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Penultimate Approximations in Statistics of Extremes and Reliability of Large Coherent Systems

Author

Listed:
  • Paula Reis

    (CEAUL
    EST-IPS)

  • Luísa Canto e Castro

    (CEAUL
    Universidade de Lisboa)

  • Sandra Dias

    (CM-UTAD
    Universidade de Trás-os-Montes e Alto Douro)

  • M. Ivette Gomes

    (CEAUL
    Universidade de Lisboa
    Faculdade de Ciências da Universidade de Lisboa)

Abstract

In reliability theory any coherent system can be represented as either a series-parallel or a parallel-series system. Its lifetime can thus be written as the minimum of maxima or the maximum of minima. For large-scale coherent systems it is sensible to assume that the number of system components goes to infinity. Then, the possible non-degenerate extreme value laws either for maxima or for minima are eligible candidates for the system reliability or at least for the finding of adequate lower and upper bounds for the reliability. The identification of the possible limit laws for the system reliability of homogeneous series-parallel (or parallel-series) systems has already been done under different frameworks. However, it is well-known that in most situations such non-degenerate limit laws are better approximated by an adequate penultimate distribution. Dealing with regular and homogeneous parallel-series systems, we assess both theoretically and through Monte-Carlo simulations the gain in accuracy when a penultimate approximation is used instead of the ultimate one.

Suggested Citation

  • Paula Reis & Luísa Canto e Castro & Sandra Dias & M. Ivette Gomes, 2015. "Penultimate Approximations in Statistics of Extremes and Reliability of Large Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 189-206, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9338-7
    DOI: 10.1007/s11009-013-9338-7
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