IEEE Technology and Society Magazine - March 2017 - 54

representing the vulnerability contributed. More specifically, it requires an approach that evaluates and delineates vulnerability contributions by the technological
system configuration. Such a measure would allow
comparison of different technological configurations,
and allow evaluation of the effectiveness of configuration changes. A quantitative method of assessing the
level of exposure of a particular device not subject to
the problems of the risk analysis technique, allows
comparisons with other devices, and assessments of
hypothetical design changes [8].
We assume that for each analysis, a service delivery
level is nominated (and hence either is, or is-not provided), and this final service delivery can then be represented by a Boolean variable. Recursively, intermediate
streams and process functionality can be considered to
have Boolean values according to whether they do, or
do-not cause failure of the final service-level delivery:
this allows the representation of streams and process
availabilities as Boolean variables. An exemplar system
is illustrated in Figure 1.
Real technological systems may also include operations that are mutually exclusive, indicating a need for a
representation of a case where IF (hypothetical process
(a) is functional) then NOT (hypothetical process (b) is
functional). Such a "NOT" construct can be used in conjunction with the definition of stream availability level, if
sufficient level of stream is available to ensure functioning of (a), the sufficient level of stream availability is not
available to ensure functioning of (b). A computationally
complete Boolean algebra expression requires only the
"AND," "OR," and "NOT" constructs, so these are sufficient in representing an arbitrary an arbitrary technological system in which a set of processes and streams
progressively create a particular product or service for
delivery to an end user. The laws of Boolean algebra
(including, for example, De Morgan's laws) may allow
simplification of derived expressions. A system in which

processes and streams progressively create a particular
product will be characterized as heterogeneous, in order
to distinguish it from a homogeneous system that simply
transfers an end product across a network of conduits.

Development and Significance of an Exposure Metric
Figure 1 illustrates a system that includes points for
which a single failure will cause the system output to
fail. This system also includes cases where a combination of two (or more) failures will need to occur simultaneously in order to cause the system output to fail,
generally describing redundancies designed into the system as duplicates of sub-systems, whose design redundancy can be represented by "OR" gates.
It is then possible to construct a composite exposure
metric of the form { E 1, E 2, E 3 f E n ) where E 1 is the
number of single points of failure. E 2 is the number
of cases where two independent failures must occur in
order for the system to fail. The E 2 value must
exclude cases where either one of the inputs would
alone have caused output failure - otherwise the values would be duplicated. Similarly, the E 3 value represents the number of cases where three independent
failures are required to cause system output failure,
and must exclude cases where a combination of two
of the failing inputs would have caused output failure.
This representation and concept expands upon the
N-1, N-2 design redundancy concept, adding rigor to
its definition, and is proposed to provide a measure of
the relevant attribute.
Consistent with ISO 31000, the definition assigned to
the term "exposure" is closely related to the concepts
described, and so for the purpose of this work, the
quantitative evaluation {E1, E2...En}, the "attribute," will
be referred to as the "exposure" of the technological
system. In situations where technological configuration
is a significant contributor to end-user's vulnerability, an
exposure metric becomes a valid method of evaluating

P5
S9

P3
P4
End User

P6
S10
P1

P2 S1 S2 S3

S7 S8

S4 S5 S6

Figure 1. Exemplar technological system, streams (S) and processes (P).

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march 2017

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