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Download a pdf copy of this help file here |
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Download a pdf copy of this help file here |
See also: ModelRisk functions and windows, Vose Risk Event window
VoseRiskEvent(Probability,
Impact distribution,U)
A risk event is a random event that may occur with some probability p and
has an impact with some distribution in the event that it does occur (its
conditional impact).
Probability - the probability of the event occuring. Should be on [0,1]
Impact distribution - should be a distribution object.
The VoseRiskEvent functions combine
the probability and conditional impact elements into one distribution.
For example:
=VoseRiskEvent(p,
VosePERTObject(Min, Mode, Max))
will simulate the impact of a risk event where p is the probability of occurrence and the PERT distribution reflects the size of the impact should it occur.
Imagine that the event has a probability p of occurrence, and its conditional impact follows a PERT distribution with known minimum, mode and maximum values. The impact of the risk can be modelled as:
=VoseBinomial(1, p) * VosePERT(Min, Mode, Max)
Or
=VoseBernoulli( p) * VosePERT(Min, Mode, Max)
The Binomial (or Bernoulli) distribution produces a 1 with probability p, and a zero otherwise, so with probability (1-p) the formulae will return a value of zero and with probability p will return a value drawn randomly from the PERT distribution.
The problem with this method of simulating the impact of a risk occurs when one performs a sensitivity analysis because the simulated impact is a combination of two random variables. A sensitivity analysis will look at sensitivity to each variable in turn (the Bernoulli and the PERT, in this case). That means that the statistical analysis of generated values will not exclude values from the PERT when the Bernoulli is generating a zero (when the PERT value has no influence on the model output), and it spreads the influence of the risk between two distributions.
The following example model provides an illustration:
The same cost model is performed twice: the first uses a Bernoulli formula, the second uses a RiskEvent formula. Using the simple rank correlation Tornado plot of sensitivity, we get the following results for the two approaches to the model:
On the left (correct) pane each risk event only appears once. On the right (incorrect) pane a risk event appears once or, more usually, twice (once if the software sees only a significant level of correlation of the output to the Bernoulli or PERT, twice if both have significant correlation).
The RiskEventObject function is also very useful in summing the impact of many risk events by using it as an argument in the VoseAggregateMC function.
VoseRiskEvent generates values from this distribution or calculates a percentile.
VoseRiskEventObject constructs a distribution object for this distribution.
VoseRiskEventProb returns the probability density or cumulative distribution function for this distribution.
VoseRiskEventProb10 returns the log10 of the probability density or cumulative distribution function.