Supplementary Materials
Engineering Risk Assessment for Emergency Disposal Projects of Sudden Water Pollution
Incidents by Bin Shi, Jiping Jiang*, Rentao Liu , Afed Ullah Khan, Peng Wang *
Contact at: [email protected]
1. The general process of emergency disposal engineering risk analysis
Risk is an event that, if it occurs, adversely affects the ability of an engineering system project to
achieve its outcome objectives. A risk event has two aspects. The first is its occurrence probability. The
second is its impact (or consequence) to an engineering system project, which must be nonzero. A general
expression for measuring risk is given by:
Risk = f (Probability, Consequence)
(s1)
An event is uncertain if there is indefiniteness about its outcome. There is a distinction between the
definition of risk and the definition of uncertainty. Risk is the chance of loss or injury. In a situation that
includes favorable and unfavorable events, risk is the probability an unfavorable event occurs.
Uncertainty is the indefiniteness about the outcome of a situation. Uncertainty is sometimes classified as
aleatory or epistemic.
We analyze uncertainty for the purpose of measuring risk. In an engineering system, the analysis
might involve measuring the risk of failing to achieve performance objectives, overrunning the budgeted
cost, or delivering the system too late to meet users’ needs.
Risk events and their
relationships are defined
Probabilities and consequences
of risk events are assessed
Assess probability and consequence
1. Risk identification
2. Risk impact assessment
4. Risk mitigation
planning,
implementation, and
progress monitoring
Risk mitigation
Risk tracking
Assess risk criticality
Reassess existing risk events
and identify new risk events
Watch-listed risks
Consequences may include
cost, schedule, technical
performance impacts, as
well as capability or
functionality impacts
3. Risk prioritization analysis
Risk events assessed as medium or high
criticality might go into risk mitigation
Decision-analytic rules applied to
planning and implementation,low critical risks
rank-order identified risk events
might be tracked/monitored on a watch-list
from “most-to-least” critical
Fig. s1 steps common to a risk management process
(source: Pinto, C.A. and Garvey, P.R. Advanced risk analysis in engineering enterprise systems, CRC Press.2015.)
Step 1: risk identification, which is the critical first step of the risk management process. Its
objective is the early and continuous identification of risks to include those within and external to the
engineering system project. As mentioned earlier, these risks are events that, if they occur, have negative
impacts on the project’s ability to achieve its performance objectives.
Step 2: risk impact (consequence) assessment, an assessment is made of the impact each risk event
could have on the engineering system project. Typically, this includes how the event could impact cost,
schedule, and technical performance objectives. Impacts are not limited to these criteria. Additional
criteria such as political or economic consequences may also require consideration-discussed later in this
book. An assessment is also made of the probability that each risk event will occur. As mentioned
previously, this often involves subjective probability assessments, particularly if circumstances preclude
a direct evaluation of probability by objective methods.
Step 3: risk prioritization analysis, the overall set of identified risk events, their impact assessments,
and their occurrence probabilities are processed to derive a ranking of the most-to-least critical risks.
Decision analytic techniques such as utility theory, value function theory, and ordinal methods are
formalisms often used to derive this ranking. A major purpose for prioritizing (or ranking) risks is to
form a basis for allocating critical resources. These resources include the assignment of additional
personnel or funding (if necessary) to focus on resolving risks deemed most critical to the engineering
system project.
Step 4: risk mitigation planning and progress monitoring, which involves the development of
mitigation plans designed to manage, eliminate, or reduce risk to an acceptable level. Once a plan is
implemented, it is continually monitored to assess its efficacy with the intent to revise its courses of
action if needed. Systems engineering practices often necessitate the use of historical experience and
expert judgments. In recognition of this, the analytical methods developed herein derive from formalisms
designed for situations in which the availability of quantitative data is the exception rather than the rule.
2. The basic conception of fuzzy fault tree analysis
(a) The basic symbol in FTA
There are some basic shape symbol represent the event happened in emergency disposal engineering
system. The rectangle symbols represent the top events, which is the target point of risk analysis. The
circular symbols represent the basic events, traditionally, it is usually assumed that the basic events within
a fault tree are independent of each other and could be represented in terms of probabilistic numbers. The
house form symbols represent the normal events, which are the events happened under normal condition.
The diamond symbols represent the events those can be omitted, which are normal events but there is no
need for analysis during the process of engineering construction and running.
Top event
Basic event
External event
Undeveloped
event
Fig. s2 Symbolic representation of events in a FTA
(b) AND-gate
An AND-gate is used to model events that must occur simultaneously in order for the output event
to occur. The AND-gate corresponds to a parallel system where the probability of failure is calculated as
the product of the n independent events’ probabilities. Let Q0 (t) is the probability of the TE occurs at
time t, qi (t) is the probability of the BE Ei occurs at time t.
Let qi (t)  P(Ei (t)
for i  1, 2...n
TE probability Q0 (t) is
Q0 (t)= P(E1 (t)  E 2 (t)  ...  E n (t))
n
 P(E1 (t)) P(E 2 (t))... P(E n (t))  q1 (t) q 2 (t)...q n (t)   q i (t)
(s2)
i 1
“AND” gate
“OR” gate
A
A
·
+
B1
...
B2
...
B1
B2
Fig.s3 Symbolic representation of “AND” and “OR” gates in a FTA
(c) OR-gate
Let qi (t)  P(Ei (t)
for i  1, 2...n
TE probability Q0 (t) is
Q0 (t)= P(E1 (t)  E 2 (t)  ...  E n (t))  P(E1 (t)) P(E 2 (t))... P(E n (t))
n
 q1 (t)+ q 2 (t)+...+ q n (t)-q1 (t) q 2 (t)...q n (t)  1- (1  q i (t))
i 1
(s3)