# L-moments and Bayesian inference for probabilistic risk assessment with scarce samples that include extremes

About: This article is published in Reliability Engineering & System Safety.The article was published on 2023-03-01. It has received None citations till now. The article focuses on the topics: Probabilistic risk assessment & Inference.

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TL;DR: KDE-bd and KDE with estimated bounded data are proposed, which randomly generates bounded data within given input variable intervals for given data and applies them to generate density functions, and are shown to be more accurate than the original KDE when the number of data is less than 10.

Abstract: The uncertainties of input variables are quantified as probabilistic distribution functions using parametric or nonparametric statistical modeling methods for reliability analysis or reliability-based design optimization. However, parametric statistical modeling methods such as the goodness-of-fit test and the model selection method are inaccurate when the number of data is very small or the input variables do not have parametric distributions. To deal with this problem, kernel density estimation with bounded data (KDE-bd) and KDE with estimated bounded data (KDE-ebd), which randomly generates bounded data within given input variable intervals for given data and applies them to generate density functions, are proposed in this study. Since the KDE-bd and KDE-ebd use input variable intervals, they attain better convergence to the population distribution than the original KDE does, especially for a small number of given data. The KDE-bd can even deal with a problem that has one data with input variable bounds. To verify the proposed method, statistical simulation tests were carried out for various numbers of data using multiple distribution types and then the KDE-bd and KDE-ebd were compared with the KDE. The results showed the KDE-bd and KDE-ebd to be more accurate than the original KDE, especially when the number of data is less than 10. It is also more robust than the original KDE regardless of the quality of given data, and is therefore more useful even if there is insufficient data for input variables.

17 citations

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TL;DR: This paper suggests a Bayesian approach and uses the inverse Bayes formula (IBF) combined with a Metropolis-Hastings algorithm to make inference on the parameters and a comparison is made with results obtained from the recently proposed α-composition method.

17 citations

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TL;DR: The Bayesian forecasting model is posed as a replacement for the logistic regression and the nonparametric approach advocated in earlier analyses of the Challenger O‐ring data, and a comparison demonstrates the inherent deficiency of the generalized linear models for risk analyses.

Abstract: A Bayesian forecasting model is developed to quantify uncertainty about the postflight state of a field-joint primary O-ring (not damaged or damaged), given the O-ring temperature at the time of launch of the space shuttle Challenger in 1986. The crux of this problem is the enormous extrapolation that must be performed: 23 previous shuttle flights were launched at temperatures between 53 degrees F and 81 degrees F, but the next launch is planned at 31 degrees F. The fundamental advantage of the Bayesian model is its theoretic structure, which remains correct over the entire sample space of the predictor and that affords flexibility of implementation. A novel approach to extrapolating the input elements based on expert judgment is presented; it recognizes that extrapolation is equivalent to changing the conditioning of the model elements. The prior probability of O-ring damage can be assessed subjectively by experts following a nominal-interacting process in a group setting. The Bayesian model can output several posterior probabilities of O-ring damage, each conditional on the given temperature and on a different strength of the temperature effect hypothesis. A lower bound on, or a value of, the posterior probability can be selected for decision making consistently with expert judgment, which encapsulates engineering information, knowledge, and experience. The Bayesian forecasting model is posed as a replacement for the logistic regression and the nonparametric approach advocated in earlier analyses of the Challenger O-ring data. A comparison demonstrates the inherent deficiency of the generalized linear models for risk analyses that require forecasting an event conditional on a predictor value outside the sampling interval, and combining empirical evidence with expert judgment.

13 citations

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TL;DR: In this article, a multidimensional PRA scenario analysis is conducted from the perspectives of scenario elements, scenario evolution, and scenario effect, and a scenario-driven dynamic stochastic model is developed based on a three-stage solution with accurate feature quantification, and effective utilization of objective factual records and subjective expert judgment.

11 citations

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TL;DR: This paper considers the statistical analysis of the Binomial Failure Rate (BFR) common-cause model in detail and the modified-Beta distribution is defined to characterize the posterior distribution for one of the model parameters.

10 citations