There are two basic probabilistic approaches to evaluate the reliability of an infrastructural system. The most direct approach is a statistical analysis of data of past failure records for similar systems. The other approach is through reliability analysis, which considers and combines the contribution of each factor potentially influencing failure. The former is a lumped-system approach requiring
no knowledge about the internal physical behavior of the facility or structure and its load and resistance. For example, dam failure data show that the overall average failure probability for dams of all types over 15 m in height is around 10-3 per dam per year (U. S. National Research Council, 1983; Cheng, 1993). This statistical approach may fit well with manufactured systems for which planned repeated tests can be made and the performance of many identical prototypes can be observed. For infrastructural systems in most cases, this direct approach is impractical because (1) infrastructures are usually unique and site-specific, (2) the sample size is too small to be statistically reliable, especially for low-probability/high-consequence events, (3) the sample may not be representative of the structure or of the population, and (4) the physical conditions of a dam may be nonstationary, i. e., varying with respect to time. The average risk of dam failure mentioned earlier does not differentiate concrete dams from earth-fill dams, arch dams from gravity dams, large dams from small dams, and old dams from new dams. If one wished to know the likelihood of failure of a particular 10-year-old double-curvature-arch concrete high dam, most likely one will find only very few failure data of similar dams, insufficient for any meaningful statistical analysis. Since no dams are identical and conditions of dams change with time, in many circumstances it may be more desirable to use the second approach by conducting a reliability analysis.
There are two major steps in reliability analysis: (1) to identify and analyze the uncertainties of each contributing factor and (2) to combine the uncertainties of the stochastic factors to determine the overall reliability of the structure. The second step, in turn, also may proceed in two different ways: (1) directly combining the uncertainties of all factors and (2) separately combining the uncertainties of the factors belonging to different components or subsystems to evaluate first the respective subsystem reliability and then combining the reliabilities of the different components or subsystems to yield the overall reliability of the structure. The first way applies to very simple structures, whereas the second way is more suitable to complicated systems. For example, to evaluate the reliability of a dam, the hydrologic, hydraulic, geotechnical, structural, and other disciplinary reliabilities could be evaluated separately first and then combined to yield the overall dam reliability. Or the component reliabilities could be evaluated first according to the different failure modes and then combined. Analysis tools
