IEEE Technology and Society Magazine - March 2017 - 55

the "vulnerability that can be attributed to the technological system" onto the attribute of "vulnerability".

Contributory Systems
Consider a scenario where added technological functionality produces an input to a system. The additional
technological system that generates the input will itself
have, and thus contribute, some degree of "exposure."
A valid basis is required for calculating what contribution is made to the total exposure.
Figure 2 illustrates a representative case in which a
sub-system (comprising a "OR" gate and four "AND"
gates (labelled A, B, C, and D) "contributes" to the exposure of another system whose final delivery is via an
"AND" function with two inputs.
For broader applications, a more generalized
approach is required. The problem presented can be
generalized by considering each input to a gate (Boolean "AND" or "OR" operation) as having a composite
exposure metric and developing a gate output calculation from these inputs (see Figure 3). For the "AND"
gate, the contributory exposure metrics are added component-wise, hence the output metric is
{(A 1 + B 1 + C 1), (A 2 + B 2 + C 2),

An autonomous malicious entity
will also actively seek weaknesses
and attempt to thwart mitigatory or
contingency measures.

prevent sudden death in patients with known, sustained
ventricular tachycardia or fibrillation. A wearer of an ICD
may then be assumed to face a high probability of
death or severe debility without the implant [9], and will
be understandably hesitant to accept additional risk
from device failure.

Limitations of the Current Risk Analysis Approach
To assess risks, historical statistics are commonly proposed as a means to understand uncertainty and inform
design decisions. For cases where a hazard is not intentional, a statistical assessment is only possible for historical risks for which significant past failure data exists;

For the "OR" gate where there are three inputs the E1
and E2 value is 0, and the E3 value is
2

((A 1 -1) +(B 1 -1) +(C 1 -1), (A 2 -1) +(B 2 -1) +(C 2 -1), (A 3 -1) +(B 3 -1) +(C 3 -1))

.

A single failure from each input must occur for the
output to fail; however each remaining combination of
failures contributes to the E3 value. The E4 and subsequent values are calculated in the same way as the
E3 value.
When the contributory system is considered, the length
of the output exposure metric is increased as the contributory system has effectively added streams and processes.
In principle, an exposure metric of considerable length
could be generated if a complex contributory system is
involved. Since the E3 combinations cannot (by definition)
include any E2 or E1 combinations - and E4 combinations
cannot include any E3, E2 or E1 combination, there will be a
tendency for higher-subscripted E values to decrease.
Upper bounds can thus be set for a system with N inputs,
(N -E 1)
, etc. In addition, if a sysand if E 1 = n, then E 2 # 2
tem with N inputs has a E(N) value of 1, then the system
can only be a single "OR" with N inputs.

{1, 0, 0, Ee}

(A 3 + B 3 + C 3) f (A n + B n + C n)} .

march 2017

∕

{2, 0}

A

B
2((An -1) + (Bn -1) + (Cn-1) + (Dn-1))

Ee =
Since one input from each gate (A-D)
must fail (but this is sufficient),
all remaining combinations contribute
to the E value

{2, 0}
C
{2, 0}
{2, 0}

D

Figure 2. Exemplar contributory system.

{A1, A2, A3, ... An)
{B1, B2, B3, ... Bn)
{C1, C2, C3, ... Cn)

{A1, A2, A3, ... An)
{B1, B2, B3, ... Bn)

Case: Implantable Cardioverter Defibrillator
Utility assists in determining the potential consequences of a technological system failure. An implantable
cardioverter defibrillator (ICD) is a device that can

{0, 0, 0, Ee}

{C1, C2, C3, ... Cn)
Figure 3. Generalized approach - contributory system.

IEEE Technology and Society Magazine

55



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