On the marshall-olkin copula model for network reliability under dependent failures

Omar Matus, Javiera Barrera, Eduardo Moreno, Gerardo Rubino

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

The Marshall-Olkin (MO) copula model has emerged as the standard tool for capturing dependence between components in failure analysis in reliability. In this model, shocks arise at exponential random times, that affect one or several components inducing a natural correlation in the failure process. However, because the number of parameter of the model grows exponentially with the number of components, MO suffers of the 'curse of dimensionality.' MO models are usually intended to be applied to design a network before its construction; therefore, it is natural to assume that only partial information about failure behavior can be gathered, mostly from similar existing networks. To construct such an MO model, we propose an optimization approach to define the shock's parameters in the MO copula, in order to match marginal failures probabilities and correlations between these failures. To deal with the exponential number of parameters of this problem, we use a column-generation technique. We also discuss additional criteria that can be incorporated to obtain a suitable model. Our computational experiments show that the resulting MO model produces a close estimation of the network reliability, especially when the correlation between component failures is significant.

Original languageEnglish
Article number8464101
Pages (from-to)451-461
Number of pages11
JournalIEEE Transactions on Reliability
Volume68
Issue number2
DOIs
StatePublished - Jun 2019

Keywords

  • Copula theory
  • failure analysis
  • network design
  • optimization methods
  • reliability

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