Combining mechanistic best-estimate analysis and level 1 probabilistic risk assessment

Traditionally, both deterministic and probabilistic methods have been used in the safety analysis of nuclear reactors. Both of these methods have evolved in recent years to a more sophisticated treatment of uncertainties in the anallyis. In particular, deterministic analysts have moved away from the traditional conservative methods to best-estimate techniques that attempt to account for uncertainties in all phases of the calculations. Because of this, a tighter and more formal coupling between the deterministic and probabilistic methods has become possible. This paper introduces a formal methodology for such combination, presents an illustrative example, and discusses a new technique for deriving acceptance criteria for deterministic analyses based on probabilistic considerations.     

Uncertainty in probabilistic risk assessment

Dealing with uncertainty is an important and difficult aspect of analyses for complex systems. Such systems involve many uncertainties, and assessing probabilities to represent these uncertainties is itself a complex undertaking utilizing a variety of information sources. At a very basic level, uncertainty is uncertainty, and attempting to distinguish between ‘types of uncertainty’ is questionable. At a practical level, on the other hand, a close look at such distinctions suggests that they are driven by important modelling issues related to model structuring, probability assessment, information gathering, and sensitivity analysis. Anything that brings more attention to these issues should improve the state of the art. However, I would prefer to attack the issues directly instead of working indirectly through the notion of ‘types of uncertainty.’     

A probabilistic approach to fatigue risk assessment in aerospace components

This paper describes a new possible approach to fatigue design of aerospace components founded on probabilistic bases compared with safe life and damage tolerance that are founded on deterministic bases.

A numerical tool has been introduced and explained together with the experimental activity for its validation analyses.

For a typical aerospace component, such as a lap-joint panel, an acceptable maximum risk level has been established and the maintenance program has been planned to ensure operating life without catastrophic failures.

The analysis has shown that this new approach introduces several benefits in fatigue design.     

Parametric estimation of time-dependent failure rates for probabilistic risk assessment

This article describes a method for modeling a time-dependent failure rate, based on field data from similar components that are repeatedly restored to service after they fail. The method assumes that the failures follow a Poisson process, but allows many parametric models for the time-dependent failure rate λ(t). Ways to check many of the assumptions form an important part of the method. When the assumptions are satisfied, the maximum likelihood estimate of λ(t) is approximately lognormal, and this lognormal distribution is appropriate to use as a Bayesian distribution for λ(t) in a probabilistic risk assessment.     

Risk-informed design of IRIS using a level-1 probabilistic risk assessment from its conceptual design phase

In this study, a probabilistic risk assessment (PRA) for the International Reactor Innovative and Secure (IRIS) has been generated to address two key areas as a part of the effort for the pre-application licensing of the IRIS design.First, the IRIS PRA is supporting the evaluation of IRIS design by providing design insights as well as a solid risk basis for the pre-licensing evaluation of the IRIS design. Second, the current PRA task is beginning the preparation of the more complete PRA analyses and documentation that will be required for Design Certification. The initial IRIS PRA is an at-power, Level-1 PRA for internal events that focuses on the evaluation of the IRIS design features to support the risk-informed design of IRIS by application of the PRA insights and the risk information to the design. To accomplish the evaluation, a reasonably complete Level-1 PRA model has been developed.The use of PRA in the early stages of the design has allowed a selection of design and performance features and an optimization of the design of several systems to reduce the potential for events that could lead to core damage via both enhanced prevention and mitigation of challenges. As a result, the total core damage frequency for internal events for the IRIS design has been calculated as 1.2×10⁻⁸ per year.     

Issues related to structural aging in probabilistic risk assessment of nuclear power plants

Structural components and systems have an important safety function in nuclear power plants. Although they are essentially passive under normal operating conditions, they play a key role in mitigating the impact of extreme environmental events such as earthquakes, winds, fire and floods on plant safety. Moreover, the importance of structural components and systems in accident mitigation is amplified by common-cause effects. Reinforced concrete structural components and systems in NPPs are subject to a phenomenon known as aging, leading to time-dependent changes in strength and stiffness that may impact their ability to withstand various challenges during their service lives from operation, the environment and accidents. Time-dependent changes in structural properties as well as challenges to the system are random in nature. Accordingly, condition assessment of existing structures should be performed within a probabilistic framework. The mathematical formalism of a probabilistic risk assessment (PRA) provides a means for identifying aging structural components that may play a significant role in mitigating plant risk. Structural condition assessments supporting a decision regarding continued service can be rendered more efficient if guided by the logic of a PRA.     

Dynamic reliability: towards an integrated platform for probabilistic risk assessment

Dynamic reliability methods are powerful mathematical frameworks capable of handling interactions among components and process variables explicitly. In principle, they constitute a more realistic modeling of systems for the purposes of reliability, risk and safety analysis. Although there is a growing recognition in the risk community of the potentially greater correctness of these methods, no serious effort has been undertaken to utilize them in industrial applications.User-friendly tools would help foster usage of dynamic reliability methods in the industry. This paper defines the key components of such a platform and for each component, provides a detailed review of techniques available for their implementation. This paper attempts to provide milestones in the creation of a high level design of such tools. To achieve this purpose, a modular approach is used. For each part, various existing techniques are discussed with respect to their potential achievements. Issues related to expected future developments are also considered.     

A framework to integrate software behavior into dynamic probabilistic risk assessment

Software plays an increasingly important role in modern safety-critical systems. Although, research has been done to integrate software into the classical probabilistic risk assessment (PRA) framework, current PRA practice overwhelmingly neglects the contribution of software to system risk. Dynamic probabilistic risk assessment (DPRA) is considered to be the next generation of PRA techniques. DPRA is a set of methods and techniques in which simulation models that represent the behavior of the elements of a system are exercised in order to identify risks and vulnerabilities of the system. The fact remains, however, that modeling software for use in the DPRA framework is also quite complex and very little has been done to address the question directly and comprehensively. This paper develops a methodology to integrate software contributions in the DPRA environment. The framework includes a software representation, and an approach to incorporate the software representation into the DPRA environment SimPRA. The software representation is based on multi-level objects and the paper also proposes a framework to simulate the multi-level objects in the simulation-based DPRA environment. This is a new methodology to address the state explosion problem in the DPRA environment. This study is the first systematic effort to integrate software risk contributions into DPRA environments.     

Application of classification trees in the sensitivity analysis of probabilistic model results

The complexity of some integrated-system models necessitates using a probabilistic approach to quantify uncertainty in model projections. In this work, we demonstrate how classification trees can be used to perform sensitivity analyses on probabilistic results. The classification tree technique is applied to results from the probabilistic total system performance assessment model used in the Yucca Mountain project. The technique proves effective in delineating the variables that most influence low and high outcomes.     

Biomechanical rupture risk assessment of abdominal aortic aneurysms based on a novel probabilistic rupture risk index

A rupture risk assessment is critical to the clinical treatment of abdominal aortic aneurysm (AAA) patients. The biomechanical AAA rupture risk assessment quantitatively integrates many known AAA rupture risk factors but the variability of risk predictions due to model input uncertainties remains a challenging limitation. This study derives a probabilistic rupture risk index (PRRI). Specifically, the uncertainties in AAA wall thickness and wall strength were considered, and wall stress was predicted with a state-of-the-art deterministic biomechanical model. The discriminative power of PRRI was tested in a diameter-matched cohort of ruptured (n = 7) and intact (n = 7) AAAs and compared to alternative risk assessment methods. Computed PRRI at 1.5 mean arterial pressure was significantly (p = 0.041) higher in ruptured AAAs (20.21(s.d. 14.15%)) than in intact AAAs (3.71(s.d. 5.77)%). PRRI showed a high sensitivity and specificity (discriminative power of 0.837) to discriminate between ruptured and intact AAA cases. The underlying statistical representation of stochastic data of wall thickness, wall strength and peak wall stress had only negligible effects on PRRI computations. Uncertainties in AAA wall stress predictions, the wide range of reported wall strength and the stochastic nature of failure motivate a probabilistic rupture risk assessment. Advanced AAA biomechanical modelling paired with a probabilistic rupture index definition as known from engineering risk assessment seems to be superior to a purely deterministic approach.     

Seismic probabilistic risk assessment and seismic margins studies for nuclear power plants

This paper reviews the seismic probabilistic risk assessment and seismic margins studies for nuclear power plants in the United States. The techniques employed in these studies are briefly described. A few comments on the evaluation of the fragility of structures and equipment are discussed. Seismic PRA is a systematic process to evaluate the safety of nuclear power plants. In the process, it integrates all the elements such as seismic hazard, component fragility and plant system. Thus, it provides the overall view of the safety of an entire plant under a seismic event.

The major tasks of a seismic PRA such as the evaluation of hazard curves, component fragility and plant system are also present in probabilistic analyses of nonnuclear facilities. The concept and technique embodied in seismic PRA for nuclear power plants can be applied to other types of engineering facilities.     

A probabilistic quantitative risk assessment model for the long-term work zone crashes

Work zones especially long-term work zones increase traffic conflicts and cause safety problems. Proper casualty risk assessment for a work zone is of importance for both traffic safety engineers and travelers. This paper develops a novel probabilistic quantitative risk assessment (QRA) model to evaluate the casualty risk combining frequency and consequence of all accident scenarios triggered by long-term work zone crashes. The casualty risk is measured by the individual risk and societal risk. The individual risk can be interpreted as the frequency of a driver/passenger being killed or injured, and the societal risk describes the relation between frequency and the number of casualties. The proposed probabilistic QRA model consists of the estimation of work zone crash frequency, an event tree and consequence estimation models. There are seven intermediate events – age (A), crash unit (CU), vehicle type (VT), alcohol (AL), light condition (LC), crash type (CT) and severity (S) – in the event tree. Since the estimated value of probability for some intermediate event may have large uncertainty, the uncertainty can thus be characterized by a random variable. The consequence estimation model takes into account the combination effects of speed and emergency medical service response time (ERT) on the consequence of work zone crash. Finally, a numerical example based on the Southeast Michigan work zone crash data is carried out. The numerical results show that there will be a 62% decrease of individual fatality risk and 44% reduction of individual injury risk if the mean travel speed is slowed down by 20%. In addition, there will be a 5% reduction of individual fatality risk and 0.05% reduction of individual injury risk if ERT is reduced by 20%. In other words, slowing down speed is more effective than reducing ERT in the casualty risk mitigation.     

Marked point process framework for living probabilistic safety assessment and risk follow-up

We construct a model for living probabilistic safety assessment (PSA) by applying the general framework of marked point processes. The framework provides a theoretically rigorous approach for considering risk follow-up of posterior hazards. In risk follow-up, the hazard of core damage is evaluated synthetically at time points in the past, by using some observed events as logged history and combining it with re-evaluated potential hazards. There are several alternatives for doing this, of which we consider three here, calling them initiating event approach, hazard rate approach, and safety system approach. In addition, for a comparison, we consider a core damage hazard arising in risk monitoring. Each of these four definitions draws attention to a particular aspect in risk assessment, and this is reflected in the behaviour of the consequent risk importance measures. Several alternative measures are again considered. The concepts and definitions are illustrated by a numerical example.     

Application of Bayesian network to the probabilistic risk assessment of nuclear waste disposal

The scenario in a risk analysis can be defined as the propagating feature of specific initiating event which can go to a wide range of undesirable consequences. If we take various scenarios into consideration, the risk analysis becomes more complex than do without them. A lot of risk analyses have been performed to actually estimate a risk profile under both uncertain future states of hazard sources and undesirable scenarios. Unfortunately, in case of considering specific systems such as a radioactive waste disposal facility, since the behaviour of future scenarios is hardly predicted without special reasoning process, we cannot estimate their risk only with a traditional risk analysis methodology. Moreover, we believe that the sources of uncertainty at future states can be reduced pertinently by setting up dependency relationships interrelating geological, hydrological, and ecological aspects of the site with all the scenarios. It is then required current methodology of uncertainty analysis of the waste disposal facility be revisited under this belief.In order to consider the effects predicting from an evolution of environmental conditions of waste disposal facilities, this paper proposes a quantitative assessment framework integrating the inference process of Bayesian network to the traditional probabilistic risk analysis. We developed and verified an approximate probabilistic inference program for the specific Bayesian network using a bounded-variance likelihood weighting algorithm. Ultimately, specific models, including a model for uncertainty propagation of relevant parameters were developed with a comparison of variable-specific effects due to the occurrence of diverse altered evolution scenarios (AESs). After providing supporting information to get a variety of quantitative expectations about the dependency relationship between domain variables and AESs, we could connect the results of probabilistic inference from the Bayesian network with the consequence evaluation model addressed. We got a number of practical results to improve current knowledge base for the prioritization of future risk-dominant variables in an actual site.     

Security risks and probabilistic risk assessment of glazing subject to explosive blast loading

A probabilistic risk assessment (PRA) procedure is developed which can predict risks of explosive blast damage to built infrastructure. The present paper focuses on window glazing since this is a load-capacity system which, when subject to blast loading, has caused significant damage and injury to building occupants. Structural reliability techniques are used to derive fragility and blast reliability curves (BRCs) for annealed and toughened glazing subjected to explosive blast, for a variety of threat scenarios. The probabilistic analyses include the uncertainties associated with blast modelling, glazing response and glazing failure criteria. Damage risks are calculated for an individual window and for windows in the facade of a multi-storey commercial building. If threat probabilities can be estimated then the paper shows illustrative examples of how this information, when combined with risk-based decision-making criteria, can be used to optimise risk mitigation strategies.     

PC-based probabilistic safety assessment in Japan

The role of PC-based programs is becoming important in the area of PSA. The PC-based program QUEST has been developed to perform level-1 PSA at PNC. This program is an effective tool to examine the effects of the change in the plant design and/or operational procedures. Also, as a part of the full scope PSA activity for the prototype liquid metal fast breeder reactor, a systems analysis code network, which involves some PC-based programs, was developed and has been utilized to perform level-1 PSA with less manpower and more consistency. Further, a living PSA tool is currently being developed for the purpose of maintenance of or improvement in operational safety.     

Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment

Traditional fault tree (FT) analysis is widely used for reliability and safety assessment of complex and critical engineering systems. The behavior of components of complex systems and their interactions such as sequence- and functional-dependent failures, spares and dynamic redundancy management, and priority of failure events cannot be adequately captured by traditional FTs. Dynamic fault tree (DFT) extend traditional FT by defining additional gates called dynamic gates to model these complex interactions. Markov models are used in solving dynamic gates. However, state space becomes too large for calculation with Markov models when the number of gate inputs increases. In addition, Markov model is applicable for only exponential failure and repair distributions. Modeling test and maintenance information on spare components is also very difficult. To address these difficulties, Monte Carlo simulation-based approach is used in this work to solve dynamic gates. The approach is first applied to a problem available in the literature which is having non-repairable components. The obtained results are in good agreement with those in literature. The approach is later applied to a simplified scheme of electrical power supply system of nuclear power plant (NPP), which is a complex repairable system having tested and maintained spares. The results obtained using this approach are in good agreement with those obtained using analytical approach. In addition to point estimates of reliability measures, failure time, and repair time distributions are also obtained from simulation. Finally a case study on reactor regulation system (RRS) of NPP is carried out to demonstrate the application of simulation-based DFT approach to large-scale problems.     

Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies

There will be simplifying assumptions and idealizations in the availability models of complex processes and phenomena. These simplifications and idealizations generate uncertainties which can be classified as aleatory (arising due to randomness) and/or epistemic (due to lack of knowledge). The problem of acknowledging and treating uncertainty is vital for practical usability of reliability analysis results. The distinction of uncertainties is useful for taking the reliability/risk informed decisions with confidence and also for effective management of uncertainty. In level-1 probabilistic safety assessment (PSA) of nuclear power plants (NPP), the current practice is carrying out epistemic uncertainty analysis on the basis of a simple Monte-Carlo simulation by sampling the epistemic variables in the model. However, the aleatory uncertainty is neglected and point estimates of aleatory variables, viz., time to failure and time to repair are considered. Treatment of both types of uncertainties would require a two-phase Monte-Carlo simulation, outer loop samples epistemic variables and inner loop samples aleatory variables. A methodology based on two-phase Monte-Carlo simulation is presented for distinguishing both the kinds of uncertainty in the context of availability/reliability evaluation in level-1 PSA studies of NPP.     

Challenges in using a probabilistic safety assessment in a risk informed process (illustrated using risk informed inservice inspection)

Many of the ongoing and expected uses of Probabilistic Safety Assessment (PSA)¹ create new challenges to ensuring that the resulting conclusions are valid. This paper provides a summary of some of these challenges. Work conducted by the authors on Risk-Informed Inservice Inspection (RI-ISI) is used to illustrate these challenges. Means to address all of the challenges are not provided in detail in this paper. Several earlier papers discuss how these challenges can be addressed. References are provided for the interested reader (Chapman JR et al. In: PSA '95, vol. 1, Seoul, 1995: 177–80; Chapman JR et al. In: ICONE-IV, New Orleans, 1996; Dimitrijevic VB et al. In: Croatian Nuclear Society International Conference, Opatija, 1996: 245–54; Dimitrijevic VB et al. In: Croatian Nuclear Society International Conference, Opatija, 1996: 255–62; Dimitrijevic VB. In: Yugoslav Nuclear Society Conference, Belgrade, 1996: 53–61; O'Regan PJ et al. In: PSA '95, Seoul, vol. 1, 1995: 403–5; O'Regan PJ. In: ICONE-IV, vol. 5, New Orleans, 1996: 277–80).