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Modeling Finite‐Time Failure Probabilities in Risk Analysis Applications
Author(s) -
Dimitrova Dimitrina S.,
Kaishev Vladimir K.,
Zhao Shouqi
Publication year - 2015
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12384
Subject(s) - risk management , reliability (semiconductor) , probabilistic logic , risk analysis (engineering) , computer science , risk assessment , joint probability distribution , reliability engineering , insolvency , engineering , statistics , mathematics , artificial intelligence , business , power (physics) , physics , computer security , finance , quantum mechanics
In this article, we introduce a framework for analyzing the risk of systems failure based on estimating the failure probability. The latter is defined as the probability that a certain risk process, characterizing the operations of a system, reaches a possibly time‐dependent critical risk level within a finite‐time interval. Under general assumptions, we define two dually connected models for the risk process and derive explicit expressions for the failure probability and also the joint probability of the time of the occurrence of failure and the excess of the risk process over the risk level. We illustrate how these probabilistic models and results can be successfully applied in several important areas of risk analysis, among which are systems reliability, inventory management, flood control via dam management, infectious disease spread, and financial insolvency. Numerical illustrations are also presented.