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Reliability computations for time-dependent models can be made for determin­istic and random cycle times. The development of a model for deterministic cycles is given first, which naturally leads to the model for random cycle times. Number of occurrences is deterministic. Consider a hydrosystem with a fixed resistance (or capacity) R = r subject to n […]

A hydraulic structure placed in a natural environment over an expected ser­vice period is subject to repeated application of loads of varying intensities. The magnitude of load intensity and the number of occurrences of load are, in gen­eral, random by nature. Therefore, probabilistic models that properly describe the stochastic mechanisms of load intensity and load […]

Repeated loadings on a hydrosystem are characterized by the time each load is applied and the behavior of time intervals between load applications. From a reliability theory viewpoint, the uncertainty about the loading and resistance variables may be classified into three categories: deterministic, random fixed, and random independent (Kapur and Lamberson, 1977). For the deterministic […]

In time-dependent reliability analysis, one is concerned with system reliability over a specified time period during which external loads can occur more than once. Therefore, not only the intensity or magnitude of load is important but also the number or frequency of load occurrences is an important parameter. Over an anticipated service period, the characteristics […]

For a hydraulic structure placed in a natural environment over a period of time, its operational characteristics could change over time owing to deterioration, aging, fatigue, and lack of maintenance. Consequently, the structural capacity (or resistance) would vary with respect to time. Examples of time-dependent characteristics of resistance in hydrosystems are change in flow-carrying capacity […]

The development of hydrosystems engineering projects often includes the de­sign of various types of hydraulic structures, such as pipe networks for water supply, storm sewer systems for runoff collection, levee and dike systems for flood control and protection, and others. Generally, the system, once designed and constructed, is expected to serve its intended objectives over […]

By the AFOSM reliability method, the design point on the failure surface is identified. This design point has the shortest distance to the mean point of the stochastic basic variables in the original space or to the origin of standard­ized normal parameter space. In the AFOSM method, the failure surface is locally approximated by a […]

Convergence criteria for locating the design point. The previously described Hasofer-Lind and Ang-Tang iterative algorithms to determine the design point indicate that the iterations may end when x(r) and x(r+1> are sufficiently close. The key question then becomes what constitutes sufficiently close. In the ex­amples given previously in this section, the iterations were stopped when […]

For most practical engineering problems, parameters involved in load and re­sistance functions are correlated nonnormal random variables. Such distribu­tional information has important implications for the results of reliability com­putations, especially on the tail part of the distribution for the performance function. The procedures of the Rackwitz normal transformation and orthogo­nal decomposition described previously can be […]

When some of the stochastic basic variables involved in the performance func­tion are correlated, transformation of correlated variables to uncorrelated ones is made. Consider that the stochastic basic variables in the performance func­tion are multivariate normal random variables with the mean matrix p, x and the covariance matrix Cx. Without losing generality, the original stochastic […]