Probable Maximum Flood PMF, overtopping, ample warning, breach of main embankment, moderate flood wave, 150-square-mile 240 sq km dation area, moderate loss of life inun-2.. PMF, piping,
Trang 1The Consequences Panel (eight people) consisted of experts in the fields of frastructure engineering, agricultural economics, dam engineering (also a member
in-of the Engineering Panel), community relations, hydrogeology, Utility corporate,ecology, and the Utility project manager
The following 16-point list shows the identified range of engineering riskevents and the nature of the resultant consequences:
1 Probable Maximum Flood (PMF), overtopping, ample warning, breach of
main embankment, moderate flood wave, 150-square-mile (240 sq km) dation area, moderate loss of life
inun-2 PMF, piping, breach of main embankment, ample warning, moderate flood
wave, 150-square-mile (240 sq km) inundation area, moderate loss of life
3 PMF, embankment instability, breach of main embankment, ample warning,
moderate flood wave, 300-square-mile (240 sq km) inundation area, ate loss of life
moder-4 Major flood, overtopping, breach of main embankment, ample warning, minor
flood wave, 300-square-mile (240 sq km) inundation area, low loss of life
5 Major flood, piping, breach of main embankment, ample warning, minor
flood wave, 300-square-mile (240 sq km) inundation area, low loss of life
6 Major flood, embankment instability, breach of main embankment, ample
warning, minor flood wave, 300-square-mile (240 sq km) inundation area,low loss of life
7 Earthquake, cracked embankment, breach of main embankment, little warning,
large flood wave, 150-square-mile (120 sq km) inundation area, high loss of life
8 Earthquake, embankment batter slip, breach of main embankment, little
warning, large flood wave, 150-square-mile (120 sq km) inundation area,high loss of life
9 Earthquake, outlet tower collapse, little warning, no flood wave, local
inun-dation, minor loss of life, long-term out of service
10 Earthquake, turbine pump station collapse, little warning, no flood wave,
local inundation, minor loss of life, long-term out of service
11 Earthquake, spillway bridge collapse, vehicle accident, minor loss of life
12 Geotechnical instability, breach of main embankment, little warning, large
flood wave, 150-square-mile (120 sq km) inundation area, high loss of life
13 Piping failure, breach of main embankment, little warning, large flood wave,
150-square-mile (120 sq km) inundation area, high loss of life
14 Guard gate mechanical or electrical failure, little warning, no flood wave,
local inundation, minor loss of life, long-term out of service
15 Turbine pump station mechanical or electrical failure, little warning, no flood
wave, local inundation, minor loss of life, short-term out of service
16 Geotechnical failure of upstream embankment, roadway collapse, vehicle
ac-cident, minor loss of life
58 / Stage 2: Identify the Risk
Trang 2The following discussion provides a full description of the first listed event(embankment overtopping during a Probable Maximum Flood event), the nature
of the subsequent releases from the dam, and the range of potential consequences
on the wider environment
The PMF is potentially the highest conceivable flood that could occur in thecatchment and has an extremely low likelihood of occurring During a PMF event,the flood spillway would not be able to pass the entire flood flow and the water inthe pond behind the embankment would overtop the embankment During over-topping, it is most likely that erosion of the embankment would occur, leading to
a major breach of the embankment A very large additional volume of water would
be suddenly released through the breach
The water released would form a moderate, 30-ft- (10 m) high flood wavewithin the confines of the valley for a distance of 8 miles (13 km) below the dam.Over the wider floodplain areas, the flood wave would then progressively de-crease in height to around 3 ft (1 m) at a distance of 50 miles (80 km) downstream.The area expected to be flooded is approximately 90 square miles (235 sq km)
It is likely that, during such a major flood event, rising water levels would beobserved and there would be ample warning that the embankment would be over-topped Despite the warning, however, it is anticipated that substantial physicaldamage and moderate loss of life would occur
The full range of potential consequences of the release is: loss of life, house andfarm property damage, livestock loss, crop losses, small business revenue losses,industry revenue losses, debris clean-up, riparian vegetation damage, fauna dam-age (from low temperature or oxygen deficient water), infrastructure damage,accessibility loss, lake amenity loss, utility revenue loss, adverse community re-action, and dam repairs
The event tree in the Water Utility example case was derived by combination
of the event trees developed by the engineering panel and the consequences panel.The example event tree considers the events that could lead to a sunny-day failureand the consequences that could occur
The combined event tree, shown in Figure 5.2, is typical of many risk ment event trees, which in effect consist of two event trees This figure demon-strates that a set of different initiating (or trigger) events can potentially havesequences of independent consequences that can all lead to a single risk event, inthis case a sunny-day failure and catastrophic release of water
assess-In the example, the engineering panel considered that two initiating events,earthquake and full storage conditions, could potentially follow five pathwaysthat all lead to a breach of the embankment and sunny-day failure The rate andvolume of water released during a sunny-day failure would be catastrophic Theconsequences panel recognized 14 major consequences and their financial impli-cations that could follow a sunny-day failure of the embankment
Figure 5.3 shows the likelihoods that the engineering panel attached to eachbranch of the engineering portion of the sunny-day failure event tree of Figure 5.2.The event tree shows that the estimated frequency of an earthquake of sufficientsize (magnitude 6 or higher) is very low, at 9 × 10-5per annum (or around 1 in
Water Utility Example / 59
Trang 3Crop losses Damages claimsCompensation and legal costs
Trang 411,000 years) Following the first branch of the event tree, the panel consideredthat if such an earthquake were to occur, then cracks would form (likelihood is 100percent) in the embankment Consequently, the relevant panel expert concludedthat there would be a 1 in 10 chance that piping would form within the crack net-work If piping were to occur, the expert assessed that there would be a 1 in 100chance that the piping would be sufficiently extensive to cause the embankment tocollapse.
Figure 5.4 shows samples of the 50 and 95 percent confidence level cost mates provided by the consequences panel and graphical representations of thecost distributions derived from the panel information The samples show cost es-timates associated with infrastructure damage and adverse community reactionthat were potential consequences of a sunny-day failure
esti-All graphical distributions were provided to the appropriate panel members forreview and to confirm the nature of the distributions
Water Utility Example / 61
Figure 5.3 Engineering component event tree showing the sequence of impacts, and their probabilities, if an initiating event occurs.
RI 5 Earthquake: Breach of Main Embankment
SUNNY-DAY FAILURE TRIGGER EVENTS
Earthquake Embankment
cracks
Piping failure
Main embankment breach
Sunny-day failure (high volume, very high rate)
Batter slip Deformation
Main embankment breach
Sunny-day failure (high volume, very high rate)
Annual Frequency Probability Probability Probability
RI 6 Geotech: Embankment Instability, Breach of Main Embankment
Storage full Residual
strength U/S stability fail
Main embankment breach
Sunny-day failure (high volume, very high rate)
Softened strength
U/S stability fail
Main embankment breach
Sunny-day failure (high volume, very high rate)
RI 7 Geotech: Piping, Breach of Main Embankment
Storage full Cracks below
FSL
Piping failure
Main embankment breach
Sunny-day failure (high volume, very high rate)
Trang 8Risk analysis using the RISQUE method involves quantification and modeling ofthe constituent probabilities and consequences for each identified risk event.The aim of risk modeling is to process the likelihood and cost information foreach risk event (derived from the panel process) Risk modeling derives a quanti-tative understanding of the characteristics and distribution of risk associated withthe situation under evaluation A number of techniques are applied to deriveranked and proportional profiles of risk quotient and to estimate the potential cost(the risk cost) that may be incurred in the future due to the occurrence of riskevents
Q UANTITATIVE M ODELING T ECHNIQUES
Spreadsheet models are the most appropriate tools for incorporating risk modelinginto the RISQUE method All risk models discussed in this book were created inMicrosoft Excel™ spreadsheets Probabilistic calculations in the analysis were per-formed using the Crystal Ball™ simulator, which is a commercial add-on softwarepackage to Microsoft Excel™ The simulation software computes spreadsheet so-lutions for at least 2,000 trials, using the Monte Carlo sampling strategy Simula-tion using Crystal Ball™ is used in the risk models to not only treat costs asprobability distributions but also to permit random distribution of events over spec-ified time intervals The @Risk™ software package is also an appropriate alterna-tive for performing the probabilistic calculations
The techniques that have been applied in the RISQUE method have been lected for their suitability to:
se-• Define risk events in financial terms, so that some provision can be made thataccounts for their likelihood of occurrence and consequences
• Account for uncertainty in the likelihood of occurrence of a risk event
• Account for uncertainty in the magnitude of the consequences of a risk event
65
Trang 9Outputs of the modeling process express the risk relationships between theevents, show the magnitude of combined risk presented by all of the events, andindicate a reasonable estimate of cost that could be incurred due to the occurrence
of risk events (risk cost)
Typical outputs of risk modeling include:
• Estimates of risk cost at three predetermined levels of confidence The ent levels are usually representative of a low (optimistic) cost, a conservativeyet realistic (planning) cost, and a high (pessimistic) cost
differ-• A risk profile that shows each risk event ranked in order of decreasing risk tient Risk profiles are essentially prioritization tools
quo-• An exposure profile, which shows the range of consequential cost for theranked risk events Exposure profiles are helpful in assessment of whether di-rect risk management action or further study of an event is more appropriate.This section describes the main aspects of the risk modeling process and key el-ements of RISQUE method models Detailed discussion of specific risk modelingtechniques is not provided here Each application of the RISQUE method requiresthat case-specific conditions and information be taken into account For this rea-son, each RISQUE method model needs to be specifically designed to integratethe unique elements of the situation under consideration with the modelingprocesses that apply to a wide range of conditions Therefore, each risk model isdifferent and cannot be constructed according to a set prescription However, arange of insights into risk model development can be gained from the case stud-ies that are presented in Part Three
M ONTE C ARLO S IMULATION
Monte Carlo simulation is a very useful tool for dealing with uncertainty MonteCarlo simulation is particularly useful in business risk assessment for incorporatinguncertainty of magnitude of consequences Many project managers have heard ofthis simulation technique but are reluctant to consider its use as a routine analyticaltool To these managers, the term “Monte Carlo simulation” conjures an image of
a sophisticated and complicated process, which they would most likely not stand and therefore would not use as a trusted decision-making tool Monte Carlosimulation is, however, not as difficult to understand or use as it might seem
under-What Is Monte Carlo Simulation and How Does It Work?
Monte Carlo simulation is a statistical technique that uses random numbers to count for uncertainty in a mathematical model Monte Carlo simulation is univer-sally available as commercial spreadsheet add-ins, such as the Microsoft Excel™add-ins Crystal Ball™ and @Risk™
ac-66 / Stage 3: Analyze the Risk
Trang 10Monte Carlo simulation recognizes variables within a calculation as ity distributions rather than single numbers For example, a network manager con-sidering the purchase of a computer (estimated price $1,600) and color printer(estimated price $1,000) for the business would expect to pay $2,600 in total Inreality, when purchasing the equipment, the budgeted cost may be more or lessthan the actual purchase price, depending on where the purchases were made.Considering the computer and printer prices as single numbers does not accountfor variation of price in the market.
probabil-In the market, the computer price could average $1,600, but the range couldvary from $1,100 to $2,100 Figure 6.1 shows a graph of the computer price in 20stores The figure is essentially a probability distribution of computer cost Thegraph shows that the distribution is uniformly bell shaped and that the most com-mon price (in four stores) is $1,600 If it is assumed that the computer will be pur-chased at any of the stores on a random basis, then there is a 4 in 20 (or 20 percent)chance that the computer will cost $1,600 The lowest price of $1,100 is availableonly in one store; therefore, there is a 1 in 20 (5 percent) chance that the price will
be $1,100 Similarly, there is a 5 percent chance that the price will be $2,100.Judging from the computer cost distribution, it can be seen that there is a 75 per-cent chance that the cost will not exceed $1,700 (the price is more than $1,700 infive out of 20 shops)
Figure 6.2 shows the cost distribution for the printer The printer cost tion is not uniformly bell shaped but is skewed heavily toward the higher end ofthe cost range This figure shows that the printer cost could vary from $500 to
distribu-$1,600, with the most common cost being $800 Considering the price in all 20stores, the average printer price is $1,000 and there is a 75 percent chance that thecost will not exceed $1,200
Taking note of the cost distributions of the computer and printer, the chancethat the network manager will pay the lowest combined price of $1,600 or thehighest combined price of $3,700 is considerably lower than the chance of payingaround the average combined price In this example, Monte Carlo simulationcalculates the combined cost of the two items not as single numbers but as costdistributions The results are expressed as a range of possible outcomes togetherwith the likelihood of each outcome
Within the modeling software, the Monte Carlo simulation is complex; ever, the overall process is simple Monte Carlo simulation essentially considers
how-Monte Carlo Simulation / 67
Figure 6.1 Computer cost distribution represented by a set of numbered balls.
4 3 2
1 11 11 12 12 13 13
14 14 14
15 15 15 15
16 16 16 16 16
17 17 17 17
18 18 18 19 19 20 20 21 21
n = 20
Σ = 320 Mdn = 16 Mean = 16
Mo = 16 Computer Cost ($ × 100)
Trang 11the cost distributions in the office computer equipment example as numbered balls
inside lottery barrels The computer barrel would therefore contain one $1,100
ball, one $1,200 ball, one $1,300 ball, two $1,400 balls, three $1,500 balls, and so
on It is therefore three times more likely that a $1,500 ball would be drawn from
the barrel than a $1,100 ball, for example In adding the two costs, the computer
randomly pulls out a ball from each barrel, calculates the combined cost, and
re-members the result The balls are replaced and the process is repeated, usually
many times Using this approach, the output of Monte Carlo simulation appears as
a frequency distribution
Table 6.1 shows Monte Carlo simulation forecast values for a small number(30) of trials In this example, for the first trial the printer price was $800 and the
computer cost was $1,700, deriving a combined cost of $2,500
Figure 6.3 shows the results of the Monte Carlo simulation in graphical form
The figure shows the frequency of each possible cost for the printer and computer
68 / Stage 3: Analyze the Risk
Figure 6.2 Printer cost distribution represented by a set of numbered balls.
4 3 2
5 6 6
7 7 7
8 8 8 8 8
9 9 9 9
10 10 10 11 11 12 12 13 13
14 14 14 16 16 15 15
n = 20
Σ = 199 Mdn = 9 Mean = 10
Mo = 8
Printer Cost ($ × 100)
Table 6.1 Office Computer Equipment Example—Forecast Values from 30 Trials
Printer Printer
Number Printer Computer Computer Number Printer Computer Computer
Trang 12It shows that several possible costs did not occur during the limited number oftrials and that the simulated range was $2,000 to $3,500, which is narrower thanthe potential range of $1,600 to $3,700 The graph also shows that the most com-mon cost derived was $2,500, which occurred in eight of the 30 trials This figurealso indicates the probability of exceeding a given cost For example, the cost in
24 (80 percent) of the trials was less than $3,200; therefore, on the basis of these
30 trials, the likelihood of exceeding a cost of $3,200 is 20 percent Thus, on thebasis of 30 trials, there is a 20 percent chance that the network manager will paymore than $3,200 for the printer and computer and negligible chance that the totalcost will exceed $3,500
Only 30 trials were performed in the preceding example While the frequencychart of Figure 6.3 provides an indication of the cost distribution (particularly cen-tral values), the forecast distribution has substantial gaps and does not includecosts from the entire range of possible outcomes The results from 30 trials clearlyshow that the distribution based on a limited number of trials is strongly affected
by random chance and is most likely not representative of the combined cost if alarger number of trials were undertaken Figure 6.4 shows the example MonteCarlo simulation frequency chart for 2,000 trials It shows a much smoother dis-tribution that also covers the entire range of possible outcomes
As a general rule, greater precision in outcome (particularly toward the tails, orends, of forecast distributions) can be obtained by performing larger numbers oftrials For example, if 100 trials are performed, then on five occasions it is expectedthat numbers would be generated that exceed the 95 percent level of confidence
Monte Carlo Simulation / 69
Figure 6.3 Monte Carlo output for computer plus printer after 30 trials showing the quency of occurrence for each number and the uneven nature of the distribution.
Trang 13limit (i.e., a probability of 5 percent of being exceeded) In this case, the five casts generated may cover a wide and uneven range of values Alternatively, if1,000 trials are performed, then it is expected that approximately 50 values wouldexceed the 95 percent level of confidence, which would provide more precise in-formation to interpret the potential cost at the high end of the range.
fore-On the basis of 2,000 trials, there is a 20 percent chance that the network ager will pay more than $2,900 for the printer and computer, and there is a 0.65percent chance that the total cost will exceed $3,500
man-In this book, 2,000 trials are usually used in the examples provided
Application of Monte Carlo Simulation to Risk Analysis
Quantification of risk involves numerical estimation of likelihoods and quences There is considerable uncertainty in estimation of potential consequencesfor most risk events As stated earlier, Monte Carlo simulation is particularly use-ful in business risk assessment for incorporating uncertainty with respect to mag-nitude of consequences
conse-Consider the potential consequences of a transport union blockade on a ical manufacturer resulting in temporary shutdown of the plant Under unionembargo circumstances, there would be direct loss of revenue (not including sub-
chem-70 / Stage 3: Analyze the Risk
Figure 6.4 Monte Carlo output for computer plus printer after 2,000 trials showing the frequency of occurrence for each number and the even nature of the distribution.
0 50 100 150 200 250