Uncertainty aleatory

Aleatory uncertainty —the roll of the die—describes risks that cannot practicably be predicted within the research process, for example, new failure modes, or modes that can only be detected in late stages of work, for example, humans. An example of aleatory uncertainty is the withdrawal in the UK of Bextra on the basis of two serious adverse events out of 40,000 patients this could only be discovered after launch [2]. This, without hindsight, was an uncontrollable risk. ... 

Spending effort on research to attempt to reduce what is really aleatory uncertainty is a waste of time. Accepting some unmanageable risks is simply part of the price of entry to the pharmaceutical industry. Once the limits of possible knowledge are accepted, research people can concentrate on discovering what is genuinely knowable. 

Apostolakis (1994, 1999) Aleatory uncertainty Epistemic uncertainty Uncertainty... 

Aleatory uncertainty The kind of uncertainty resulting from randomness or unpredictability due to stochasticity. Aleatory uncertainty is also known as variability, stochastic uncertainty. Type I or Type A uncertainty, irreducible uncertainty, conflict, and objective uncertainty. 

Uncertainties can be categorized as either aleatory or epistemic uncertainties (Apostolakis, 1993). Aleatory uncertainty reflects our inability to predict random observable events. Epistemic uncertainty represents our confidence in the model and the numerical values of its parameters. This type ofuncertainty is also called state-of-knowledge uncertainty or just uncertainty (Zio and Apostolakis, 1996). 

The aleatory uncertainty is that addressed when the events or phenomena being modeled are characterized as occurring in a "random" or "stochastic" manner, and probabUistic models are adopted to describe their occurrences. It is this aspect of uncertainty that gives PRA the probabihstic part of its name. Therefore, the aleatory uncertainty is built into the structure of the PRA model itself... 

Uncertainty that arises because of natural, unpredictable variations associated with the system or the environmental - aleatory uncertainty. This type of uncertainty is outside the control of the decision maker, e.g. the 100 years big storm, variations in the material fatigue in specific system components, etc. 

Simple Monte Carlo simulations was performed to illustrate the stochastic uncertainty in z(t). Only one variable, the temperature, was investigated. The temperatures were drawn fi"om a PERT distribution, with (minimum mean maximum) values assumed known hence the aleatory uncertainty was investigated. One may also expect that the mean value is not known, or that uncertainty in earlier measured data would affect the expected values, but this was not investigated at this time. Simulations were performed for temperatures between 20 and 120°C as this could be reahstic temperatures for a real process. Four temperature ranges were investigated, ah with a temperature range of 30°C (20 35 50), (50 65 80), (70 85 100), (60 69 90 and (90 105 120)°C. 

In other contexts we encounter the distinction between aleatory uncertainty (due to the stochastic nature of a process or system) and epistemic imcer-tainty (due to our lack of knowledge) - see e.g. (Stamatelatos et al. 2002). This distinction can be useful to recognize the fact that even with perfect information available, there will still be imcertainty related to our decisions - i.e. that the decision making process will not converge into a deterministic analysis no matter the extent of our knowledge. 

In engineering risk analysis a distinction is commonly made between aleatory (stochastic) and epistemic (knowledge) imcertainty see e.g. Apostolakis (1990) and Helton Burmaster (1996). Aleatory imcertainty refers to variation in populations epistemic uncertainty refers to lack of knowledge about phenomena, and usually translates into uncertainty about the parameters of the model used to describe the variation. Whereas epistemic uncertainty can be reduced, aleatory uncertainty cannot and for this reason it is sometimes called irreducible uncertainty. 

In the so-called probability of frequency approach (Kaplan Garrick 1981, Aven 2003), relative frequency-based probabilities are used to describe aleatory uncertainty and subjective probabilities to describe epistemic uncertainty. The probability of frequency approach differs fundamentally in philosophy but not much in practice fiwm a standard Bayesian approach (Aven 2003). In the Bayesian approach all uncertainty is epistemic, and probability is always considered an expression of belief it is not a property of the world in the way that a relative frequency-based probability is. The notion of aleatory uncertainty, sometimes just referred to as variation in the Bayesian approach (Aven 2003), is captured by the concept of chmce, defined as the limit of a relative frequency in an exchangeable, infinite Bernoulli series (Lind-ley 2006). A chance distribution is then the limit of... 

Irrespective of the taxonomy used, epistemic and aleatory uncertainty, or uncertainty and variation, alternatives to probability have been suggested for the representation of the epistemic concept. These include interval or imprecise probabihty (Coolen 2004, Coolen Utkin 2007, Utkin Coolen 2007, Weichselberger 2000), fuzzy set theory and the associated theory of possibility (Zadeh 1965, Zadeh 1978, Unwin 1986), and the theory of behef functions (Shafer 1976), also known as evidence theory or the Dempster-Shafer theory of evidence. 

Aleatory uncertainty refers to uncertainty caused by probabilistic variations in a random event. 

Like with continuous aleatory uncertainties, the influence of epistemic uncertainties is considered by Monte Carlo (MC) simulation (see chapter 2). The approach applied to account for both types of uncertainties is a double loop nested MC simulation Sets of values of the parameters subjected to epistemic uncertainty (epistemic variables) are sampled in the outer loop. For each of these sets, different sets of values for the continuous aleatory variables are sampled and contribute to the generation of different Dynamic Event Trees... 

Besides the timings of human actions, the individual performances of all systems and components designated to be applied for fire detection, alarm, confinement and suppression were considered as subjected to aleatory uncertainty. Epistemic uncertainties were taken into account as well. Those ones which were considered as potentially important refer to parameters of the FDS code and failure criteria specified for cable targets. 

The model has been coded in MATLAB and is implemented as a two-loop Monte Carlo simulation (Bier Lin, 2013 Wu Tsang, 2004). The outer loop determines realizations of the epistemically uncertain parameters, whereas the inner loop is a nested loop that performs iterations given the parameters determined in the outer-loop. This code configuration allows us to distinguish between the epistemic and aleatory uncertainty variation within the inner loop is linked to aleatory uncertainty whereas variation across the outer loop is a representation of epistemic uncertainty. 

We found that it was very important to carefully explain the difference between state-of-knowledge uncertainty and the aleatory uncertainties associated to lifetimes of the subassemblies our experience was that after some initial confusion the experts quickly understood. It was the explanations of epistemic uncertainties as arising through triggers that helped to create this understanding. 

As well as populating our availability model using the elicited expert judgment from our panel, we also used sources such as Reliawind (REF) to provide generic data for this example. We make additional assumptions about the timing of major interventions to address the realization of weaknesses that trigger a drop in reliability to illustrate their effect on availability estimates and their uncertainties. We have run the Matlab model as a simulation with 50 outer-loop (i.e. epistemic uncertainties) and 50 inner-loop iterations (i.e. aleatory uncertainties). 

Figure 7. Estimated weekly farm availability-informed capability with 95% combined epistemic and aleatory uncertainties from simulation model of example scenario.

For each time instant, the specific solutions of the DSTE approach give the bounds of the probabilities of finding the SSC in the 4 degradation states, and the associated uncertainties, described in terms of Belief and Plausibility functions. These encompass both epistemic and aleatory uncertainties and, roughly speaking, can be regarded as the lower and upper bounds, respectively, of all the possible CDFs encoded by the imprecise estimations provided by the experts on the model parameters. 

Note that the inputs in Platypus are distributions into the non-parametric BBN s and that the results are distributions from those BBN s. That is why the standard deviation that represents aleatory uncertainty is reported along with the central estimate. 

Firstly, the use of a BBN as an advanced method for risk calculations yields new possibilities for risk analysis. Platypus generates risk analyses that yield risk distributions rather than point estimations. These risk distributions automatically address aleatory uncertainties in risk analysis (whose origin lies in randomness) and identifies instances of high risk that are overlooked in setting risk standards. The distribution will also yield new leading risk indicators and new methods and instruments for risk management. When estimates of epistemic uncertainty ranges are available, these can be incorporated in the overall distributions as well. 

Two types of uncertainties are generally distinguished in PSA analysis, namely epistemic and aleatory uncertainty. Epistemic uncertainty evaluation is assessed during the review of the model and is suitably substantiated in the development and commenting of ETs/FTs. The main assumption of the model are reviewed in the PSA documentation... 

Aleatory uncertainties due to inherent variability of the observed parameter affected by properties of rod winding and service conditions,... 

Methods of mathematical statistics provide efficient tools for the analysis of monitoring data concerning energetic devices. Important steps of the analysis include selection of a suitable regression model and estimation of probability of exceeding a limiting value. Aleatory uncertainties due to randomness and trend of the observed parameter as well as epis-temic uncertainties due to lack of data and imprecision of a test method should be taken into account. 

Segregation of uncertain parameters into two groups (epistemic and aleatory uncertainties) has given ... 

Treatment of the aleatory uncertainties within a probabilistic framework (i.e. Monte Carlo simulation) and treatment of the epistemic uncertainty within an extra-probabilistic framework (i.e. DSTE). 

In the safety analysis of complex systems, the treatment of uncertainty must distinguish the aleatory uncertainties, which represent the intrinsic randomness of the phenomena, from the epistemic uncertainties resulting from a lack of knowledge. This separation has to be done through a two-level uncertainty propagation the internal level concerning the aleatory variables and the external level the epistemic variables. For the propagation of epistemic uncertainties, it appears more appropriate to use extra-probabilistic approaches such as interval analysis or Dempter-Shafer Theory of Evidence (DSTE). 

A key notion here is the recognition that there is uncertainty involved in the assessment of system dependability it is (almost) never possible to claim with certainty that a dependability claim is true. In the jargon this kind of uncertainty is called epistemic (Littlewood and Wright 2007). It concerns uncertainty in an expert s beliefs-about-the-world . It contrasts with the more common aleatory uncertainty, which deals with uncertainty-in-the-world e g. uncertainly about when a software-based system will fail next. It is now widely accepted - even for soft-ware-based systems - that the latter is best measured using probabilities, such as probability of failme on demand. 

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