*Threat Capability and Resistance Strength in the FAIR taxonomy are among the more abstract and difficult concepts to get a firm grasp on. The standard seeks to fix ideas with the analogy of a weight on a rope. This note models that analogy in detail and uses it to explore these concepts.*

The FAIR taxonomy [1] uses the term “vulnerability” in a
special way that differs significantly from how it is used by CERT and many
network and software scanners.
“Vulnerability” in FAIR is “the probability that a threat event will
become a loss event.” The usual meaning of “vulnerability” in information
security is a flaw or suboptimal configuration in software or hardware. The
taxonomy breaks Vulnerability into two component drivers, Threat Capability and
Resistance Strength. (I’ll use initial
capitals to make it clear where FAIR-defined words are meant. I’ll also use the standard abbreviations
Vuln, TCap, and RS.) Note that since
Vulnerability is a probability, it is a number between 0 and 1, or 0% and 100%.

Threat Capability is defined as “the probable level of force
that a threat agent is capable of applying against an asset,” leaving it to
analyst to identify what kind of “force” is to be considered for the scenario
at hand, and how to quantify it. “Probable
level” is a hint that TCap is a probability distribution, though it could be a
single number in a simple case. Resistance Strength is defined as “the strength
of a control as compared to a baseline unit of force.” The accompanying discussion in the standard emphasizes
that RS is to be measured on the same scale as TCap, which is helpful to the
extent that one understands force for the TCap.
To help fix ideas for all three concepts, the standard offers the
example of a weight (the Threat Agent) on a rope (which is a control that
protects an asset – maybe your toes beneath the weight). The force is gravity, the measure of force is
pounds-force or Newtons, and the Resistance Strength is the tensile strength of
the rope, and so it too is measured in pounds or Newtons. The Vulnerability is then the probability
that a specific weight, or population of possible weights, will exceed the
tensile strength of the rope.

Let us model this scenario to see if it can help us understand
these three ideas better. First we define
the scenario.

**Scenario Description**

Purpose: To assess
the risk posed by weights on a construction site being hoisted over a
partially-completed building.

Assets: A building
under construction, materials and equipment on the site, life safety of the workers.

Threats: Heavy
construction materials, such as steel beams and loads of wet concrete to be
hoisted.

Threat Event: A load
being hoisted over the building or the site.

Loss Types: Structural
integrity of the building, availability of the building on the site for further
work, availability of the building for delivery to the owner on the contracted
date (using the C-I-A loss categories).

Risk Scenario: A
construction load being hoisted into position breaks its rope (Threat Event) and
crashes into the building or the site, damaging the building, materials, and
equipment, and causing injury or loss of life (Loss Event).

Threat Community: The
set of loads planned to be hoisted, ranging from a very light load to 35
kiloNewtons (7875 pounds of force to us Yanks), with an uncertainty of +/- 5 kN
(one standard deviation).

Threat Agent: The
specific member of the Threat Community we’ll start with is the maximum weight
of 35 kN +/- 5 kN.

Control: a steel rope
with a specified tensile strength of 40 kN (9675 pounds), with an uncertainty
of +/- 3 kN (one standard deviation). We’ll assume the specification is one
standard deviation lower than the mean breaking strength of 43 kN.

**Analysis**

The problem is to determine how likely it is that the load
exceeds the strength of the rope, or in FAIR terms the probability that a
Threat Event becomes a Loss Event. That
is precisely the FAIR Vulnerability. In
any given hoisting operation, we have a load of uncertain weight imposing a
force on a rope of uncertain tensile strength.
If the load exceeds the rope strength, the rope breaks and we have a
Loss Event. We need to determine how
likely it is (the probability) that the uncertain load will exceed the
uncertain tensile strength.

Like a B-minus sociology student, we shall naively assume
that all probability distributions are normal (Gaussian), and casually ignore
the infinitesimal probabilities of negative weights and negative tensile
strengths. Given that, here is the
probability distribution of the biggest planned load (Threat Agent).

The density function peaks at 35 kN, which is also the 50%
point on the cumulative distribution, as it should.

The tensile strength has a similar probability distribution,
but I find it more natural to think of it in terms of its cumulative
distribution – that is, what is the probability of breaking at or below any
given load – rather than its density function.
Here it is:

Notice that the cumulative curve is a similar shape to the
one for the load but shifted a bit to the right (we should hope that the
strength is at least a bit greater than the load).

Here is what we do to figure the Vulnerability. (Plus one point if you smell a Monte Carlo
simulation coming.)

**Procedure**

2. For each realization of the load random variable, look up the probability of the rope breaking, and record it. For 40 kN, it is 0.16.

3. Do this a bunch of times, say 1000.

4. Average the thousand probabilities you got in step 2.

The answer is a single number, the probability of the rope
breaking, averaged over the probable load weights for the given load (Threat
Agent) and rope strengths. This is the
Vulnerability, the probability for this load size (Threat Agent) that a Threat
Event becomes a Loss Event. The number I
got was 0.079. (There will be some run-to-run variation in a MC simulation.)

(Another procedure is to generate two random variables, one
for load and one for strength. You
record a 1 if load is greater than the strength and 0 otherwise. The average of the 1’s and 0’s is the answer.
This is the method Jack Jones uses in
his video on the CXOWARE web site. It
gives the same answer but I find the procedure above easier to understand. It
can be shown that the two procedures are equivalent.)

**Vulnerability for Various Threat Agents**

We could repeat the analysis for a whole range of loads we
see lying around in the construction site.
In FAIR words, there are other Threat Actors in the Threat Community,
and they have different Threat Capabilities.
After putting away my steel-toed work boots, I did that. Here’s what I got. Each dot represents the probability of
breaking for a load whose mean size is shown on the x axis. The standard deviations of all the loads is
5.0 kN.

We see that the probability of failure (Threat Event becomes
a Loss Event) increases with the load (that’s reassuring) and gets pretty high
as we approach the specified tensile strength of the rope of 40 kN (that is
too).

This set of points looks an awful lot like the curve for the
rope, but it’s not the same. Here are
both sets of data plotted on the same chart.

For small loads (TAs), the probability of the rope breaking
is greater than the probability of the rope breaking for the average of the
load. Why? Because a load of say 35 kN average has some
probability of being more than 35 kN, which has a bigger break probability. The opposite is true for large average loads,
above about 45 kN. The curve for the
dots is flatter than the curve for the rope because it includes the uncertainty
in Vuln of the sizes of the loads as well as the uncertainty in the rope
strength.

**Vulnerability for the Threat Community**

Each dot in the previous chart represents a specific member
of the Threat Community, a specific Threat Agent. In our scenario, it is a load or group of
loads with a certain average weight and a certain standard deviation. The dot is the Vulnerability for that load
size (TA).

Now suppose we want to generalize to the whole Threat
Community. After all, the job is to
finish the building, not just to hoist one kind of load. In surveying the job we might see that there
or a 50 or 100 kinds of small loads, and only a few of the very largest loads. In that case we would do this:

- Take a census of loads to be hoisted. This is the Threat Community.
- Classify them into a reasonable number of relatively homogeneous subsets. Each is a Threat Agent. Estimate their means and standard deviations. Count the number in each subset.
- For each TA, do the MC simulation like we did above for the 35 kN load, and so get the probability of failure (Vulnerability, conditional for that particular TA).
- Compute the weighted sum of these conditional Vulnerabilities. The weights are relative frequencies of occurrence of the various TAs (subsets). Each hoisting job counts as one.

The weighted sum is the Vulnerability for the entire Threat
Community. It is just a number, like
0.01 or 0.50 or 0.97. Unlike Threat
Event Frequency or Annual Loss Expectancy itself, it is not a distribution.

What do you expect to find?
You expect that the Vulnerability to the entire TC is less than the
worst-case TA. This may be confusing. As risk managers, what should we plan for, the
entire TC (which gives us a happier number) or the worst-case TA? Well, that depends on your scenario. Obviously if your scenario is a mix of TAs
you expect to encounter, the Vuln is going to be lower than for the worst-case
TA. You think, in your risk-averse mind,
“Gosh, I need to plan for the worst case.”
But now is the time to think carefully (well, again, not for the first
time!). This is the root of
disagreements about whether risk should be assessed based on the worst case or the
whole range of expected possibilities.
(Another problem with “worst case” is that it is usually ill-defined, if
defined at all. There is practically no
limit how bad a worst case can be.
Leaving it to the analyst will lead to uncontrolled biases, inability to
compare results, and lack of reproducibility.)

Yes, you need to be aware of, and understand the
consequences of, the (plausible) worst case.
But that is not an accurate description of your expected overall
experience. Yes, the worst-case could
happen, and sooner or later it will happen, and it needs to be accounted for in
the analysis, but it is a mistake to over-weight it.

How do we properly weight the worst case with all of the
non-worst cases? The answer is with Threat
Event Frequency. If the scenario is the
worst-case TA, then the TEF is presumably lower than if the scenario is for the
entire Threat Community. If the scenario
is for the entire Threat Community, not just the worst-case TA, then the
worst-case TA will be in there, with its appropriate weight, along with all the
lesser TAs in the TC. In the end, when
you roll the results up to the Annual Loss Expectancy, the worst-case TA will
be in there, appropriately weighted. In
other words, Yeah, it could happen, but not that often.

Which scenario to choose for analysis depends on what you
need to know for making decisions. In
the case of our construction site, it may well be that the scenario that
management needs to understand is the worst plausible TA (who cares about the
lesser ones?). In another situation,
maybe it is a broader Threat Community.
What you get depends on what you want, all of which goes to show how
critical it is to define the scenario carefully, and get agreement it is the
right one.

**Safety Factors**

Nobody in his (or her) right mind would, I hope, even
consider hosting a 40 kN load on a 43 kN rope, or even a much smaller load. In fact I am sure there are workplace safety
regulations about that.

Now suppose you are a regulator whose job it is to place a
limit on the permissible load for a certain-size rope. Limits are commonly stated as the safety
factor, the ratio of the rope strength (e.g.) to the permissible load (RS to
TCap in FAIR terms). How do you do
that? One way is to use the method
described above as a first step to quantify the probability of failure. You would need reams of data on material
testing. But it’s only an initial step
because setting final rules will of course be as much a values-driven and
political process as a technical one.
Nevertheless it is interesting to think how such things can be done, and
what kind of logic underlies safety factors of 1.5, 2, or more.

What would it mean to our industry if a safety factor (RS/TCap)
of 1.5 or 2 were required by regulation?

**Further Questions**

If the analysis of the rope example aids your understanding
of TCap and RS in cyber risk, it nevertheless raises some other questions. How can we understand “force” in cyber
risk? What exactly are TCap and RS? And what exactly is the Threat Community, on
which the whole analysis hinges? I’ll
address some of these questions in future notes.

However, if nothing else is clear, I hope you believe now
that FAIR is applicable much more broadly than only to information risk. In fact it can be applied to any risk
scenario whose losses can be quantified in a single number, commonly
dollars. Multi-dimensional risk is a
whole different beast.

**References:**

[1] The Open
Group,

*Risk Taxonomy (O-RT),*version 2.0, document number C13K
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