### Model Risk Probability and Impact and Assess its Effect using Monte Carlo Simulation Microsoft Office 365 Stock Photo

Pirisk is an educational simulator that helps analyse risk by modelling the probability and impact of potential risks and estimating their effects through Monte Carlo Simulation. The tool is designed to support a lecture on Quantitative Risk Analysis.

#### Key Ideas

The sim focuses on a Key Performance Indicator (KPI) that risks (such as the delivery time of a project) can influence. The default value assigned to this factor is referred to as the baseline (365 days, for example).

Risks (adverse weather-induced delays, for example) can induce deviations from the baseline . They are usually characterised by two factors: (1) impact, i.e., the severity of the consequences that could potentially arise, and (2) the probability that this impact will occur.

In Pirisk, the impact can be set as uncertain and characterised by a distribution, typically a triangular or log-normal distribution.

#### Main Assumptions and Calculation Steps

Pirisk assumes that all risks (and stochastic variables) are independent of each other and that their impacts are additive :

`b`: baseline; `d`: deviation from the baseline; `k`: risk index (1 to n); `n`: number of risks; `pk`: probability associated with risk #`k`; `ik`: impact associated with risk #`k`.

The tool leverages the Latin Hypercube Sampling (LHS)  functionality of the (ROOT-based) URANIE Platform  to create 10,000 (ten thousand) combinations of input variables (risks’ probabilities and impacts) and determine the variability, range, and distribution of the KPI at risk.

The model supporting the calculations being linear, Pearson Correlation Coefficients are used as a basis for identifying risks affecting most project outcomes. Risk ranking is key to effective risk prioritisation and mitigation.

#### Monte-Carlo Simulation Results

The Monte-Carlo Simulation can be launched through the   Simulate   button of the app toolbar. The calculations require an API Key that can be obtained by creating an account on Bora, as explained here.

Simulation outputs are available for visualisation and download in the results panel, which is automatically shown at the end of the calculations.

##### Possible Deviations from the Baseline

The first tab of the results panel illustrates possible deviations from the baseline and the associated probabilities in the form of a Probability Distribution and a Cumulative Probability Distribution.

The tab also provides an interactive Percentile Calculator.

##### Risk Impact and Ranking

The second tab of the panel lists different risks and their attributes, including their probability distributions and their impacts, as measured by Pearson correlation coefficients.

Based on these coefficients, the top three risks are marked , , and .

##### Export of Simulation Results

The third and last tab makes it possible to download simulation results as a CSV file (with raw data) and a PDF report.

#### Notes and References

 Dale Shermon on Uncertainty and Risk (2017).

 In reality, when multiple risks occur simultaneously, or one after another, impacts tend to compound — not simply add to each other —.

 Helton, Jon C., and Freddie Joe Davis. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering and System Safety 81.1 (2003): 23-69.

 Blanchard, Jean-Baptiste, et al. The Uranie platform: an open-source software for optimisation, meta-modelling and uncertainty analysis. EPJ Nuclear Sci. Technol. 5, 4 (2019).

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