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Civil and critical infrastructure systems such as transportation, communication, power, and financial systems have provided the foundation for modern society. Not surprisingly, much of the research work in many areas of engineering was directed over the years at the advancement and application of scientific principles to the design, maintenance and improvement of the critical infrastructures in our society. Risk assessment and systematic consideration of risk in the design and operation of infrastructure is a relatively new phenomenon that emerged within the last fifty years. While many engineering disciplines still do not consider probability and statistics as essential basic knowledge for engineers, like physics for instance, consideration of risk has penetrated all engineering disciplines. In most cases, however, such considerations take the form of setting thresholds and safety margins so as to avoid "unacceptable" risk, where acceptability levels are typically determined by experts. In power systems for instance, the common wisdom has traditionaly been to build sufficient capacity so that the system will fail to meet demand no more than one day in ten years. Similarly, power system operation is governed to a large extent by the "N-1 security criterion" which requires that the system as a whole can sustain failure of any one element (e.g. generator, transmission line, transformer etc.).