D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange

Dealing with Known Unknowns: A Goal-based Approach 13
where the configuration is not useful. To be more conservative, in this paper we
consider as risk measure the complement of the Total Belief and namely the sum
of the total chances that a configuration would turn out to be utterly useless.
Building on the above considerations, we introduce two quantitative metrics:
Residual Risk 1 and Max Belief as follows.
Max Belief (MaxB): of an configuration C is a function that measures the maximum
belief supported by Domain Expert such that C is useful after evolution
happens.
Residual Risk (RRisk): of an configuration C is the complement of total belief
supported by Domain Expert such that C is useful after evolution happens.
In other words, residual risk of C is the total belief that C is not useful when
evolutions happen.
They offer two independent dimensions upon which a designer can chose.
Given an evolutionary enterprise model 〈EM, r o,r c〉, max belief and residual
risk can be formally defined as follows.
MaxB(C) max p i
∀EM p i
−→EM i .EM i ∈SDA(C)
X
RRisk(C) 1 −
∀EM p i
−→EM i .EM i ∈SDA(C)
p i
(1)
where SDA(C) is the set of design alternatives which a configuration C comprises
(or support), also called as design alternative set of a configuration C.
The residual risk, as discussed, is the complement of total belief. Hence, for
convenience, the Total Belief of C is denoted as:
RRisk(C) = 1 − RRisk(C)
The selection between two configurations based on max belief and residual risk
is obvious: “higher max belief, and lower residual risk”. However, it is not always
a case that a higher max belief configuration has lower residual risk. Thus decision
makers should understand which criterion is more important. In this sense, these
metrics could be combined using weighted harmonic mean. Suppose that w 1 , w 2
are weights of max belief and residual risk, respectively. The harmonic mean is
defined as follow.
w 1 + w 2
MaxB(C) · (1 − RRisk(C))
H(C) = w 1
MaxB(C) + w 2
= (1 + β)
β · MaxB(C) − RRisk(C) + 1
1 − RRisk(C)
where β = w 1/w 2 means max belief is β times as much important as residual risk.
1 One should not confuse this notion of residual risk with the one in security risk analysis
studies which is different in nature.