Approximating the risk for time-to-failure models through using statisticsof extremes

This paper studies the approximation of the partitioned multiobjective risk method's (PMRM) extreme event risk function for time-to-failure models. Th e analytic expression of the approximation for the extreme event risk funct ion is derived through the use of the statistics of extremes for the case w here the underlying distribution is of an extreme-value type III for minima . This analytic expression provides an effective theoretical tool for under standing the behavior of conditional expected values for time-to-failure mo dels for a large class of distribution functions used in reliability. The r esults are confirmed for example problems of exponential and uniform distri butions. (C) 1999 Elsevier Science Ltd. All rights reserved.