Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T23:02:10.286Z Has data issue: false hasContentIssue false
  • English
  • Français

On a new stochastic model for cascading failures

Part of: Special processes Applications

Published online by Cambridge University Press:  23 November 2020

Hyunju Lee
Hyunju Lee*
Affiliation:
Hankuk University of Foreign Studies
*
*Postal address: Department of Statistics, Hankuk University of Foreign Studies, Yongin17035, Republic of Korea. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, to model cascading failures, a new stochastic failure model is proposed. In a system subject to cascading failures, after each failure of the component, the remaining component suffers from increased load or stress. This results in shortened residual lifetimes of the remaining components. In this paper, to model this effect, the concept of the usual stochastic order is employed along with the accelerated life test model, and a new general class of stochastic failure models is generated.

Keywords

Cascading failurestochastic intensityaccelerated life test modelusual stochastic orderk-out-of-n system

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62P30: Applications in engineering and industry
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1150 - 1161
Check for updates
Copyright
© Applied Probability Trust 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability. Springer, New York.10.1007/b97596CrossRefGoogle Scholar
Aven, T. and Jensen, U. (2000). A general minimal repair model. J. Appl. Prob. 37, 187–197.Google Scholar
Badía, F. G. (2011). Hazard rate properties of a general counting process stopped at an independent random time. J. Appl. Prob. 48, 56–67.10.1017/S0021900200007634CrossRefGoogle Scholar
Badía, F. G. and Sangüesa, C. (2014). Log-concavity for Bernstein-type operators using stochastic orders. J. Math. Anal. Appl. 413, 953–962.10.1016/j.jmaa.2013.12.014CrossRefGoogle Scholar
Cha, J. H. (2006). A stochastic model for burn-in procedures in accelerated environment. Naval Res. Logistics 53, 226–234.10.1002/nav.20135CrossRefGoogle Scholar
Cha, J. H., Mi, J. and Yun, W. Y. (2008). Modelling a general standby system and evaluation of its performance. Appl. Stoch. Models Business Industry 24, 159–169.10.1002/asmb.704CrossRefGoogle Scholar
Finkelstein, M. (2007). On statistical and information-based virtual age of degrading systems. Reliab. Engrg System Safety 92, 676–681.10.1016/j.ress.2006.03.001CrossRefGoogle Scholar
Finkelstein, M. (2007). On some ageing properties of general repair processes. J. Appl. Prob. 44, 506–513.10.1239/jap/1183667417CrossRefGoogle Scholar
Finkelstein, M. (2008). Failure Rate Modeling for Reliability and Risk. Springer, London.Google Scholar
Finkelstein, M. and Esaulova, V. (2006). On mixture failure rates ordering. Commun. Statist. Theory Meth. 35, 1943–1955.10.1080/03610920600762871CrossRefGoogle Scholar
Lee, H. and Cha, J. H. (2016). Point process approach to modeling and analysis of general cascading failure models. J. Appl. Prob. 53, 174–186.10.1017/jpr.2015.17CrossRefGoogle Scholar
Leemis, L. M. (2009). Reliability, Probabilistic Models and Statistical Methods, 2nd edn. Prentice Hall.Google Scholar
Meeker, W. Q. and Escobar, L. A. (1993). A review of recent research and current issues of accelerated testing. Internat. Statist. Rev. 61, 147–168.10.2307/1403600CrossRefGoogle Scholar
Navarro, J. and Rubio, R. (2010). Comparisons of coherent systems using stochastic precedence. Test 19, 469–486.10.1007/s11749-010-0207-1CrossRefGoogle Scholar
Navarro, J. and Shaked, M. (2006). Hazard rate ordering of order statistics and systems. J. Appl. Prob. 43, 391–408.Google Scholar
Navarro, J., Belzunce, F. and Ruiz, J. M. (1997). New stochastic orders based on double truncation. Prob. Eng. Inf. Sci. 11, 395–402.Google Scholar
Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. Wiley, New York.10.1002/9780470316795CrossRefGoogle Scholar
Shaked, M and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.10.1007/978-0-387-34675-5CrossRefGoogle Scholar
Swift, A. W. (2008). Stochastic models of cascading failures. J. Appl. Prob. 45, 907–921.10.1239/jap/1231340223CrossRefGoogle Scholar