Karanki Durga Rao, Kushwaha Hari Shankar, Verma Ajit Kumar, Ajit Srividya
Risk and Human Reliability Group, Paul Scherrer Institut, Villigen PSI, Switzerland.
Risk Anal. 2009 May;29(5):662-75. doi: 10.1111/j.1539-6924.2009.01221.x. Epub 2009 Mar 12.
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.
在对工程系统进行安全评估的过程中，不可避免地会引入各种各样的不确定性。如果该分析要作为决策过程中的一种工具，就必须考虑所有这些不确定性的影响。模型输出的组件（模型的输入参数或基本事件）中存在的不确定性会进行传播，以量化其对最终结果的影响。文献中有几种可用的方法，即矩量法、离散概率分析、蒙特卡罗模拟、模糊算法和Dempster-Shafer理论。所有这些方法在组件层面的特征描述以及向系统层面的传播方面都有所不同。所有这些方法都有不同的优缺点，这使得它们在不同情况下或多或少都有用。在最广泛使用的概率框架中，概率分布用于描述不确定性。然而，在无法指定（1）输入分布的参数值、（2）精确的概率分布（形状）以及（3）输入参数之间的依赖关系的情况下，这些方法存在局限性且被发现是无效的。为了解决其中一些局限性，本文基于概率界（PB）方法，在一级概率安全评估（PSA）的背景下进行不确定性分析。PB分析将概率论和区间算法结合起来，生成概率盒（p盒），这种结构允许通过严格的计算进行全面传播。还使用基于PB方法开发的代码进行了一个实际案例研究，并与两相蒙特卡罗模拟结果进行了比较。
