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Modeling Finite‐Time Failure Probabilities in Risk Analysis Applications

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  • Dimitrina S. Dimitrova
  • Vladimir K. Kaishev
  • Shouqi Zhao

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.

Suggested Citation

  • Dimitrina S. Dimitrova & Vladimir K. Kaishev & Shouqi Zhao, 2015. "Modeling Finite‐Time Failure Probabilities in Risk Analysis Applications," Risk Analysis, John Wiley & Sons, vol. 35(10), pages 1919-1939, October.
    • Handle: RePEc:wly:riskan:v:35:y:2015:i:10:p:1919-1939
    DOI: 10.1111/risa.12384
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    References listed on IDEAS

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    Cited by:

    1. Mei Choi Chiu & Chi Seng Pun & Hoi Ying Wong, 2017. "Big Data Challenges of High‐Dimensional Continuous‐Time Mean‐Variance Portfolio Selection and a Remedy," Risk Analysis, John Wiley & Sons, vol. 37(8), pages 1532-1549, August.
    2. Dimitrova, Dimitrina S. & Ignatov, Zvetan G. & Kaishev, Vladimir K. & Tan, Senren, 2020. "On double-boundary non-crossing probability for a class of compound processes with applications," European Journal of Operational Research, Elsevier, vol. 282(2), pages 602-613.

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