On competing risk and degradation processes

Lehmann's ideas on concepts of dependence have had a profound effect on mathematical theory of reliability. The aim of this paper is two-fold. The first is to show how the notion of a ``hazard potential'' can provide an explanation for the cause of dependence between life-times. The second is to propose a general framework under which two currently discussed issues in reliability and in survival analysis involving interdependent stochastic processes, can be meaningfully addressed via the notion of a hazard potential. The first issue pertains to the failure of an item in a dynamic setting under multiple interdependent risks. The second pertains to assessing an item's life length in the presence of observable surrogates or markers. Here again the setting is dynamic and the role of the marker is akin to that of a leading indicator in multiple time series.Comment: Published at http://dx.doi.org/10.1214/074921706000000473 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Criteria for and extrapolation in overstress models

Accelerated life test models, criteria for model selection, and extrapolation in overstress model

Network routing in a dynamic environment

Recently, there has been an explosion of work on network routing in hostile environments. Hostile environments tend to be dynamic, and the motivation for this work stems from the scenario of IED placements by insurgents in a logistical network. For discussion, we consider here a sub-network abstracted from a real network, and propose a framework for route selection. What distinguishes our work from related work is its decision theoretic foundation, and statistical considerations pertaining to probability assessments. The latter entails the fusion of data from diverse sources, modeling the socio-psychological behavior of adversaries, and likelihood functions that are induced by simulation. This paper demonstrates the role of statistical inference and data analysis on problems that have traditionally belonged in the domain of computer science, communications, transportation science, and operations research.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS453 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org