Modeling Finite-Time Failure Probabilities in Risk Analysis Applications

Dimitrova, D. S., Kaishev, V. K. & Zhao, S. (2015). Modeling Finite-Time Failure Probabilities in Risk Analysis Applications. Risk Analysis, 35(10), pp. 1919-1939. doi: 10.1111/risa.12384

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Abstract

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.

Item Type: Article
Additional Information: This is the peer reviewed version of the following article:Dimitrova, D. S., Kaishev, V. K. & Zhao, S. (2015). Modeling Finite-Time Failure Probabilities in Risk Analysis Applications. Risk Analysis, 35(10), pp. 1919-1939, which has been published in final form at http://dx.doi.org/10.1111/risa.12384. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Uncontrolled Keywords: Alarm time; Appell polynomials; dam overtopping; dependent risk modeling; finite-time failure probability
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/11951

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