzed evaluations of 1264 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 his lungs isolated would result in death, 

there are three chances in ten that he might 

convert his failure into a partial success. For this 

reason, Ufailing" 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 (in 1264 trials). 

Critical 

Secondary 

Missed steps 

Missed steps Corrected steps subsequently corrected 

525 

780 

172 

336 

32.8 

43.1 

Table 2_ SCSR donning probabilities_ 

Skill Level 

Failing 

Poor 

Marginal 

Adequate 

Perfect 

Probability (%) 

30 

50 

70 

90 

100 
SCSR 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 his SCSR after donning it. The Bureau of 

Mines and Mine Safety and Health Administration 

(MSHA) have conducted field audits of SCSRs, and 

both agencies have investigated actual mine 

escapes involving the apparatus. The results of 

this research have yielded a 10% use-failure rate 

for the devices and suggest two reasons why a 

SCSR might be abandoned. First, the apparatus 

State 

fails to provide life support due to a manufacturing 

defect, or because of damage caused by the in-mine 

environment. A second reason the device might be 

abandoned is that the miner is unfamiliar with 

how a 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 presented here: 

Probability 

SCSR integrity = Miner keeps SCSR = True 

Miner abandons SCSR = False 

Pr(Keeps SCSR) 

PrCAbandons SCSR) = 

1 - Pr(Keeps SCSR) 

Oxygen Consumption 

The third component in the mine escape model 

is oxygen consumption. Attrition occurs if a miner 

is not supplied 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. The miner's body weight, which simply 

refers to how much the escaping miner 

weighs, and is modeled as a normal distribution. 

2. Escape distance (that is, the length of the 

escape route). 

3. The oxygen cost of a mine escape. 

Oxygen cost, given in terms of standard temperature and pressure with dry bulb (STPD), is a 

parameter 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: 

Walking upright = 0.3 mL 02 CSTPD)lkg-m 

Bent posture = 0.5 mL 02 CSTPD)lkg-m 

Crawling = 0.7 mL 02 CSTPD)lkg-m 

In other words, a miner consumes twice as much 

oxygen while crawling during his attempt to 

escape as he would use ifhe 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 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 ofthe 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 escape distance is doubled, 

oxygen consumption is doubled. 

A miner who must escape a fatal hostile 

environment has two survival strategies available. 

Ifhe cannot don his SCSR, or the apparatus fails 

to function, there is a "worst-case" strategy-the 

miner can simply hold his breath, consuming the 

residual oxygen in his lungs, and make a short-
distance escape attempt. 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 breath and attempts to reach 

fresh air within a short-distance, the oxygen 

consumption ratio (or Holds_Breath_Ratio) equals 

Oxygen_ConsumptioniResidual_Oxygen available 

in the lungs. For a miner using his SCSR, the 

oxygen consumption ratio (or SCSR Ratio) is equal 

to the Oxygen_ConsumptioniOxygen_Supplied by 

the SCSR. 

In both of the survival scenarios mentioned 

above, the oxygen consumption ratios will al ways 

be positive. If a calculated ratio is less than one, 

then that particular escape strategy supplied the 

miner with enough oxygen to pennit a successful 

escape. If the ratio calculated was greater than 

one, however, a successful escape from the hostile 

mine atmosphere would be considered impossible, 

since the miner would not have enough oxygen 

available under that escape strategy. Our choices 

for oxygen consumption parameters are given in 

Table 3. 

Table 3. Oxygen consumption parameters. 

Oxygen (STPD)8 

Body weight SCSR 

87 kgb 100 L 

8STPD = Standard temperature and pressure 

with dry bulb 

bStandard deviation, 10 kg 

Residual 

0.5 L 

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 activated, it will generate randomly a combination of Training, SCSR Integrity and Oxygen 

Consumption. This combination describes: 

1. Whether or not the miner was able to don 

his SCSR successfully; 

2. Whether the miner possesses a functional 

SCSR, or an apparatus that he will abandon immediately after donning; and 

3. How much oxygen the miner must consume 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 oftimes to accumulate 

statistics on the number of successful escapes, 

using the following logic: 

Pr(Escape) = Probability of a successful mine escape. 

= Number of successful 

escapeslNumber of 

trials_ 

Mathematically, escape probability is calculated by introducing a special function called 

Is_A_Success that tests for a successful escape. 

Is_A_Success has the following properties: 

= 1, if the miner made a 

successful escape. 

= 0, if the escape attempt 

fails. 

The Is_A_Success function takes two logical 

variables as arguments: U ses_SCSR and 

Holds_Breath. 

U ses_SCSR = True, if [(Outcome=True) and 

(SCSR Integrity=True) and (SCSR Ratio S ill. 

= False, otherwise. 
Holds_Breath = True, if CHolds 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: 

= 1, if [CU ses_SCSR) or 

CHolds_Breath) = True]. 

= 0, otherwise. 

Let's look at what happens if we evaluate 

Is_A_Success for a large number of trials, and 

accumulate the results according to the following 

program: 

Step 1: Let j be an index, representing each 

trial: j = 1 to N_Trials. Pick N_Trials = 1000 for a 

valid simulation. 

Step 2: Randomly generate values for 

Holds_Breath(j) and Uses_SCSR(j) for th e jth trial, 

and evaluate Is_A_Success. 

= 1, if thejth trial was a 

success. 

= 0, otherwise. 

Step 3: Calculate an expected value for 

Is_A_Success, ECls A Success). The expected value 

is the successful escape probability: 

SumCls_A_Success) = Number of successful 

PrCEscape) 

escapes in N trials. 

= SumCls_A_Success)/ 

N_trials. 

= Number of successful 

escapes/N_trials. 

= ECls_A_Success). 

By varying the escape distance, and repeating 

the probability calculation, the user can map out 

the functional dependence of survival odds based 

on escape distance and parameter choices. A 

complete listing of computer pseudo-code for the 

simulation algorithm is listed in the Appendix l. 

Because the mine escape model was written in 

Lotus 1-2-3, Appendix 2 is an example of a 

worksheet template, and Appendix 3 is a cell-bycell listing of the worksheet. 

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, and 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 by the pie 

charts in Figure 1. In other words, the family of 

survival probability curves was generated by 

changing SCSR donning 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 dispersion of 

ability levels may be quite different between two 

sites without affecting 20 overall outcomes. For 

instance, the survival probability curves for mines 

A and B almost overlap, although the pie charts 

are not divided the same way. This is because the 

expected number of workers at each mine who 

would actually succeed in using SCSRs 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. This is shown in Figure 3. Region 1 

covers short distances, from 0 to approximately 20 

m. Over this range, the miner can simply hold his 

breath, consuming the residual oxygen in his 

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 
>-

r-

::::i 

iii 

<t 

lD 

~ a.. 

I .0.---.---..,----.--.---..----...,.----, 

.8 

.6 

.4 

.2 

o 

.. :.:&-.-h--............. . . ............. ~.-..:e 

I \ b---o----o- ~--"G' 

KEY ••••••• Mine A 

.~. Mine B 

--0-- Mine C 

- MineO 

q500 1,000 1,500 2,000 2,500 3,000 3,500 

DISTANCE, m 

Figure 2. Probability of successfully escaping an unbreathable atmosphere while wearing 

an SeBA. 

1.0 

.8 

>-

r- .6 ::::i 

iii 

~ 

~.4 a.. 

.2 

o 

....... Mine 

' . • ~. Mine B 

. --0-- Mine C 

:-MineO 

1,000 

DISTANCE, m 

Figure 3. Survival strategy regions. (Patterns from left to right indicate regions 1,2, and 3, 

as described in the text.) 
to nearly 2000 m, using the SCSR while escaping 

is the best course of action. Finally, no survival 

strategy dominates when escape distance greatly 

exceeds 2000 m, which is the case in Region 3, 

because a miner would not have enough oxygen 

available under either strategy. 

Discussion 

The chances of a miner making a successful 

escape while wearing a 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 Cost-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 used to show these 

odds change when SCSR training improves. The 

computer simulation was applied to four mines 

that were part of a 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 a SCSR is the best 

survival strategy, and the only one that is tenable 

over long distances. The real limitation on escape 

distance is that SCSRs make available only a finite 

quantity of useable oxygen. This must be taken 

into account in planning for mine emergencies. 

Because theoretical issues are clearly segregated and the mathematical structure ofthe model 

is open to modification, it seems likely that the 

computer simulation can be extended naturally to 

cover other factors affecting survival odds: 

1. The location of SCSR caches along escape 

routes; 

2. Decision making under uncertainty, with 

regards to choice of escape routes; and 

3. Group dynamics in mine emergencies. 

These will be topics for future research. 

References 

Palisade Corp., At Risk: Risk Analysis and Modeling for the P.C. Computer software, (Newfield, NY) 

1988. 

u.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 Standard- Underground Coal Mines, sec. 75.1714; July 1, 1988. 
Appendix 1 

Simulation Algorithm-Computer pseudo-code for the mine escape model is listed below. Variable 

names in the program are concatenated for the sake of clarity. Commands or reserved words in the 

pseudo-language are shown in bold type. 

REMARK Stipulate parameter set 

REMARK Donning Skill level 

ENTER Fl,F1,F3,F4,F5 

REMARK Donning Probability 

ENTER Pl,P1,P3,P4,P5 

REMARK Create Look Up-Table 

LET LOOK UP TABLE(l) :-Pl 

LET LOOK=UP=TABLE(1) :-P1 

LET LOOK UP TABLE(3) :-P3 

LET LOOK-UP-TABLE(4) :-P4 

LET LOOK=UP=TABLE(5) :-P5 

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_trhl s 

REMARK Initialize variables used as counters or accumulators 

LETj:=O 

LET Sum (ls_A_Success) :- 0 

REMARK Begin while loop 

WHILE j <- N_trials 

REMARK Training 

REMARK Randomly as,s1qn a skill level to an escaping miner 

GENERATE Donning-Proficiency :- DISCRETE(l,Fl;1 , F1; 3,F3;4,F4;5,F5) 

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 :- DlSCRETE(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_Ratto :- Oxygen_Consumptton/Residua'_Dxygen 
REMARK Calculate Uses_SCSR and Holds_Breath 

IF [(Outcome' TRUE) AND (SCSR Integrity - TRUE) AND 

(SCSR Ratio (-1)] THEN TRUE, 

ELSE FALSE 

IF (Holds_Breath_Ratio (.1) THEN TRUE ELSE FALSE 

REMARK 

Is_A_Success ;. IF (Uses_SCSR OR Holds_Breath. TRUE) THEN 1, ELSE 0 

REMARK Accumulate Statistics 

END WHILE 

REMARK Calculate Survival Odds 

Appendix 2 

Worksheet Representation-An example of a worksheet template for the mine escape model, 

written in Lotus 1-2-3 with the @Risk add-on, is listed below. 

Probability of Mine Escape 

Independent Variable 

Distance 1000 m 

Survival Strategies 

02 Available SCSR 100 L 

Residual 02 lungs 0.5 L 

Physiological Parameters 

02 Cost 0.5 mL/Kg-m 

Body Weight Avg 87 Kg Std Oev 8 Kg 

Site Specific Training Results 

Rating 

Fail 

Poor 

Marginal 

Adequate 

Perfect 

Total 10~ 

Percentage 

6.9% 

6.9% 

6.9% 

44.8l\ 

34.5% 

Look-up Table for Training Outcome 

Rating Grade Outcome 

Fail 0 0 

Poor 1 0 

Marginal 2 1 

Adeq'Jate 3 1 

Perfect 4 1 

Outcome (0 - fail, 1 - success) Integrity (0 - fail, 1- success) 

Body Weight 02 Used 

87 43.50 

SCSR Ratio Holds Breath Ratio 

0.44 

Training 

3 

Is-A-Success 

Outcome 

87.00 

Integrity 
Appendix 3 

Cell-by-cell Worksheet Listing-A cell-by-celllisting, showing how to reconstruct the worksheet 

template is presented below. 

AI: (FO) 'Probability of Mine Escape 

A3: (FO) 'Independent Variable 

A4: (FO) \-

B4 : (FO) \-

AS: (FO) '~istance 

B5: (FO) 1000 

C5: (FO) 'm 

A7: (FO) 'Survival Strategies 

AS: (FO) \-

BS : (FO) \-

A9: (FO) '02 Available SCSR 

C9 : (FO) 100 

09: 'L 

AlO: (FO) 'Residual 02 lungs @ 

CIO: (Fl) 0.5 

010: 'L 

A12: 'Physiological Parameters 

A13: \-

B13: \-

C13: \-

A14 : '02 Cost 

B14: (FI) 0.5 

CI4: 'ml/Kg -m A16: 'Body Weight 

C16 : 'Avg 

016 : (FO) B7 

E16: 'Kg 

C17: 'Std Oev 

017 : (FO) 8 

E17: 'Kg 

A19: 'Site Specific Training Results 

A20 : \-

B20: \-

C20: \-

020: \-

A21- "Rating 

C21: ' Percentage 

A22: 'Fail 

C22: (PI) 0.069 

A23: 'Poor 

E49: 

A50: 

C50: 

E50: 

A52 : 

A53: 

B53 : A54: 

\-

036: 

A37: 

C37: 

037: 

A3B: 

C38: 

038: 

A40: 

A41: 

A44: 

C44: 

E44: 

G44: 

A45: 

B45: 

C45: 

045: 

E45 : F45: 

G45 : 

H45: 

A46: 

C46: 

E46: 

G46 : A48: 

C48: 

E4B: A49: 

B49: 

C49: 

049 : 

(FO) @oISCRETE(0,0.3,I,O.7,2) 

'Adequate 

(FO) 3 

(FO) @0ISCRETE(O,O.I,I,O . 9,2) I Perfect 

(FO) 4 

(FO) I 

'Outcome (0 = fail t 1 '"' success) 

'Integrity (0 - fail, I - success) 

'Body Weight 

'02 Used 

'SCSR Ratio 

'Holds Breath Ratio 

\-

\ -

\-

\-

\-

\-

\-

\-

(FO) @NORMAL(016,o17) 

(F2) .BI4*A46*B5/1000 

(F2) .C46/C9 

(F2) .C46/ClO 'Training 

'Outcome 

'Integrity 

\-

\-

\-

\-

0) laoISCRETE(O, C22 , I , C23 

(FO) @VLOOKUP(A50,C34 .. 03B,I) 

(FO) @DISCRETE(O,O . l,l,O.9,2) 

(FO) 'Is-A-Success 

, 2 ,C24, 3 , C25, 4, C26, 5) 

(FO) \-

(FO) \-

(FO) 

C23 : (PI) 0.069 

A24: 'Marginal 

C24: (PI) 0.069 

A25 : 'Adequate 

C25 : (PI) 0.448 

A26 : 'Perfect 

@I F«G46<-I)#0 R# «E46<-I) #ANo#(C5 0=1) #ANo#(E50-1», I , 0) 

C26: (PI) 0.345 

e27: \-

A2B: ' Total 

C28: (PO) @SUM(C22. _C26) 

A31: 'Look·up Table for Training Outcome 

A32: \-

B32: \-

C32: \-

032: \-

A33: ' Rating 

C33: "Grade 

033 : ttOutcome 

A34 : 'Fail 

C34 : (FO) 0 

034: (FO) @oISCRETE(O,O.7,I,O.3,2) A35: I Poor 

05: (FO) I 

035: (FO) @oISCRETE(O,O.5,I , O.5,2) 

A36: 'Marginal 

C36: (FO) 2 @