**2. Basics of risk assessment**

There are many concepts of risk used in different scientific, technological, or organization areas. In a general sense, risk can be defined as the potential of loss (e.g., material, human, or environment) resulting from exposure to a hazard (e.g., fire, explosion, or earthquake). Sometimes, risk is measured through the assessment of the probability of occurrence of an undesired event and the magnitude of consequences [2]. In this way, risk assessment encompasses the answers to the following questions [3]:


Therefore, risk, *Ri*, for a scenario *Si*, can be quantitatively expressed as function of these three variables, as given by Eq. (1):

$$R\_i = f(\mathbb{S}\_i, F\_i, \mathbb{C}\_i). \tag{1}$$

the sequences of events following these IEs. The latter are the critical events that initiate an accident, such as pipe rupture, overpressures, or explosion. The sequences of events are the combinations of success or failure of the barriers or controls requested by IEs (defense-in-depth layers), for example, emergency shutdown systems, human actions, or physical protection. Each sequence can lead to a desired or undesired outcome (end state) such as uncontrollable release of toxic

*Framework for probabilistic risk assessment under uncertainty (based on Refs. [5, 6]).*

Fault trees (FTs) and event trees (ETs) are often used in PRAs for quantifying the likelihood of event sequences. FTs quantify frequencies or probabilities of top events (such as IEs or failure of defense-in-depth layers) through causal relationship of basic events (e.g., system components, human actions, or subsystems). ETs identify and evaluate each sequence frequency using data generated by FTs [5]. The consequence assessment of each accident scenario to people, property, or environment depends on many factors, such as magnitude of the event, number of people exposed to harm, atmospheric conditions, mitigating measures, etc. The consequence modeling involves the use of analytical or empirical physical or phenomenological models, such as plume dispersion, blast impact (TNT equivalent), or

Risk analysis is the combination and integration of the probabilities (or frequencies) and the consequences for identified hazards, taking into account the effectiveness of any existing controls and barriers. It provides an input to risk evaluation and decisions about risk treatment and risk management strategies [6]. There are many uncertainties associated with the analysis of risk related to both probability and consequence assessments. An assessment of uncertainties is necessary to perform risk evaluation and to take decisions. The major categories of uncertainties are associated with data, methods, and models used to identify and analyze risks. Uncertainty assessment involves the determination of the variation or

imprecision in the results, based on uncertainties of basic parameters and assumptions used in the analyses. Uncertainty propagation of failure probability distributions in FTs and ETs, as well as variability analysis of physical processes (named stochastic uncertainty) and the uncertainties in knowledge of these processes (named epistemic uncertainty), have to be properly accounted for in

Risk evaluation involves comparing estimated levels of risk with risk criteria defined, once the context of analysis has been established. Uncertainty assessment is important to adjust the categorization of the risk ranking, supporting the

gases, radiation exposure, or facility shutdown [6].

*Treatment of Uncertainties in Probabilistic Risk Assessment*

*DOI: http://dx.doi.org/10.5772/intechopen.83541*

Monte Carlo simulation [7, 8].

**Figure 1.**

PRA results [9].

**127**

According to Christensen et al. [4], hazard is an inherent property of a risk source potentially causing consequences or effects. This hazard concept does not include the probability of adverse outcome, which is the core difference from risk term. In this chapter, hazard is then considered as the properties of agents or situations capable of having adverse effects on facilities, human health, or environment, such as dangerous substance, sources of energy, or natural phenomena.

#### **2.1 Probabilistic risk assessment (PRA)**

PRA provides an efficient way for quantifying the risks, even in an environment of uncertainties regarding possible scenarios, data, or modeling. Risk assessment is part of risk management carried out before deciding about risk treatment and prioritizing actions to reduce risks (risk-based decision-making). **Figure 1** shows a framework for PRA under uncertainty environment [5, 6].

PRA starts with the hazard identification and scenario development, proceeds through quantification of frequencies and consequences, and ends with risk analysis and evaluation [5].

The first step of a PRA process consists of finding, recognizing, and recording risk sources (hazard identification). The accident scenario development (sequence or chain of undesired events) consists of identifying the initiating events (IEs) and *Treatment of Uncertainties in Probabilistic Risk Assessment DOI: http://dx.doi.org/10.5772/intechopen.83541*

inaccuracies in the parameters used as inputs to PRA (e.g., component reliabilities,

A framework to use the method of moments for determining the likelihoods of different outcomes from event trees in an uncertain data environment using fault trees is described in this work. Illustrative examples using this approach for propagating uncertainty in basic events of fault trees, following log-normal distributions, are also presented. The probability distributions of top events are compared with analyses available in the literature using different approaches, such as Monte Carlo

There are many concepts of risk used in different scientific, technological, or organization areas. In a general sense, risk can be defined as the potential of loss (e.g., material, human, or environment) resulting from exposure to a hazard (e.g., fire, explosion, or earthquake). Sometimes, risk is measured through the assessment of the probability of occurrence of an undesired event and the magnitude of consequences [2]. In this way, risk assessment encompasses the answers to the following

• What can go wrong that may lead to an outcome of hazard exposure

• How likely is this to happen, and if so, what is its frequency (*Fi*)?

Therefore, risk, *Ri*, for a scenario *Si*, can be quantitatively expressed as function

According to Christensen et al. [4], hazard is an inherent property of a risk source potentially causing consequences or effects. This hazard concept does not include the probability of adverse outcome, which is the core difference from risk term. In this chapter, hazard is then considered as the properties of agents or situations capable of having adverse effects on facilities, human health, or environment, such as dangerous substance, sources of energy, or natural phenomena.

PRA provides an efficient way for quantifying the risks, even in an environment of uncertainties regarding possible scenarios, data, or modeling. Risk assessment is part of risk management carried out before deciding about risk treatment and prioritizing actions to reduce risks (risk-based decision-making). **Figure 1** shows a

PRA starts with the hazard identification and scenario development, proceeds through quantification of frequencies and consequences, and ends with risk analysis

The first step of a PRA process consists of finding, recognizing, and recording risk sources (hazard identification). The accident scenario development (sequence or chain of undesired events) consists of identifying the initiating events (IEs) and

*Ri* ¼ *f Si; Fi* ð Þ *;Ci :* (1)

• If it happens, what are the likely consequences (*Ci*)?

framework for PRA under uncertainty environment [5, 6].

of these three variables, as given by Eq. (1):

**2.1 Probabilistic risk assessment (PRA)**

and evaluation [5].

**126**

failure probabilities, and human error rates).

*Reliability and Maintenance - An Overview of Cases*

**2. Basics of risk assessment**

questions [3]:

(scenario *Si*)?

simulation and Wilks and Fenton-Wilkinson methods.

**Figure 1.** *Framework for probabilistic risk assessment under uncertainty (based on Refs. [5, 6]).*

the sequences of events following these IEs. The latter are the critical events that initiate an accident, such as pipe rupture, overpressures, or explosion. The sequences of events are the combinations of success or failure of the barriers or controls requested by IEs (defense-in-depth layers), for example, emergency shutdown systems, human actions, or physical protection. Each sequence can lead to a desired or undesired outcome (end state) such as uncontrollable release of toxic gases, radiation exposure, or facility shutdown [6].

Fault trees (FTs) and event trees (ETs) are often used in PRAs for quantifying the likelihood of event sequences. FTs quantify frequencies or probabilities of top events (such as IEs or failure of defense-in-depth layers) through causal relationship of basic events (e.g., system components, human actions, or subsystems). ETs identify and evaluate each sequence frequency using data generated by FTs [5].

The consequence assessment of each accident scenario to people, property, or environment depends on many factors, such as magnitude of the event, number of people exposed to harm, atmospheric conditions, mitigating measures, etc. The consequence modeling involves the use of analytical or empirical physical or phenomenological models, such as plume dispersion, blast impact (TNT equivalent), or Monte Carlo simulation [7, 8].

Risk analysis is the combination and integration of the probabilities (or frequencies) and the consequences for identified hazards, taking into account the effectiveness of any existing controls and barriers. It provides an input to risk evaluation and decisions about risk treatment and risk management strategies [6].

There are many uncertainties associated with the analysis of risk related to both probability and consequence assessments. An assessment of uncertainties is necessary to perform risk evaluation and to take decisions. The major categories of uncertainties are associated with data, methods, and models used to identify and analyze risks. Uncertainty assessment involves the determination of the variation or imprecision in the results, based on uncertainties of basic parameters and assumptions used in the analyses. Uncertainty propagation of failure probability distributions in FTs and ETs, as well as variability analysis of physical processes (named stochastic uncertainty) and the uncertainties in knowledge of these processes (named epistemic uncertainty), have to be properly accounted for in PRA results [9].

Risk evaluation involves comparing estimated levels of risk with risk criteria defined, once the context of analysis has been established. Uncertainty assessment is important to adjust the categorization of the risk ranking, supporting the

decision-makers in meeting risk criteria of standards and guidelines, as well as in visualizing and communicating risks [10].
