Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair

Troffaes, Matthias; Gledhill, Jacob; Škulj, Damjan; Blake, Simon

Abstract

We explore how imprecise continuous time Markov chains can improve traditional reliability models based on precise continuous time Markov chains. Specifically, we analyse the reliability of power networks under very weak statistical assumptions, explicitly accounting for non-stationary failure and repair rates and the limited accuracy by which common cause failure rates can be estimated. Bounds on typical quantities of interest are derived, namely the expected time spent in system failure state, as well as the expected number of transitions to that state. A worked numerical example demonstrates the theoretical techniques described. Interestingly, the number of iterations required for convergence is observed to be much lower than current theoretical bounds.

Citation

Troffaes, M., Gledhill, J., Škulj, D., & Blake, S. (2015, July). Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair. Presented at ISIPTA 2015, 9th international symposium on imprecise probability : theories and applications., Pescara, Italy

• Presentation Conference Type: Conference Paper (published)
• Conference Name: ISIPTA 2015, 9th international symposium on imprecise probability : theories and applications.
• Start Date: Jul 20, 2015
• End Date: Jul 24, 2015
• Acceptance Date: May 19, 2015
• Publication Date: Jul 24, 2015
• Deposit Date: Feb 18, 2015
• Publicly Available Date: Jun 12, 2015
• Pages: 287-294
• Book Title: ISIPTA ’15 : proceedings of the 9th International Symposium on Imprecise Probability : Theories and Applications, 20-24 July 2015, Pescara, Italy.
• Public URL: https://durham-repository.worktribe.com/output/1153097
• Publisher URL: http://www.sipta.org/isipta15/?pag=proceedings
• Additional Information: 20-24 July 2015