Monte Carlo risk analysis modeling

Vose, D. (1997). Monte Carlo risk analysis modeling. In Fundamentals of Risk Analysis and Risk Management, Molak, V., ed., Lewis Publishers, New York. 

In Section 20.2, equations for tlie reliability of series and parallel systems are established. Various reliability relations are developed in Section 20.3. Sections 20.4 and 20.5 introduce several probability distribution models lliat are extensively used in reliability calculations in hazard and risk analysis. Section 20.6 deals witli tlie Monte Carlo teclinique of mimicking observations on a random variable. Sections 20.7 and 20.8 are devoted to fault tree and event tree analyses, respectively. 

Cronin WJ, Oswald EJ, Shelley ML, et al. 1995. A trichloroethylene risk assessment using a Monte Carlo analysis of parameter uncertainty in conjunction with physiologically-based pharmacokinetic modeling. Risk Anal 15 555-565. 

Monte Carlo—A statistical technique commonly used to quantitatively characterize the uncertainty and variability in estimates of exposure or risk. The analysis uses statistical sampling techniques to obtain a probabilistic approximation to the solution of a mathematical equation or model. 

Monte Carlo simulation An iterative resampling technique frequently used in uncertainty analysis in risk assessments to estimate the distribution of a model s output parameter. 

Due to the uncertainty involved in the evaluation of new products, financial analysis tools that consider risks and opportunities are more appropriate and valuable than deterministic approaches. These new approaches to project financial evaluation that consider imcertainty include options analysis and Monte Carlo simulation. Due to their proactive handling of uncertainty, these tools can more accurately calculate the risks and opportunities of a new product concept. With the use of a financial analysis model, basic tradeoff statements can be developed by the project manager to assist in understanding the importance of each objective. In the pain management product example, a statement emphasizing the value of time would be a week delay in the project costs 1 million in today s money. ... 

An added benefit of Monte Carlo analysis is that a common by-product of this computerized examination is a sensitivity analysis that shows how much each predictor variable contributed to the uncertainty or variability of the predictions. This, in turn, tells both the risk assessor and risk manager which portion of the variability is from natural fluctuation versus how much is caused by lack of knowledge. Given this information, decisions can be made as to where the most cost-effective allocation of resources may occur to refine the estimate of exposure and risk. In the example, the sensitivity analysis shown in Figure 4 presents the apportionment of variance for the model. 

These simulation models use probabilistic approaches, but are much more complex than the simply Monte Carlo models described above that have been used in exposure assessments. Monte Carlo analysis has been applied to simple spreadsheet calculations of dose using add-in software programs such as Risk or Crystal Ball. These analyses seek to understand the uncertainty and variation in the predictions of these simple dose models. In contrast, these new models are stand-alone computer... 

Vose D (1996) Quantitative Risk Analysis A Guide to Monte Carlo Simulation Modeling. New York Wiley. 

Monte Carlo analysis is a specific probabilistic assessment method that can be used to characterize health risks and their likelihood of occurrence based on a wide range of parameters (Shade and Jayjock 1997). The U.S. EPA s Stochastic Human Exposure and Dose Simulation (SHEDS) model allows for the quantification of exposures based on a probabilistic assessment of multiple exposure pathways and multiple routes of exposure (Mokhtari et al. 2006 US EPA 2003b). Additional applications of probabilistic techniques wiU be discussed in the section below on conducting an uncertainty analysis of reconstructed exposure values. 

To do so, we first provide in Section 2 a brief overview of Markov Chains and Monte-Carlo simulations. Section 3 presents the structure of our Markov model of failures and replacement as well as its imder-lying assumptions. In Section 4, we run Monte-Carlo simulations of the model and generate probability distributions for the lifecycle cost and utility of the two considered architectures that serve as a basis for our comparative analysis. Important trends and invariants are identified and discussed. For example, changes in average lifecycle cost and utility resulting from fractionation are observed, as well as reductions in cost risk. We conclude this work in Section 5. 

Performing estimation and risk analysis in the presence of uncertainty requires a method that reproduces the random nature of certain events (such as failures in the context of reliability theory). A Monte-Carlo simulation addresses this issue by running a model many times and picking values from a predefined probability distribution at each run (Mun 2006). This process allows the generation of output distributions for the variables of interest, from which several statistical measures (such as mean, variance, skewness) can be computed and analyzed. 

Mun, J., 2006. Modeling Risk Applying Monte Carlo Simulation, Real Options Analysis, Forecasting and Optimization Techniques. Hoboken, NJ Wiley. 

Vose, D. 2000. Quantitative risk analysis a guide to Monte Carlo simulation modelling. 2nd edition. Chichester John Wiley and Sons. 

The stochastic analysis framework, that has shown its value in financial mathematics (e.g. Glasserman, 2004), is exploited by the TOPAZ methodology to develop Monte Carlo simulation models and appropriate speed-up factors by risk decomposition. The power of these stochastic analysis tools lies in their capability to model and analyse in a proper way the arbitrary stochastic event sequences (including dependent events) and the conditional probabilities of such event sequences in stochastic dynamic processes (Blom et al., 2(X)3c Krystul Blom, 2004). By using these tools from stochastic analysis, a Monte Carlo simulation based risk assessment can mathematically be decomposed into a well-defined sequence of conditional Monte Carlo simulations together with a subsequent composition of the total risk out of these conditional simulation results. The latter composition typically consists of a tree with conditional probabilities to be assessed at the leaves, and nodes which either add or multiply the probabilities coming from the subbranches of that node. Within TOPAZ such a tree is referred to as a collision risk tree (Blom et al., 2001, 2003). 

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