Time-dependent probability analysis evaluation

There exist different methods like Fault Tree Analysis (FTA), Event Tree Analysis (ETA) and Monte Carlo Simulation (MCS) that can be applied and combined for the purpose of evaluating the frequency and probability of initiating events. However, the MCS can be handled much easier in order to accoimt for bormdary conditions like stochastic dependence, time dependence and physical impact (Hauschild Meyna 2007). The MCS has been apphed successfully for PSA in order to assess the safety of nuclear power plants (Devooght Smidts 1996, Woltereck2001) and especially for taking into account uncertain input data (BfS 2005). 

The phenomenon risk obeys a necessary causation. According to the ISO 12100 standard, which is meant to explain the Machinery Directive (MD) 2006/42/EG for the practical design, the risk assessment is the combination of risk analysis and risk evaluation. Risk analysis subsumes specifying the machine s limits (e.g., spatial and temporal limit), identifying the hazards involved, and estimating the extent of damage and the probability of its incidence. The risk fH is thus defined as a two-dimensional variable (damage severity S and expected frequency EF) which due to the EF element features a time-dependence ... 

The application of the Porod equation or of the Debye-Bueche approach are particularly attractive because they offer the possibility to evaluate the interfacial area between the phases of the blend, and they are probably the only way to quantify such feature in polymer blends and composites. In fact, when the two polymers are mixed together in a blend, traditional methods based on the adsorption of small molecules, i.e. the BET approach, are inapplicable. Image analysis of TEM micrographs can in principle be an option, but it is extremely time consuming and it suffers from a number of limitations, such as dependence on sample preparation, on projection effects, and on image defocus. The validity of SAXS for the study of interpenetrating networks has been shown for several systems. ... 

The choice of the value of N is very critical in Monte Carlo analysis. As it can be seen from Eq. 14, the accuracy depends on the number of samples used. Eurther, in many engineering applications, the true probability of failure could be smaller than 10. Therefore, on average, only 1 out of 100,000 samples would correspond to failure. Thus, at least 100,000 samples are necessary to observe failiue. Eor a reliable estimate of failure probability, at least 10 times, this minimum (one million samples, in this case) is usually recommended. Sometimes, if G consists of a complex computer code (e.g., a finite element analysis), it may not be computationally feasible to evaluate G a million times. In such cases, it is necessary to resort to other alternative techniques for stmctural reliability estimation. 

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