Durga Rao Karanki

Reliability and Safety Engineering

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Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment.

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Probabilistic Safety Assessment

A wide range of uncertainties will be introduced inevitably during the process of performing a safety assessment of engineering systems. The impact of all these uncertainties must be addressed if the analysis is to serve as a tool in the decision-making process. Uncertainties present in the components (input parameters of model or basic events) of model output are propagated to quantify its impact in the final results. There are several methods available in the literature, namely, method of moments, discrete probability analysis, Monte Carlo simulation, fuzzy arithmetic, and Dempster-Shafer theory. All the methods are different in terms of characterizing at the component level and also in propagating to the system level. All these methods have different desirable and undesirable features, making them more or less useful in different situations. In the probabilistic framework, which is most widely used, probability distribution is used to characterize uncertainty. However, in situations in which one cannot specify (1) parameter values for input distributions, (2) precise probability distributions (shape), and (3) dependencies between input parameters, these methods have limitations and are found to be not effective. In order to address some of these limitations, the article presents uncertainty analysis in the context of level-1 probabilistic safety assessment (PSA) based on a probability bounds (PB) approach. PB analysis combines probability theory and interval arithmetic to produce probability boxes (p-boxes), structures that allow the comprehensive propagation through calculation in a rigorous way. A practical case study is also carried out with the developed code based on the PB approach and compared with the two-phase Monte Carlo simulation results.

A dynamic event tree informed approach to probabilistic accident sequence modeling: Dynamics and variabilities in medium LOCA

Probabilistic safety/risk assessment provides a quantitative framework to estimate risk and identify risk contributors. This chapter introduces the concept of risk and gives an overview of probabilistic safety assessment steps. Special emphasis is given to event tree analysis, importance measures, common cause failure analysis, and human reliability analysis, which are essential and important elements of any safety assessment. Several examples are given to supplement the understanding of these approaches. Some of the remaining important analysis approaches such as fault tree analysis and uncertainty analysis are already covered in rest of the book.

Quantification of Dynamic Event Trees – A comparison with event trees for MLOCA scenario

In Probability Safety Assessments, accident scenario dynamics are addressed in the accident sequence analysis task. In an analyst-driven, iterative process, assumptions are made about equipment responses and operator actions and simulations of the scenario evolution are performed. To calculate how scenario dynamics and stochastic variabilities may affect the results of this process in terms of estimated risk, this work applies Dynamic Event Trees (DETs) to more comprehensively examine the accident scenario space. Alternative event tree models are developed and the core damage frequency is quantified to reveal the effects of different delineations of the sequences and of the bounding assumptions underlying success criteria. The results from a case study on Medium-break Loss of Coolant Accident scenarios in a Pressurized Water Reactor are presented, considering the break size, available injection trains, and the timing of rapid cooldown and the switchover to recirculation. The results show not only that estimated risk can be very sensitive to the numerous assumptions made in current accident sequence analysis but also that bounding assumptions do not always result in conservative risk estimates, thereby confirming the benefits that DETs provide in terms of characterizing scenario dynamics.

Epistemic and aleatory uncertainties in integrated deterministic and probabilistic safety assessment: Tradeoff between accuracy and accident simulations

Abstract Dynamic event trees (DETs) provide the means to simulate physical system evolutions, the evolution of system states due to stochastic events, and the dynamic interactions between these evolutions. For risk assessment, the framework avoids the need to specify a priori the sequence of stochastic events prior to the plant response simulation and to iterate between the definition of the sequences and simulation of the responses. For nuclear power plants, DETs have been applied to treat scenarios up to core damage as well as post-core damage accident scenarios. The quantification of the frequencies of the sequences leading to the undesired system outcomes, while conceptually straightforward, faces several implementation issues. These include, for instance, the treatment of support system dependencies and of events characterized by a continuous aleatory variable. Some solutions to these issues are proposed and applied in a case study dealing with Medium Break Loss of Coolant Accident (MLOCA) scenarios. Additionally, the results obtained from DET quantification are compared with those estimated with a “classical” event tree model for these scenarios. This comparison provides some case-specific results on the impact of the improved modeling of dynamics on risk estimates.

System Reliability Modeling

The coupling of plant simulation models and stochastic models representing failure events in Dynamic Event Trees (DET) is a framework used to model the dynamic interactions among physical processes, equipment failures, and operator responses. The integration of physical and stochastic models may additionally enhance the treatment of uncertainties. Probabilistic Safety Assessments as currently implemented propagate the (epistemic) uncertainties in failure probabilities, rates, and frequencies; while the uncertainties in the physical model (parameters) are not propagated. The coupling of deterministic (physical) and probabilistic models in integrated simulations such as DET allows both types of uncertainties to be considered. However, integrated accident simulations with epistemic uncertainties will challenge even todays high performance computing infrastructure, especially for simulations of inherently complex nuclear or chemical plants. Conversely, intentionally limiting computations for practical reasons would compromise accuracy of results. This work investigates how to tradeoff accuracy and computations to quantify risk in light of both uncertainties and accident dynamics. A simple depleting tank problem that can be solved analytically is considered to examine the adequacy of a discrete DET approach. The results show that optimal allocation of computational resources between epistemic and aleatory calculations by means of convergence studies ensures accuracy within a limited budget.

Uncertainty analysis in PSA with correlated input parameters

This chapter presents basic system reliability modeling techniques such as reliability block diagram , Markov models, and fault tree analysis . System reliability is evaluated as a function of constituting components’ reliabilities.

Reliability of Complex Systems

The probability of occurrence of top event of a fault tree in probabilistic safety assessment (PSA) is estimated from the probabilities of the basic events which constitute the fault tree. However the failure probabilities of basic events are subjected to statistical uncertainty. While analyzing the uncertainty of top event, the basic events are assumed uncorrelated or independent in most of the situation, but are not the case every time. Such statistical correlations are introduced into failure data by many causes. To handle the propagation of uncertainties in the presence of correlations, there are three methods: (i) Method of moments, (ii) P-box approach and (iii) Monte Carlo simulations. However the first two methods are difficult for implementation in large scale problems when partial correlations are present instead of fully correlated data. The paper presents a methodology based Monte Carlo simulation with Nataf Transformation of generating correlated random variables for uncertainty analysis in PSA. Computer code has been developed to implement the proposed methodology and a case study from NPP has been carried out.

A comparison of dynamic event tree methods – Case study on a chemical batch reactor

This chapter presents two advanced reliability modeling techniques, i.e. Monte Carlo simulation and dynamic fault tree analysis. They are particularly useful for modeling the reliability of complex systems.