Srividya Ajit

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

Probabilistic Safety Assessment

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.

System Reliability Modeling

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

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.

Uncertainty Analysis in Reliability/Safety Assessment

This chapter presents the basics of uncertainty analysis in reliability or risk assessment. Although probabilistic representation of uncertainty is very popular, alternate methods of representing uncertainties are also presented, which are useful when limited information is available. Different methods of uncertainty propagation are discussed, which include analytical methods, Monte Carlo simulation, interval and fuzzy arithmetic based approaches. Two methods to build input parameter distributions are also explained in detail viz., Bayesian and expert elicitation techniques.

Basic Reliability Mathematics

The basics of mathematical theory that are relevant to the study of reliability and safety engineering are discussed in this chapter. The basic concepts of set theory and probability theory are explained first. Then the elements of component reliability are presented.

Risk Analysis of Nuclear Power Plants

Post Fukushima accident [1], a new problem has arisen for the nuclear community with respect to the establishment of new power plants in the country.

Advanced Methods in Uncertainty Management

Uncertainty management encompasses identification and characterizing elementary uncertainties, propagation of model input uncertainties, and prioritizing the measures to reduce the uncertainties. This chapter primarily focuses on complex issues in uncertainty management such as treating correlations among uncertain parameters, separating epistemic and aleatory uncertainties, and ranking the parameters. Alternative uncertainty methods, Dempster-Shafer approach and probability bounds based approach, are discussed with a few numerical examples. Further, a comparison of different approaches on a plant case study is presented, where the benefits and limitations of each approach are given.

Electronic System Reliability

The dominating failure mechanisms for various electronic components such as resistors, capacitors, relays, silicon devices, etc. and the corresponding failure modes are briefly explained.

Applications of PSA

Probabilistic safety assessment (PSA) studies not only evaluate risk but also their results are very useful in safe, economical and effective design and operation of the engineering systems. This chapter presents various practical applications of PSA. The use of PSA in evaluating surveillance test interval and in-service inspection intervals at acceptable risk and reduced cost for nuclear power plant (NPP) is discussed.