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

This paper studies the approximation of the partitioned multiobjective risk method's (PMRM) extreme event risk function for time-to-failure models. The analytic expression of the approximation for the extreme event risk function is derived through the use of the statistics of extremes for the case where the underlying distribution is of an extreme-value type III for minima. This analytic expression provides an effective theoretical tool for understanding the behavior of conditional expected values for time-to-failure models for a large class of distribution functions used in reliability. The results are confirmed for example problems of exponential and uniform distributions.