Рубрика: Hydrosystems Engineering Reliability Assessment and Risk Analysis

Antithetic-variates technique

The antithetic-variates technique (Hammersley and Morton, 1956) achieves the variance-reduction goal by attempting to generate random variates that would induce a negative correlation for the quantity of interest between separate sim­ulation runs. Consider that Gq and ©2 are two unbiased estimators of an un­known quantity в to be estimated. The two estimators can be combined […]

Importance sampling technique

The importance sampling technique concentrates the distribution of sampling points in the part of the domain that is most “important” for the task rather than spreading them out evenly (Marshall, 1956). Refer to the problem of evaluating an integral in Eq. (6.49) by the sample-mean method. The importance sampling technique attempts to generate M sampling […]

Variance-Reduction Techniques

Since Monte Carlo simulation is a sampling procedure, results obtained from the procedure inevitably involve sampling errors, which decrease as the sam­ple size increases. Increasing the sample size to achieve a higher precision generally means an increase in computer time for generating random vari­ates and data processing. Variance-reduction techniques aim at obtaining high accuracy for […]

Efficiency of the Monte Carlo algorithm

Referring to Monte Carlo integration, different algorithms yield different esti­mators for the integral. A relevant issue is which algorithm is more efficient. The efficiency issue can be examined from the statistical properties of the esti­mator from a given algorithm and its computational aspects. Rubinstein (1981) showed a practical measure of the efficiency of an algorithm […]

Directional Monte Carlo simulation algorithm

Consider the reliability computation involving a multidimensional integral as Eq. (6.48). Without losing generality, the following discussions assume that the stochastic variables in the original X-space have been transformed to the independent standard normal Z’-space (see Sec. 2.7.2). Consequently, the orig­inal performance function W(X) can be expressed as W(Z’). In terms of Z Eq. (6.48) […]

Monte Carlo Integration

In reliability analysis, computations of system and/or component reliability and other related quantities, such as mean time to failure, essentially involve inte­gration operations. A simple example is the time-to-failure analysis in which the reliability of a system within a time interval (0, t) is obtained from where ft (t) is the failure density function. A […]

Generating multivariate random variates subject to linear constraints

Procedures described in Sec. 6.5.2 are for generating multivariate normal (Gaussian) random variables without imposing constraints or restriction on the values of variates. The procedures under this category are also called uncon­ditional (or nonconditional) simulation (Borgman and Faucette, 1993; Chiles and Delfiner, 1999). In hydrosystems modeling, random variables often exist for which, in addition to […]

Generating multivariate random variates with known marginal pdfs and correlations

In many practical hydrosystems engineering problems, random variables often are statistically and physically dependent. Furthermore, distribution types for the random variables involved can be a mixture of different distributions, of which the corresponding joint PDF or CDF is difficult to establish. As a practical alternative, to replicate such systems properly, the Monte Carlo simulation should […]