The Quantification of Safety and Risk: A Critical Review

Current measures of safety for demined areas are
inadequate because they do not accurately reflect the safety of
a demined area. A new standard, termed "risk factor,"
better describes the results of demining processes. However,
even this equation works poorly when dealing with the small
numbers in a demined field.

by Dr. Peter A. Schoeck
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Summary
It is shown that the concept "safety
factor," as presently used as a criterion for declaring a demined
area safe for use, is impractical and should be replaced by its
complement, called "risk factor," which stands for the ratio
of the size of the minepolluted portion of a demined field to its total
area. An equation expressing the risk as a function of the efficiencies
of the demining processes applied is developed. The limitations of
applying this equation in the quantification of the risk are then shown
by means of a case study. The necessity of an error analysis for all
figures quoted to express the efficiency of detection methods is
emphasized, while the limitations of advanced scientific approaches with
respect to the ultimate goal of humanitarian demining—zero risk—are
discussed. A revision of demining standards is proposed.
Introduction
According to the
"Standards for Humanitarian Demining Operations" as issued by
the Geneva International Center for Humanitarian Demining, "safety
factor" is a measure of the efficiency of a certain demining, or
more precisely, mine detection method. The prescribed standard is an
efficiency of 99.6 percent, meaning that of all mines present, 99.6
percent must have been detected and removed before an area can be
considered safe. It is obvious that such a definition makes no sense for
the simple reason that the safety of an area does not depend on how many
mines it contained in the beginning, but how many mines are left
undetected after the detection process.
Therefore, a reasonable definition of safety would be
the ratio between that portion of the total area on which one could
safely set foot, denoted by Am, to the total area, A. With this
definition, the safety factor s, is expressed by:
s = 1 – Am / A (1)
The area Am is the sum of all individual
"sensitive cross sections" (denoted by a), which are defined
as the area around each mine that would cause an ignition when subjected
to a minimum pressure force. With this definition and denoting the
number of mines left undetected after i demining processes as ni, we can
write:
Am = a ni (2)
with the simplified assumption that a
represents an average value for all ni mines. Inserting (2) into (1), we
obtain:
s = 1 – a ni / A (3)
To calculate the value of s, we must know besides A
(the area of the mine field) the quantities ni and a. Leaving for
the moment the question as to their determination, we shall show in the
next section why the concept "safety" should be replaced by
the concept "risk."
Introduction to the
Risk Factor
Let us assume that a mine field
of size A=100m x 100m = 10,000 m2 has been demined up to a degree
that ni= 10 AP mines are left undetected. The sensitive cross section of
each mine will be a= 0.05m2 corresponding to a circle of diameter 0.25m.
Nobody would dispute the fact that entering such a "demined"
area, which is approximately the size of a football field, entails a
tremendous risk, a fact that should manifest itself by the safety
factor. But surprisingly its calculation by (3) yields the deceiving
value of s = 99.995 percent, which is so close to 100 percent that one
might be tempted to consider the safety of the demined field to be
sufficient for all practical purposes.
Let us now apply a further demining process to the
mine field by which we succeed in detecting and removing half of the
mines left. Undoubtedly, the risk of an accident will thereby be reduced
by 50 percent. How does this reflect on the safety factor? Our
calculation based now on ni = 5 yields s = 99.9975 percent. In other
words, a risk reduction by 50 percent expresses itself with only a
minute rise of the safety factor.
This example shows that the application of the safety
factor s as a measure for the degree of safety when entering a demined
area is impractical. Its replacement by its complement Am/A, which may
be called "risk factor," expressed by:
r= Am / A (4)
therefore suggests itself. With (2) it takes on the
form
r= a ni/A (5)
Quantification of
Risk
When defining the safety factor
s and replacing it by the risk factor r, the essential point was that
both are unrelated to the original number of mines (n0) or, for
that matter, to the original density of mines on the field expressed by
n0/A. For the safety of an area does not depend on its demining history,
but solely on its present state.
Let us now assume that by a sufficient number of
experiments, in each of which the number of mines was large enough for
achieving a result based on statistics under typical average conditions,
we have found that a certain demining process leads statistically to the
detection of a fraction of the original number of mines expressed by:
d=(n0 – n1) / n (6)
where:
n0= original number of mines, and
n1= number of mines left undetected.
We can then define an efficiency of the respective
demining process by:
h1= 1 n1/n0 (7)
Applying three demining processes successively, the
number of undetected mines left is expressed by:
n3 = n0 ( 1h1) ( 1h2 ) (1 h3) (8)
with h1, h2, h3 standing for the efficiency of each
process.
To minimize the influence of system inherent errors,
the Standards for Humanitarian Demining Operations prescribe that the
three processes applied in succession must be independent of each other.
This means that processes applied in a row must be based on different
principles. As an example, if a mine field was first probed manually by
prodding the ground, the subsequent process applied must be detection by
using dogs or groundpenetrating radar, for instance.
From (5) and (8) it follows that the risk of stepping
on a mine after the application of three consecutive demining processes
would be:
r3 = (n0/A) a ( 1h1) ( 1h2 ) (1 h3) (9)
The question now arises as to the usefulness of (8)
and (9) in practice. We shall attempt to answer this question by a
practical example. Let us assume that a demining process has been
applied to a mine field of A=100,000 m2, the efficiency of which had
been experimentally determined to be h1= 0.9, and that 100 mines have
been detected and removed. This justifies the assumption that
approximately 10 mines are left undetected in the area. If we now apply
a second process, its efficiency also being 0.9, we must take into
account that this efficiency has been statistically determined with a
large number of mines representing average conditions. But with only 10
mines left to be detected, the application of the statistical efficiency
value of 0.9 is not tolerable. In other words, the assumption is not
justified that the number of mines left undetected after application of
the second demining process will be reduced to one, as would result from
(8). From this we can conclude that the calculation of the remaining
risk by (9) leads to a value not corresponding with reality. What, at a
glance, had the appearance of a neatly derived formula for expressing
the risk of stepping on a mine in a "demined" area turns out
to have limited practical value as far as its accuracy is concerned.
Conclusions
Because experimentally
determined statistical values of demining efficiency always refer to a
large number of mines, they are not valid after a minefield has been
cleared to such an extent that only a small number of mines are left
undetected.
Furthermore, quantitative results obtained by
measurements are of no value without an error analysis. Applied to the
efficiency of a certain mine detection method expressed by h= 99.6
percent = 0.996, corresponding to a risk of 0.4 percent= 0.004, implies
that this figure must be measured with an accuracy of 103. Which method
applied in the field of mine detection would justify such an assumption?
In humanitarian demining, each mine left unidentified
and unremoved represents an unacceptable safety risk, as opposed to
military operations, where casualties are taken into account from the
beginning. With due respect for all efforts regarding the application of
advanced technologies in optics, electronics and chemistry to mine
detection, they inevitably contain systematic and random errors. The aim
must be zero risk. This can be guaranteed only by probing the soil in
such a manner that every item, down to the smallest possible sized mine,
is detected and removed.
While achieving this objective is extremely difficult
in demined residential areas, it represents no problem in the case of
mechanized demining of farmland where all of the soil is being milled.
If, down to the smallest possible size of a mine, all soil has been
subjected to a mechanical impact, the risk factor defined above has been
reduced to zero. To apply a second independent process merely to comply
with standards established by reasoning not valid for this case makes no
sense. For the sake of avoiding unnecessary costs while demining, a
reexamination of present demining standards seems therefore advisable.
Biography
Dr. Peter A. Schoeck, a U.S.
citizen, received his scientific education in Mechanical Engineering and
Physics at the University of Karlsruhe/Germany and at the University of
Minnesota. He has been active in Polar Geophysical Research in the
Arctic and Antarctic and in the field of Thermodynamics of Jet
Propulsion, holding a professorship at the University of Tennessee Space
Research Institute of Tullahoma, Tennessee. From 1966 to 1974, he was
Director of Research and Development of the BOSCH Group of Companies,
Stuttgart/Germany. He is now a consultant to a Scandinavian firm engaged
in the development of demining equipment and the demining of farmland in
the Balkans.
Contact Information
Dr. Peter A Schoeck
Runkelsstr.27 FL Triesen / Liechtenstein
Email: schoeck@schoeck.lol.li 