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GENERATING UPLOADING AND MONITORING PROJECT RISK
PROFILES
Y. Cohen1 and B. Keren2
1
Department of Industrial Engineering, The Open University of Israel
118 Ravutzki, P.O.Box 808, Raanana 43107
2
Department of Industrial Engineering, Sami Shmoon College of Engineering,
Beer-Sheva 84100
ABSTRACT
This paper presents a new technique for modeling and monitoring risks in projects. The generated
risk profile could be a major contributor to risk analysis, risk leveling and risk mitigation in project
planning and scheduling. The proposed methodology illustrates how a project risk profile could be
constructed utilizing a dynamic Poisson compound process for the project risks. The proposed risk
profiles visually illustrate the vulnerabilities of the project, identifying the problematic issues and
periods. The difficulties in constructing and maintaining the risk profiles will be discussed and
ways to overcome these difficulties.
1. INTRODUCTION
Project risk management is one of nine major project management knowledge areas
defined by the Project Management Institute (PMI) [1]. Significant part of this knowledge is
documented in the Project Management Body of Knowledge (PMBOK). Most of the project
management literature contains trials to quantify the probability and the damage of risks [2].
Typically time dimension in risk-management is related to delays [3].
It is customary to map risks into four general categories [4]: (1) High probability and high
damage risks (2) High probability and small damage risks, (3) Low probability and high
damage risks, and (4) Low probability low damage risks. In general, corporations try to avoid
or eliminate the risks in the first category (the most probable and expansive), they try to
mitigating the chances and effects of the second category, they try to insure large parts of the
third category, and the risks in the fourth group are tolerable so in many cases they are simply
Cohen & Keren
assumed. Kendrick [5] differentiates between schedule risks, resources risks, and activity
risks.
This paper assumes that risks with high probabilities are being managed perfectly and
concentrate on the low probability risks with chances of less than 10% of occurrence. Many
risks may fall in this category during a project's lifetime. Some examples are: fires, storms,
traffic accidents, job hazards, strikes, blackout, litigation, etc. In this paper we develop the
time dimension of the risks as risk profiles. The basic assumption in this paper is that different
risky events (such as a traffic accident, a blackout, and jump in the prices of raw materials)
are independent of each other. The independence between different risky events provide
sound theoretical basis for the proposed model. Overall the model seeks to represent profile of
risks along the project and to enable managing risks .
The major idea in this paper is to represent risk profile on a time line and spot the most
risky time-intervals. Obviously the risks and their intensity are strongly related to various
activities. This means that project scheduling is a pre-requisite to risk profiling. Once each
activity start time is determined the risk profile can be constructed.
Unlike resource leveling, risk leveling can be done in several ways, and re-scheduling is
only one of them. Mitigating risks could be done by reducing the probability for risk
realization, reducing its damage, insuring, and sharing the risks with partners, investors, or
banks. The treatment of each risky interval must consider the specific activities that are being
carried out in the specific interval. Since the situation is very unique for each individual
interval, this paper does not deal with mitigating risks, and is focused only on the part of
generating the risk profile .
Any process that generates independent events along the timeline must generate
independent intervals between any two adjacent events. This means that a realization of a risk
does not change its probability to occur in the future. In other words the distribution of
intervals between any two sequential events is memory-less, and the only memory-less
distribution type that exists is the exponential distribution [6]. Any arrival process with
exponentially distributed intervals has a Poisson distributed arrival rate [7]. Therefore, we can
conclude that if the occurrences of risks of certain type are independent of each other, they
form a Poisson process [7].It is customary to express the expected rate value of a Poison
process as lambda (). The sum of several Poisson arrivals is a Poisson process with expected
value being the sum of the expected rates:
Cohen & Keren
If: yi  Poisson(i )
n
y
Then:
i
i 1
.1
n
 Poisson(   i )
i 1
In case that the process intensity changes over time, the process is defined as a nonhomogeneous Poisson process having expected value as a function of time - (t) [8]. The
Poisson distribution only deals with the frequency of occurrence. For each risk type the
damage has a certain probability distribution. So the overall damage of a specific type of risk
is a compound non-homogeneous Poisson process [9]. For a monetary value of damage x,
having expected value E(x) - the expected value of the compound Poisson process is (t)E(x).
So it is not so surprising that the sum of a compound Poisson processes is also a compound
Poisson process: While (t) is just the sum of the individual i(t), E(x) is a weighted average
of the E(x)i:
n
E[ x] 
  E[ x ]
i
i 1
i
n

i 1
n
and
 (t )   i (t )
.2
i 1
i
2. GENERATING THE PROFILE FOR A SINGLE RISK TYPE
In this section we shell construct a risk profile for falling in a construction site. This will
show the most risky time intervals for falling in a house construction project. Fall occurrences
are assumed to be independent of each other, and arrive at an average rate that is related to the
state of the building and the activities done. So what do we do? What steps do we take?
2.1 The Steps for Risk Profile Construction
Step 1: Schedule the project in any regular manner that is used in the company (determining
the start and finish time of each activity).
Step 2: Once an initial schedule exists, execute resource leveling, and move the activities so
that resource consumption never exceeds the resource availability. At the end of this stage we
must have a clear plan of exactly when each activity is done and by whom. Only after such a
plan is in place can we start dealing with risk.
Step 3: Identify the most falling prone construction stages . Suppose that the most risk prone
stages are as follows:
 After digging for foundations and before putting the foundation concrete.
 After concrete foundations were built and before covering them with supporting material.
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 Special vulnerabilities exist before laying the floor
 High risk exist while constructing the roof
Step 4: Draw the construction schedule on a time line. If needed, resource leveling may be
employed to ensure the feasibility of the time line.
Step 5: Draw a graph of the average risk rate in the project as a function of time. The
monetary risk is estimated according to the vulnerabilities at each moment. An example of
this graph is depicted in figure 1.
Risk rate:
(t)E(x)
[($)(Pr)]
Time
Start digging
foundations
Supporting
foundations
Completing
concrete work
External
Roof
paving installed
Project
completion
Figure 1. Example of risk profile of worker safety hazards as a function of time, for a house
construction project.
3. RISK PROFILE FOR SEVERAL INDEPENDENT RISK TYPES
A general rule in stochastic processes is that the sum of Poison processes is a Poisson process
and sum of compound Poisson processes is also a compound Poisson process [9]. This
powerful rule enables generating the aggregate risk profile for the project as a stacked graph
of all the considered risk profiles. This is depicted in figure 2. In figure 2 we see that several
graphs of different and independent risk sources could be summed to give the overall risk
curve. However, figure 2 also show that this could lead to very risky intervals (with very high
risk level). This gives the motivation for risk leveling.
3. CONCLUSIONS
This paper has shown that significant part of risk management could be modeled using
compound Poisson processes. The paper explained how to construct a profile for a single risk
type, and how to generate an inclusive project risk profile. It then discussed ways of risk
leveling, and showed some new insights as to the reasons for insurance.
Cohen & Keren
Risk rate: (t)E(x)
[($)(Pr)]
4
3
2
1
Time
Start digging Supporting
foundations foundations
Completing
concrete work
External
Roof
paving installed
Project
completion
Figure 2. Example of aggregate risk profile of 4 independent risk factors
4. REFERENCES
[1] PMI Standards Committee. A guide to the project management body of knowledge (forth
edition). Project Management Institute: Newtown Square, PA. 2008.
[2] Kerzner, H. Project management: a systems approach to planning, scheduling, and
controlling (10th edition). Haboken, NJ: John Wiley and Sons. 2009.
[3] Van de Vonder, S., Demeulemeester E., Leus R. and W. Herroelen, Proactive-reactive
project scheduling trade-offs and procedures .In: Josefowska J. & Weglarz J. (Eds.).
Perspectives in Modern Project Scheduling, pp. 25-51, Springer: New-York: NY. 2006.
[4] Marrison C., . The Fundamentals of Risk Measurement, McGraw-Hill. 2002.
[5] Kendrick T., Identifying and Managing Project Risk: Essential Tools for FailureProofing Your Project, Second edition, AMACOM. 2009.
[6] Ross, M. S., Introduction to Probability Models, Ninth Edition. Elsevier-Academic Press:
Burlington, MA. 2007.
[7] Ross, M. S.. Stochastic Processes, second edition. Wiley; New York, NY. 1995.
[8] Majeske, K. D., A non-homogeneous Poisson process predictive model for automobile
warranty claims. Reliability Engineering and System Safety, 92 (2), pp. 243-251. 2007.
[9] Grandell, J., Mixed Poisson Processes (Monographs on Statistics & Applied Probability),
Chapman & Hall/CRC: London/Suffolk, UK. 1997.