Working PaperPDF Available
Confidential Draft for publication 1/3/2012
Risk Matrix Basics
Ben Ale (University of Delft), Pete Burnap and David Slater (Cardiff
There is a growing volume of discussion on the value or otherwise of the ubiquitous “Heat Maps”,
which have become de facto, the weapon of choice in discussing and comparing corporate,
national and global risks, whether for regulation, governance, or political justifications. This note
sets out to remind us of the strengths and limitations of blindly following standard recipes and
blithely extrapolating into inappropriate areas or applications. It all depends on understanding the
basis of their derivation and the limitations of inherent approximations from dumbing them down.
Risk management is an increasingly important task in managing enterprises, companies, countries
and societies. The most prominent risks, which attract the public eye the most, are risks that involve
human life or health or the state of the environment. But in many cases the stakes are of a different
nature. In the financial markets risk usually is associated with losing money as a consequence of
investments turning bad, mortgages not being paid back or fraudulent bookkeeping. In construction
the risks are associated with completing a railroad in time and within budget or a building collapsing.
All these have in common that the outcome of an action, a decision or an activity is to a certain level
uncertain. The uncertainty not only pertains to the magnitude of the potential loss but also to the
question of the likelihood of a particular loss.
The political debate is often laden with confusion about the representation of risks, the magnitude
of risks and the decision-making tools and mechanisms. A typical example is the discussion about the
validity of risk matrices. In this discussion the presentation of the risk as points or lines is confused
with the decision mechanism - usually some red, yellow, green coloring scheme and the choice of
the demarcations between these areas.
In this report we try to take away at least some of the confusion in the hope that the discussion will
depart from discussion about methods and focus on what should be important, which is the
discussion about acceptability. The latter discussion is completely and utterly political (Ale, 2003).
The need for graphical representations of risk often stems from the need to get around the physical,
chemical and mathematical instruments that play a role in safety science. This unfortunately
introduces many misconceptions, even about what has been published earlier. In order to
understand the discussions and to take away these misconceptions the reader is invited to bite the
bullet. In the following things will be kept as simple as possible but also be made as complicated as
necessary. The mathematical formulas are there to illustrate a point and sometimes give
mathematical proof for those who otherwise would not be convinced. They can also be skipped by
those who are willing to believe that everything stated as being fact in this report can be proven.
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Risk management
In order to deal with uncertainty in an organised way the concept of probability is introduced.
Probability is the measure the likelihood that something will happen. It has an exact mathematical
definition. Organised risk management starts with the estimation of the “magnitude” of the risks
involved followed by some process of decision making. The first known form of a decision making
principle was formulated by A. Arnaud in 1662
Fear of harm ought to be proportional not merely to the gravity of the harm, but
also to the probability of the event
Risk therefore is a combination of consequences and probabilities. In Arnauds view the true measure
of risk is the multiplication of probability and consequence. Risk is probability times effect. What in
mathematical terms is designated by the expectation of the consequences. We will see that
decisions that follow Arnauds rule in having the acceptability of an activity directly proportional to
this measure of risk are common in economics. However the more contentious decisions, and these
are often related to issue of life and death, do not seem to follow this rule. Many attempts have
been made to capture apparently different relationships between acceptability, probability and
Therefore the process of risk management can be summarised as in figure 1 (van Leeuwen en
Hermens, 1995). After identification of all the potential adverse events, the probabilities and
consequences are modelled and quantified. The risks are also qualified. Qualification in this context
means establishing other attributes of the activity with which the risk is associated and which are
important for the decision to undertake the activity. These attributes are often value laden
especially when the risk involves potential harm to human life or health. Although it may seem that
establishing the magnitude of risk is value free, it often is not, because, as we will see later, the way
Figure 1: Steps in the risk management cycle
(when required)
Kind of Risk
and Probabilities
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this magnitude is expressed may itself contribute to the framing of the decision. After this work has
been done the information is ready for use in a decision making process. After it has been decided
whether the risk is acceptable or has to be reduced, the risk is monitored and a new cycle may start
depending on whether the risk seems to remain acceptable or not. Although decision is only a small
block in the diagram of figure 1, this usually is takes the most time and the most discussion.
Especially the discussions about the use of nuclear power, about the risks of chemical industry and
the associated transport and about the long term effects of human activities on the climate of the
earth have shown that in decision making there is often more than consequence and probability
alone (Gezondheidsraad, 1993)
In real life the risk management process is not as clean as the schematic suggests. As said before,
value judgements are often made in the steps where information is assembled and in this way the
gathering and presentation of information becomes a part of the decision making. As Harry Ottway
(1973, 1975) put it:
Risk estimation may be thought of as the identification of consequences of a
decision and the subsequent estimation of the magnitude of associated risks.
Risk evaluation is the complex process of anticipating the social response to risks;
… this could be termed as the “acceptability of risks”
We could also make a distinction between risk management and risk governance. Risk management
may be thought of as keeping risk within defined limits against define costs. Risk governance is the
process in which we deal with a problem that involves risk, but also many other things.
In the sometimes heated discussions about risk acceptability, risk has been defined and redefined
countless times, often to reflect those aspects or arguments that a proposer or author deemed
important. This is not discussed here any further but serves as the argument why for this report a
number of definitions need to be given, as they will be used in this report, without prejudice about
the validity of any other definition one can give. Let event be an occurrence or happening resulting
from a decision.
Consequence (c) is the outcome of an event
Probability (p) is the chance that the event will occur. Probability is a number between 0 and 1.
Frequency is the average rate per unit time (usually a year) that an event will happen. It is often also
called the probability per year. The latter is mathematically imprecise and leads to much confusion.
As an example take car accidents. There a few hundred of these each year. Therefor the probability
of a car accident is 1. (At least 1 has already happened so the probability cannot be smaller). For the
future one might think that form tomorrow there is a chance that no more accidents will happen. In
that case the probability of car accidents is smaller than 1. These probabilities however are highly
uninformative. It is much handier to work with the (expected) number of accidents per year.
Riskpoint is the combination the outcome and the probability/frequency of an event
Riskset is the set of riskpoints all possible events of a decision.
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Risk (R) is the magnitude of riskset. R can be evaluated in various ways.
In many cases the discussion about risks involves an argument of uncertainty. This will be dealt with
later. For now it is sufficient to assume that consequences and probabilities can be established or
In its simplest form the magnitude of risk is the total value of the expected outcomes or expectation
value. This is also referred to as risk is probability times consequence or
*R p c
If there is a range of consequences and the probabilities for the different outcomes are different
then the risk in general is
R p c
This definition of Risk is used in finance and insurance. It is a single number. Therefor risks measured
in this way can easily be compared.
Unacceptable consequences
The problem with measuring risks in the simple way described earlier is that it implies that the
decision maker will attach equal value to risks for which the R is equal; that it does not matter
whether there is a 1/100 chance of winning 100 euro or a 1/1000 chance of winning 1000 euros. In
normal life betting games this is often the case. However if the consequences are very high this
might no longer be the case. As an example after 9/11 insurance companies were no longer
prepared to insure losses in excess of 1 billion euro’s regardless of the probability. In such
circumstances the consequences and the probabilities or frequencies have to be presented and
considered separately.
Intermission: presenting risks
At this stage in this report it is necessary to introduce the various ways risk can be presented and
how uncertainty can be taken into account leading to even more complications.
The presentation of R as product of c and f or the sum of the products of c’s and f’s is a single
number. The R of 100 euro’s with is probability of 1/100 is 1. This presentation is necessarily a two
dimensional picture. Usually f (frequency) is given as a function of c (consequences).
FN diagrams
Suppose the following list of events with consequences and frequencies is known:
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The R for this set is 1.56. A graph using linear scales depicting these points looks like figure 2.
This is a very unfortunate representation as most points seem to be on the vertical axis. Therefor a
smarter way of presenting these numbers is in a so-called “double logarithmic” diagram in which the
value at the “tick marks” increase exponentially instead of linearly as given in figure 3..
The frequencies in this example have been chosen to decrease with increasing consequences, but
that does not have to be the case. Suppose we have a list of events as follows:
Fig 2 Frequencies and consequences on a linear scale
0 2000 4000 6000 8000 10000 12000
Fig 3 Frequencies and consequences on a double logarithmic scale
C ->
f ->
110 100 1000 10000 100000
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That would on a double log scale look like figure 4
The graph would sort of wander about. A much neater way of doing this is to add the frequencies up
from the largest consequence to the lowest. This always leads to a decreasing line (figure 5)
It should be noted that the frequency axis in figures 2-4 have f and in figure 5 it says F, making the
Fig 4 Frequencies and consequences on a double logarithmic scale
C ->
f ->
110 100 1000 10000 100000
Fig 5 Cumulative Frequencies and consequences on a double logarithmic scale
C ->
F ->
110 100 1000 10000 100000
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difference between regular and cumulative frequencies. However this is not always done and
especially in the older literature, when the typesetting options were much more limited one has to
refer to the original paper to know. The graph with cumulative frequencies is called a
complementary cumulative distribution function (CCDF) and is the regular form of the FN diagram.
It should also be noted that there is no line drawn in any of these diagrams. That is because if the
consequences would be number of people killed, such a number could only be an integer. Before an
FN diagram can be converted into an FN curve a few further steps have to be taken.
This will be done after the histogram representation has to be dealt with
In many cases the potential consequences are not precisely known. In such cases a number is
presented as a range of numbers and all events having consequences in that range are put in the
same bin.
Suppose that in total 40 accidents have been found with the following numbers of people affected:
1000 -
This could be presented in a bar chart: (Fig 6 left)
Now suppose that these numbers could be refined to the following table:
1 - 3
4 - 9
10 - 39
40 - 99
101 - 399
400 - 999
1000 -
Then the bar chart would look like figure 6 right. It should be noted that the numbers in each of the
bins on the right hand side are lower than that on the left hand side. This has implications when
these numbers are used in any measure of acceptability, but that will be dealt with later.
Figure 6: Bar charts for numbers of events.
1 - 9 10 - 99 100 - 999 1000
1 - 3 4 - 9 10 - 39 40 - 99 101 - 399 400 - 999 1000 -
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If on would convert both diagrams into curves one could plot them in the same plot as given in
figure 7. The advantages of this representation are immediately obvious. The plot is invariant for the
size of the bins. Even if every bin would only be one person wide i.e N = 1; N= 2 etc even then the
figure would look the same. That is why in risk presentations the FN diagram or CCDF is the
preferred presentation.
It can be easily seen that should these numbers be found in a period of 1000 years the only thing left
to do is divide the values on the vertical axis by 1000 to get the number of events per year.
If one were to represent this data as continuous curves one could end up with curves such as in
figure 8. It is only for the reason that the numbers of cases do not decrease with increasing N that
one can see that the “bargraph” curve cannot be an FN diagram. Therefore these representations of
Figure 7 FN diagrams for numbers of events.
110 100 1000 10000
Figure 8: curves.
110 100 1000 10000
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discrete data are dangerous for later interpretation and uses, but this habit is nonetheless
A math trick
There is one trick however that does not change the shape nor the values in the presentation of an
FN diagram, but increases its useability. This trick is to define the FN curve for non integer number as
For r N < M < N+1 F(M) = F(N). This converts the FN diagram into a stepwise continuous function.
This means that it can be integrated. As has been shown by Ale (1996) and by Jongejan (2008) the
integral under the curve is equal to the expectation value of the risk. Another advantage is that the
summation and abstraction rules for functions apply.
Risk Criteria
In the previous section nothing has been said about criteria. Until now, all diagrams were just
representation of risk calculations, be it simple invented ones just for illustration.
It is obvious that the simplest way of limiting a risk is to set a maximum to the expectation value R.
The simplest way to compare risks is on the basis of their expectation value. There are however two
Fig 9: Examples of risk matrices
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persistent problems with this approach. One is that in political choices higher consequences
sometimes weigh heavier than smaller consequences and that it is sometimes desirable and
sometimes necessary to do something about the so called “high consequence low probability” risks.
Since the accident with the Deepwater Horizon this is also referred to as ruin prevention.
The other is that consequences are often multidimensional. They involve money lost, environment
damaged, people killed and injured.
To deal with the latter first it is obvious that that depicting all these dimensions separately would
result in an dimensional diagram. Given the problems people already have understanding a two
dimensional diagram as will be seen later people often choose to translate the consequences in
a single entity. The magnitude of that entity then is no longer a defined number expressed in
definable measures. It is a brew of all the consequences together. What is often forgotten is that
making this brew implies value judgments with respect to the mutual valuation of all the dimensions
involved. As it was put in judgments about airports in which people killed figure next to noise levels:
it implies the answer to the question how much dB a dead person is worth. That is one of the
reasons why larger companies refrain from brewing a one dimensional consequence thingy and treat
these kinds of risks separately.
The qualifications given to these consequences are often in terms of severe or mild and the
frequencies in terms of often or rare, which than can be put nicely into a diagram such as in figure 9.
In the top half of figure 9 it is only indicated when things get worse (redder). In passing it is noted
that the direction of the consequence axis runs from right to left, which is in mathematical terms at
least non-intuitive. In the lower half the suggestion already is made that the yellow boxes have
about the same “value” in terms of risk.
Unfortunately there are numerous examples of these risk matrices where the suggestion of equal
value is implied.
It is likely, but not certain, that the frequency axis is thought of to be non cumulative.
Figure 10: Figure 3 made into a risk matrix
Low impact High impact
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Risk matrices
With these ingredients one can convert figure 3 into a risk matrix as in figure 10. However it is very
difficult not to interpret the boxes as having some numerical value. Obviously the demarcation
between acceptable and unacceptable can be put anywhere. But be aware: the frequencies are not
cumulative. Neither were they in the often cited Farmer curve (Farmer, 1987, Ball, 1998). That
Farmers curve looks like an FNH curve is purely by accident. In nuclear energy industry High dose
events are less frequent that low dose events and thus Farmers curve is descending.
Every attempt to make a qualitative risk matrix into a quantitative one, in which the surface area
actually stands for a value and a constant valuation is assumed along some diagonal is asking for
trouble. In every step therefor implied weightings should be made explicit and probably debated in a
political arena.
Risk Criteria
The development of Fault Tree and Event tree techniques, from Second World War logistics,
through to high risk/consequence applications such as space flight and nuclear reactor reliability, is
the source of much of the modern risk manager’s repertoire. Some of the early ground breaking
work included comparisons of nuclear risks to “normal” risks, such as natural disasters and
transportation. This was displayed as a log/ log plot of frequency (of an event) versus the
Consequences (as number of fatalities caused) of that event, as seen in Figure 11 (Rasmussen, 1975).
Figure 11: fN curves for manmade risks (from Rasmussen 1975)
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In the UK, Farmer (Farmer, 1987, Ball, 1998) utilised the frequency / dose plot to assess the likely
exposure of the public to the operation of a nuclear reactor. (Figure 3)
This gave him a total level of exposure, (societal dose, risk) normalised to specific local population
distributions. This was another form of PIG but capable of quantitative derivation of individual and
total (societal) fatality risk levels for specific sites. The consequences were calculated from
representative “model” loss of containment events, but the plot allowed an envelope of total impact
to be assessed.
As will be discussed later, there were a number of disadvantages associated with this
representation. That is why, in a further development, cumulative risk curves were developed in
which the vertical axis did not represent the frequency of a certain consequence, but rather the
frequency of exceeding a certain consequence.
These cumulative FN curves are usually concave curves. There is generally a finite intercept on the N
axis and as N tends to 0, the cumulative risk frequency tends to increasingly large numbers as the
impact becomes more and more trivial.
FN curves have been used in all kinds of industries, where quantitative risk analysis was introduced
as a means to gain insight into these risks and as a basis for subsequent decision making. Examples
are the Canvey Island study (HSE, 1978) and the COVO study (Cremer and Warner, 1981) (see Figure
4). The propagation of quantified risk analyses led to the further development of comprehensive
Figure 12: The Farmer curve (from Griffith (1982)
C (
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techniques, by which detailed fault-tree and event tree analyses could be summarized in information
ready form, for decision making (Cox, 1982; Ale, 1986, 1987)
These techniques were introduced back to the nuclear industry (full circle) in the independent risk
assessment done for the Sizewell B public Inquiry (Slater 1982), and were clearly more helpful than
the reams of computer generated Fault tree submissions (Westinghouse 1982). Finally some ten
years later the UK Nuclear Inspectorate published their own version. (Harbison NII 1993))
In fact as early as 1976 the province of Groningen in the Netherlands published their views on the
acceptability of risk, given in figure 18. as an FN plot. In this diagram, there weren’t any colours (yet),
but the areas of acceptable, conditionally acceptable and non acceptable can clearly be seen. It can
also be seen that they thought that a consequence of 1000 people killed was too much. The
numbers killed below 1 were included (and rated) because they counted an injured person as 0.1 of
a kill. The figure shows that they were less risk averse when people were not killed.
Figure 13, FN curves from the COVO study
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In most of the later diagrams published by HSE, the Governments of the Netherlands, Switzerland,
Australia and Hong Kong, only one straight line was given (the demarcation of unacceptability or
intolerability) and in some cases also a maximum as an anchor point. (As a straight line can then be
drawn given its anchor point and its slope). The slope is the expression of the risk aversion index
described above. The limits of acceptability can be summarised in a table as below: (Pikaar, 1995;
Ball, 1998)
Table 1 Selection of National Risk criteria
Anchor N
Anchor F
ACMH UK HSE Advisory
Committee on Major Hazards
Groningen -NL
Kinchin UK Nuclear
Hong Kong
TK (1988); acceptable
line factor 100 lower
-1 and
HSE Off shore
As 1988 but acceptable
line removed
For transport per km
For transport per instn.
Figure 14. The risk map of the province of Groningen
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The bodies setting these standards have been numerous and diverse; but the methods of
presentation have been the same, with the one exception of Farmers original curve, which was non-
cumulative, hence an fN curve rather than an FN curve. Demarcations (limit lines), between
acceptable and non acceptable regions, are given as straight lines or steps following the gridlines or
as curves. Areas in between such as “conditionally acceptable” can be given as well. With the
improvement of typesetting techniques, colours were added. The colouring scheme of traffic lights
are universally recognised, so that naturally, the unacceptable area became red, the acceptable area
green. With the introduction of fading colours in the Microsoft drawing packages, continuous
coloration made these diagrams look like heat maps. (As in Figure 10).
As discussed previously, in an FN curve, the total risk set is depicted as a cumulative frequency
distribution presentation. This means that the “risk” is not a single point in the diagram, but a line
that may or may not cross the limit line (figure 15).
There is however no real reason why the demarcations should follow the gridlines that happen to
result if one uses a base 10 number system and a logarithmic scale. If the demarcation between
acceptable and non acceptable is plotted as a straight line on a double log graph, the line represents
the equation F (M>N) = C/N-α. Alpha is also called the aversion factor. Several attempts have been
made to derive this factor in a scientific way. The results vary from 1.2 (Okrent, 1981) to 2 (Hubert,
1990). In these cases, such a risk averse demarcation does not follow the economic rule that f*c
Figure 15: Unacceptable disasters.
110 100 10000.1
Disasters you
cannot afford
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should be constant. Many arguments against risk aversion, explicitly or implicitly, are rooted in the
assumption that they should (Evans). Nevertheless even if an alpha of 1 is chosen there is an
element of risk aversion, sometimes reflected in setting a maximum number of people affected or a
maximum acceptable loss. It should also be borne in mind that a so called “risk neutral” limit (when
interpreted as the acceptable F (cumulative) is equal to A/N (A = constant) for each of the (f,c) points
in the riskset. . It is also pointed out that even an F=1/N limit implies some aversion (in these terms)
as f = dF/dN. So for F = A/N, f would be A/N2
This could give rise to, in principle, an unlimited expectation value as the area under the curve grows
with increasing N without limit (The integral of 1/N is log(N)). That is probably one of the reasons
why all the 1/N curves have an upper limit. A variety of criteria lines is shown below in Fig 16
showing the range of slopes and maxima.
Figure 16: graphs in FN of acceptability criteria. (from Cox R.A.)
110 100 1000 10000
Number of Fatalities (N)
Comparison of International Societal Risk Guidelines
Scrutiny (ACDS whole
Intolerable (UK ACDS
single port)
Scrutiny (UK ACDS
single port)
Negligible (UK ACDS)
Hong Kong RG Upper
Hong Kong RG Lower
Frequency of N or more fatalities
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The technique is still applied (Fig 17) to industrial installations (onshore and offshore) worldwide and
developments of this fully quantitative approach are still valid, available, but now sadly little used in
the UK due to resource considerations (time, cost and expertise availability).
Fig 17 FN plots and Risk Contours from the SAFETI package.
What has emerged is the increasing use of the visual image of a plot that is helpful in picturing
where the seriousness of risks are perceived to be a so called “heat map” to identify hot spots.
Currently, the requirements of corporate governance (Cadbury) and many regulatory bodies (HSE)
include risk registers and often some form of “risk matrix” to display the perception of risk exposure
and measures (justified) to prevent, minimise or manage them. In its most basic form, a corporate
group discusses a list of potential threats and assigns notional likelihoods and estimates of
seriousness (consequences), often against guidelines, (e.g. examples in classes, say 0 5 for each
identified candidate threat). In order to assess the relative importance of these “risks”, (and perhaps
to prioritise responses), they are often plotted on a two dimensional “heat map”. This is an example
of a probability impact graph, often referred to as a PIG (see Figure 5).
As qualitative visualisation techniques to aid decision making, these PIGS have been found by many
to be very helpful and by some indispensible. The problems arise when additional, often quantitative
outputs are required or attempted. (Creswell) Such as:-
What are the correct ordinates? Probabilities, frequencies, of events, outcomes, etc.?
One or both linear scales, or Logs, Powers?
Discrete points or area averages?
Single points or distributions?
“Level of Risk” ( Total, components)
Criteria, Acceptability, Tolerance, Appetite.
Calibration with records, reality?
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So far we have concentrated on the historical development and original intent of Probability Impact
Graphs (PIGs). We have seen that they do have a legitimate mathematical basis and that their
utilisation without awareness of the “rules” can be at best misleading and at worst disastrous. But
the main driver for their continued use is that, as a way of assessing the relative positioning of
identified risks (from the Risk Register), in terms of qualitative seriousness (notional relative
immininence and scale?), it has proved useful in stimulating discussion, awareness and even action
from non specialist, but crucial decision makers in an organisation.
Recent work on the neuroscience of risk (Burke 2011)), seems to support this innate ability of people
to process and make decisions on risk in a relatively sophisticated way. At the neuron level,
mammals seem to have a “hard wired” ability to handle very rapidly and effectively, probability,
uncertainty, size of risk and promise of reward. This is a basic survival evolutionary skill: and it is
claimed (Linked in ref) that an analysis of the neuroscience data indicates a “risk aversion/
incentivisation factor of N to the 1.54.(Fig 18)
110 100 1000 10000
Figure 18. An Intelligent PIG with Aversion Criteria
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All of these factors as we have seen, can be accommodated in the risk matrix approach. Can we
therefore continue to utilise legitimately, what has become an integral part and some think, that
indispensible tool in the armoury of corporate Risk Management (and ISO standards) the PIG? How
can we build useful plots in a resource efficient way and still get the added value from their
Group assignments of frequencies and consequences, while subjective, have some basis in proven
Delphic techniques. So there is no reason to stop employing PIGS as long as the limitations and
necessary assumptions are documented and understood. (Note ISO 31010 fails to comment on
whether the frequencies plotted are cumulative or not - fN or FN). But can we get more? We believe
the answer is to set out the rules of their utilisation, explicitly in the standards.
Recognise there are two distinct categories
1. The Post it or heat map” (Qual) Pig
2. The “Intelligent” or “Groningen” (Quant) Pig.
If we wish to rank individual risks on a presentation plot that allows us to appreciate the
implications of a group discussion on their (relative) importance and seriousness, then a Post
it PIG is helpful.
Any discussion on their individual acceptabilities, needs, however to be done on a risk by risk
basis and generalisations are difficult, (not allowed) unless some further quantification and
standardisation is employed.
Quantification is not difficult, but we should follow the rules. Currently most benchmarking,
or guides as to scale of consequence and likelihood, are given as implicit log scales. Some
actually quote frequency ranges. It helps presentation to ensure that the underlying scale is
actually logarithmic.
For simple comparisons and heat map ranking, fN plots are OK. Maxima in allowed
consequences (Nmax) are always a good idea. Risk aversion can even be incorporated by
multiplying the consequence scale by say 1.2, 1.5, or 2, (or whatever the corporate risk
appetite indicates).
For more ambitious outputs such as criteria and risk levels the (Intelligent) cumulative FN
plot is needed,
On the FN plot the group can look at a more rigorous definition and assignment of
frequencies and consequences, but risk aversion, Maximum allowed risk and acceptability
criteria are all now real and really useful outputs.(Figure 22)
The area under the FN curve is then the RISK or EXPECTATION LEVEL. This cannot be
legitimately derived from the qualitative versions
a Risk “Level” can be derived as - the area under the CCDF curve
i.e The Risk Level is approx = ½(Nmax N1)x(F1 Fmax)]
The inference from this is that, we can use these plots and derive significantly more information, as
long as we are very careful. Spreadsheets can make the required mathematical transmutation of the
raw “post it” sessions relatively painless and provided the basis is understood and regularly queried
we could produce useful results
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Risk matrices are perceived as a convenient and understandable way of presenting risk and
displaying limits. In today’s management and policy making arena, this simplicity is preferred over
the perceived complexity of more mathematical expressions. The presentation of risk as an FN curve
is seen as exceptionally difficult to understand. In addition consequences tend to be valued as single
factor impacts, rather than the multidimensional effects, which they usually are in practice. This
development has led to an increasingly strident debate about risk matrices and methods of risk
management, to the extent that that there seems to be a call to give up on using them at all in risk
With recent disasters in mind, we think they can make a real contribution, but it would be helpful to
appreciate what is behind traditional FN representations of risk and thus enable a more intelligent
(pre incident?) discussion of the dimensions and implications of risk decisions; of such things as
appetite, accountability and its limits of acceptability/tolerability (societal and corporate), in
whatever form helps; even in such FN diagrams, if it helps us manage these risks more responsibly
and effectively.. (Casting PIG’s before-----! )
Literature References
Ale, B.J.M. (1986) and R. Whitehouse, A computer based system for risk analysis of process plants.
In Heavy Gas and Risk Assessment III, 5. Hartwig (Ed) D. Reidel, Dordrecht, The Netherlands.
Ale, B.J.M. (1987) D. van Nierop, M. Seaman, safety zoning around a major industrial complex in the
Netherlands (World Congress on Chemical Hazards, July, Rome)
Ale,B.J.M. (1996) G.M.H. Lahey, P.A.M. Uijt de Haag, Zoning Instruments for Major Accident
Prevention, International Conference on Probabilistic Safety Assessment and Management, Crete
Ale, B.J.M. (2003) Keynote Lecture: Living with Risk: a management question, in ESREL 2003, Safety
and Reliability, - Bedford en van Gelder (eds), Swets en Zeitlinger, Lisse, ISBN 90 5809 551 7
Ale, B.J.M. (2009), L.J. Bellamy, R. van der Boom, J. Cooper, R.M. Cooke, L.H.J. Goossens, A.R. Hale,
D. Kurowicka, O. Morales, A.L.C. Roelen, J. Spouge, Further development of a Causal model for Air
Transport Safety (CATS): Building the mathematical heart, Reliability Engineering & System Safety,
Volume 94, Issue 9, September 2009, Pages 1433-1441
Ale, B.J.M. (2011), D. Hanea, C. van Gulijk, P.-H. Lin, S. Sillem & P. Hudson, Towards an integrated risk
model for hydrocarbon industry operation, Proceedings of the European Safety and Reliability
Conference, ESREL 2011 18-22 September 2011 - Troyes France ,Advances in Safety, Reliability and
Risk Management renguer, Grall & Guedes Soares (eds), Taylor & Francis Group, London, ISBN
Arnaud, A. (1662), La Logique, ou l’art de penser, 1662
Confidential Draft for publication 1/3/2012
Ball, D.J. (1998) and P.J. Floyd, Societal Risks, HSE,
C. J. Burke and P. N. Tobler(2011) Coding of reward probability and risk by single neurons in animals.,
Laboratory for Social and Neural Systems Research, Department of Economics, University of Zurich,
Zurich, Switzerland. Frontiers in Decision Neuroscience, October 2011, volume 5, article 121.
Chapman & Stephen Ward (2011). How to manage Project Opportunity and Risk. Chp 2. The
Probability-impact grid - a tool that needs scrapping. Pp 49-51. 3rd Ed. Wiley.
Lee, B. Preston, Green, G. Preparing for High Impact, Low probability Events,(2012), Chatham
House, London
Louis Anthony (Tony) Cox, Jr (2008)., What’s Wrong with Risk Matrices? Risk Analysis, Vol. 28, No. 2,
Cox, R.A. (1982) Improving risk assessment methods for process plant Journal of Hazardous
Materials, Volume 6, Issue 3, May 1982, Pages 249-260
Cremer and Warner (1981), Risk Analysis of Six Potentially Hazardous Objects in the Rijnmond Area,
London 1981; Also published by Springer Verlag 1982, ISBN 9027713936
Cresswell.(2011) 'Qualitative Risk & Probability Impact Graphs: Time for a rethink? from
Gezondheidsraad (1993) Risico is meer dan een getal
Griffith, R.F (ed) (1982) Dealing with Risk, Manchester University Press, ISBN 0-7190-0894-8
Harbison, S. (1995)
Health and Safety Executive (1978) Canvey, - an investigation of potential hazards from operations in
the Canvey Island/Thurrock are, HMSO, London
Hopkins, A (2000) Lessons from Longford: the Esso Gas Plant Explosion, Sydney, NSW, CCH Australia
Hubbard, (2009) The Failure of Risk Management. Chp 7. Worse than Useless? The most popular risk
assessment method and Why it doesn't work.Wiley & Sons.
Hubert, Ph, M.H. Barni, J.P. Moatti,(1990) Elicitation of criteria for management of major hazards,
2nd SRA conference, April 2-3 1990, Laxenburg, Austria.
ISO Standards 2700,2800, 3700
Jongejan, R, How Safe is Safe Enough?, PhD Thesis TU Delft, ISBN 978-90-9023432-8
Kinchin, G.H. (1978) Assesment of Hazards in Engineering Work, Proceedings of the Institute of Civil
Engineers, vol 64, pp431-438
Leeuwen, C.J. van and J.L.M. Hermens, (eds) Risk Assessment of Chemicals: An Introduction, Kluwer,
NN (1976) Nota Milieuhygienische Normen, Provincie Groningen, 1976
Confidential Draft for publication 1/3/2012
Okrent, J. (1981), Industrial Risk, Proc. R. Soc. 372 (1981) 133-149, London
Otway, Harry J. (1973), Risk Estimation and Evaluation, in Proceedings of the IIASA Planning
Conference on Energy Systems, IIASA-PC-3, International Institute of Applied Systems Analysis,
Laxenburg, Austria.
Otway, Harry J. (1975), Risk Assessment and Social Choices, IIASA Research Memorandum,
International Institute of Applied Systems Analysis, Laxenburg, Austria.
Pikaar, M.J. (1995) and en M.A. Seaman, A review of Risk Control, Report nr SVS 1994/27A ministerie
VROM, Den Haag.
Rasmussen N. (1975), Reactor Safety Study, An assessment of accident risks in U.S. commercial
nuclear power plants; WASH 1400; NUREG 75/014)
Rasmussen N, (2000) Accimaps
Slovic, P., Fischoff, B. and Lichtenstein, S., Read, S and Combs, B.,(1978) How safe is safe enough, a
psychometric study of attitudes towards technological risks and benefits, Policy Sciences, 8: 127-152,
Slater, D. (1982) , Proof of evidence to the Sizewell Inquiry, HMSO
Slater, D. (2012) Risk Assessment: from the Top, The Chemical Engineer February Issue, p. The
Institution of Chemical Engineers, London
Slater, D. Burnap, P et al (2010) - Managing Risks in Complex Interdependent Systems TSB Fast
Track Project BK016A Final Report
UK National Risk Strategy 2011
WEF Global Risks Landscape 2012
Vessely, W.E. (1981), F.F. Goldberg, N.H. Roberts, D.F. Haasl, The Fault-tree Handbook, Systems and
Reliability Research Office of the NRC, Washington DC NUREG 0492,
Westinghouse Evidence to the Sizewell B Inquiry
Confidential Draft for publication 1/3/2012
!967 - Farmer, F.R. (1967) Siting criteria a new approach, atom (128) pp 152-70
1976 Groningen Criteria (FN (fn ) plot with limits)
197? - Rasmussen Comparisons with natural disasters (fn curves)
1981 - Rijnmond Risk Output (risk contours and (log axes)fn curves)
1982 - Sizewell B (Cox - independent” Farmer” type fn curve)
1984 - Technica - SAFETI (“All” Failure cases generation) uses Groningen criteria
!985 - Dutch External Safety Criteria (Individual and Societal Criteria, SAFETI Fn curves and
!980’s - Slovic Risk Aversion (fxn2, fxn1.2)(note on log scales)
!988 - Risk Lite - “Semi quantitative” Risk estimation (still fxn Matrices))
1990 - Corporate Risk Management (Red Amber Green Traffic Lights /Matrices)
1992 Big Four discover Risk Matrices and move on from mere quantified inputs
1995 - Cadbury Corporate Governance Risk required Registers and produced Matrices based on
Board discussions.
2000 - Enterprise wide Risk Management tools include Risk lite graphics
2010 - ISO 3100 PIGS - organized guesses
2011 Linked in groups - How do we get a Level of risk from this? How do we get the total summed
2012 back to Farmer?
... Problems of assessing risk in matrices are discussed for a very long time in scientific literature [8,9,10,11,12,13,14]. When compiling risk matrices, a fundamental mistake is made when assigning linear numerical values for the rows and columns of the matrix. ...
... However, only the outcome of damage appears in the basic definition of risk. Multidimensional assessments in weak scales are the reason for the long-debated problem of "weak consistency" in strict risk matrix assessment [8,10]. Therefore, the vast majority of practiced risk management methods cannot be recognized as scientifically justified. ...
... Risk assessment using this profile is an alternative to the accepted probability measure metric. In contrast to the analogs, the advantage of the proposed matrix is the resolution of the problem of "weak consistency" of the matrices: the elimination of mismatch of color and numeric values [8,10]. ...
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The existing normative definition of risk, based on probability theory, is a particular definition of risks and does not correspond to the variety of measures for calculating life risks. Calculating risks in other fuzzy measures: likelihood, possibility, confidence, necessity, opens up new possibilities to assign numerical values to objects and complex events. This paper presents a method of design and soft computing in risk matrices, which instead of a single outcome measure called a consequence, represents samples of several qualifiers, evaluation areas, parameters, and semantic rows of natural language. For the first time, the risk matrix definition is presented, a template for designing risk matrices and samples for use in practice are developed. The purpose of risk matrices is to make it possible to assign numerical values to the properties of evaluated objects through expert subjective judgments. The randomness measure absorbs a wide class of soft measures likelihood, necessity, confidence, conviction, possibility, probability. The measure of the magnitude of the outcome combines the concepts of severity, damages, losses, and victims. The method is aimed at direct application of expert assessments of any objects and their components.
... Оценка рисков evaluation рассматривается как процесс прогнозирования социального отклика на риски или «приемлемость рисков». Различают понятия управления рисками risk management как нормативное управление ресурсами, и управления рисками risk governance как способ разрешения проблем, вовлеченных в риск [165]. Данные описания расширяют содержательное представление предмета риска, хотя являются нечеткими и требуют теоретической проработки. ...
... В работе [176] для исследования данного свойства вводится понятие weak consistency «слабая состоятельность 50 ». Данная работа вызвала дискуссию в литературе рискологии, особенно относительно доказательств двух лемм о слабой состоятельности [76,165,176]. 49 Например, в ISO 31000 отсутствуют комментарии, являются ли частоты кумулятивными. 50 consistency, также согласованность, последовательность ...
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Книга посвящена транспортным комплексам как сложным объек-там. Методом исследования и проектирования является ресурсный подход. Работа адресуется представителям аэрокосмической инду-стрии.
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PREFACE This work is a collection of articles written a last decade and combined in a new scientific approach of the ontological designing of organizational air transport objects. Ontological design ing in general terms is considered by the author as a scientific approach to the study and solution of complex-structured scientific problems, the solution of which by known theories and methods is not attainable and is not achieved over long periods of time. The area of knowledge of the ontological designing of reality, united on a resource basis, is understood as a new discipline of resource methodology (resourcology). Resource science is based on the resource representation of reality. The resource complex is understood as transformable sources of energy, information and substances involved in expedient activity. The applied domains are devoted to acute imminent problems of flight safety and aviation security of world aviation. The book consists of two parts. The first part presents the basics of the resource designing methodology and soft computing of the properties and states of organizational objects for the purposes of effective management. The second part contains articles devoted to the development of the theory of dependability, experiments and soft computing of the properties and states of individuals and social groups on the example of flight crews and civil aviation pilots. Most of the articles are published by well-known editions and indexed in international data bases. The first edition is expected to be continued. SCOPE OF THE EDITION o Applied ontology of designing domains o Engineering of ontology formalization languages o Engineering psychology and human-machine interfaces o Human resource management o Resource management of organizational and social objects o Methods and technologies for decision making and decision taking o Management of transport complexes
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One of the fundamental questions addressed by risk-benefit analysis is How safe is safe enough? Chauncey Starr has proposed that economic data be used to reveal patterns of acceptable risk-benefit tradeoffs. The present study investigates an alternative technique, in which psychometric procedures were used to elicit quantitative judgments of perceived risk, acceptable risk, and perceived benefit for each of 30 activities and technologies. The participants were seventy-six members of the League of Women Voters. The results indicated little systematic relationship between perceived existing risks and benefits of the 30 risk items. Current risk levels were generally viewed as unacceptably high. When current risk levels were adjusted to what would be considered acceptable risk levels, however, risk was found to correlate with benefit. Nine descriptive attributes of risk were also studied. These nine attributes seemed to tap two basic dimensions of risk. These dimensions proved to be effective predictors of the tradeoff between acceptable risk and perceived benefit. The limitations of the present study and the relationship between this technique and Starr's technique are discussed, along with the implications of the findings for policy decisions.
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Probability and risk are important factors for value-based decision making and optimal foraging. In order to survive in an unpredictable world, organisms must be able to assess the probability and risk attached to future events and use this information to generate adaptive behavior. Recent studies in non-human primates and rats have shown that both probability and risk are processed in a distributed fashion throughout the brain at the level of single neurons. Reward probability has mainly been shown to be coded by phasic increases and decreases in firing rates in neurons in the basal ganglia, midbrain, parietal, and frontal cortex. Reward variance is represented in orbitofrontal and posterior cingulate cortex and through a sustained response of dopaminergic midbrain neurons.
The development of the Netherlands international airport Schiphol has been the subject of fierce political debate for several decades. One of the considerations has been the safety of the population living around the airport, the density of which has been and still is growing. In the debate about the acceptability of the risks associated with the air traffic above, The Netherlands extensive use has been made of statistical models relating the movement of airplanes to the risks on the ground. Although these models are adequate for the debate and for physical planning around the airport, the need has arisen to gain a more thorough understanding of the accident genesis in air traffic, with the ultimate aim of improving the safety situation in air traffic in general and around Schiphol in particular. To this aim, a research effort has started to develop causal models for air traffic risks in the expectation that these will ultimately give the insight needed. The concept was described in an earlier paper. In this paper, the backbone of the model and the way event sequence diagrams, fault-trees and Bayesian belief nets are linked to form a homogeneous mathematical model suitable as a tool to analyse causal chains and quantify risks is described.
This paper considers the usefulness of risk assessment in the analysis of hazards due to chemical process plant and similar installations. Risk assessment is first defined as a technique in which the probabilities and consequences of all possible accidents are quantified. The outputs from such an analysis may take the form of ‘frequency versus magnitude’ graphs, contours of constant risk or overall average rates of death or injury. The applications of the technique include siting and layout studies, comparison of alternative designs, ordering priorities for remedial action and setting insurance rates. Criticisms of the method include: inaccuracy (mainly in the probabilities); incompleteness; difficulty of checking final results; inadequate criteria for evaluating the results; and complexity and laboriousness of the method. Each of these criticisms is considered in the paper, and it is concluded that, while they all have some merit, the problems they represent can be overcome. Moreover, risk assessment is the only method available for dealing with the inherently probabilistic nature of the problems. Finally, priorities for future improvements in the methods are identified; these include achieving a consensus regarding the prediction of consequences and probabilities, developing labour-saving analytical techniques, and testing the final results against the actual experience of accidents.
Public authorities started to be really involved in risk management of hazardous materials some 30 years ago. Recent developments have led to fresh attention for this matter and many further developments are underway. The history of risk management and safety regulation is one of strongly variable interest, forgotten lessons and rude awakenings. The impetus exerted by accidents is short lived. Safety cases become documents to satisfy regulation rather than instruments to reduce risk. Deregulation, privatisation, and outsourcing pose new challenges to safety and risk management. Some of the unfortunate side effects have already become apparent. This invariably leads to the next disaster, which will have a striking resemblance to the previous one when abstracted from the immediate technological context. Lessons can be learned if we really want. The question remains: ‘Do we?’.
Disasters can never be completely ruled out. The Dutch national government has therefore committed itself to the concept of risk rather than the false promise of absolute safety. The objectives of this study were to evaluate current regulatory practices in the domains of industrial and flood safety in the Netherlands, and to formulate proposals for improvement. The outcomes of such an endeavor depend heavily on the chosen yardstick to distinguish between superior and inferior policy alternatives. Throughout the thesis, social improvements are defined in a way that is consistent with the approach followed in societal cost-benefit analyses. The three main topics covered by the thesis are: 1. The Dutch industrial and flood safety policies: underlying rationales, current practices, opportunities for mutual learning. 2. Methods for risk evaluation and their conformity with a utilitarian ethic: cost-benefit analysis, FN-criteria, the precautionary principle. 3. Dealing with losses: optimizing disaster preparedness, the (un)insurability of large-scale floods, the relations between insurance and system safety.
Risk Assessment: from the Top, The Chemical Engineer February Issue, p. The Institution of Chemical Engineers
  • D Slater
Slater, D. (2012) Risk Assessment: from the Top, The Chemical Engineer February Issue, p. The Institution of Chemical Engineers, London