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2 results

  • 4 - Static Systems: Probabilistic Structural Uncertainty

  • Alejandro D. Domínguez-García, University of Illinois, Urbana-Champaign
  • Book:
    Large-Scale System Analysis Under Uncertainty
    Published online:
    17 January 2022
    Print publication:
    17 February 2022, pp 91-129

  • Summary

    This chapter studies static systems under structural uncertainty. The first part of the chapter is devoted to the development of a model describing the system stochastic behavior. To this end, we assume that the system can only adopt a finite number of input-to-state mappings, and that transitions among these different mappings are random and governed by a Markov chain. We consider both discrete- and continuous-time settings and provide expressions governing the evolution of the probability distribution associated with the resulting Markov chains. The second part of the chapter tailors the techniques developed earlier to analyze multi-component systems subject to component failures and repairs. Techniques for constructing the system input-to-state model are extensively covered, as this is in general the most difficult part of the analysis when analyzing systems with a large number of components.

  • Ordering of repairable systems

  • Nader Ebrahimi
  • Journal:
    Journal of Applied Probability / Volume 27 / Issue 1 / March 1990
    Published online by Cambridge University Press:
    14 July 2016, pp. 193-201
    Print publication:
    March 1990

  • The problem of how to compare repairable systems has long been of interest to those who are engaged in reliability analysis. In this article we have introduced a type of comparison of two counting processes. Various properties and applications of our stochastic comparison are also studied.