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

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• 作者：Paula Reis (1) (2)
  Lu铆sa Canto e Castro (1) (3)
  Sandra Dias (4) (5)
  M. Ivette Gomes (1) (3) (6)
  
  1. CEAUL ; Lisboa ; Portugal
  2. DMAT ; EST-IPS ; Set煤bal ; Portugal
  3. DEIO ; FCUL ; Universidade de Lisboa ; Lisboa ; Portugal
  4. CM-UTAD ; Vila Real ; Portugal
  5. Universidade de Tr谩s-os-Montes e Alto Douro ; Vila Real ; Portugal
  6. DEIO ; Faculdade de Ci锚ncias da Universidade de Lisboa ; Campo Grande ; 1749-016 ; Lisboa ; Portugal
  
• 关键词：Extreme value theory ; Monte ; Carlo simulation ; Penultimate and ultimate approximations ; System reliability ; Primary 62G32 ; 62N05 ; 62G20 ; Secondary 65C05
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：17
• 期：1
• 页码：189-206
• 全文大小：816 KB
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• 刊物主题：Statistics, general; Life Sciences, general; Electrical Engineering; Economics general; Business/Management Science, general;
• 出版者：Springer US
• ISSN：1573-7713

文摘

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.