Library builder

Despite the system under consideration being a series or parallel system, the evaluation of system reliability or failure probability involves probabilities of union or intersection of multiple events. Without losing generality, the deriva­tion of the bounds for P (A1U A2 U—U AM) and P (A1 n A2 П—П AM) are given below. For example, consider […]

The solution approaches to system reliability problems can be classified broadly into failure-modes approach and survival-modes approach (Bennett and Ang, 1983). The failure-modes approach is based on identification of all possible fail­ure modes for the system, whereas the survival-modes approach is based on the all possible modes of operation under which the system will be […]

From the reliability computation viewpoint, classification of the system depends primarily on how system performance is affected by its components or modes of operation. A multiple-component system called a series system (see Fig. 7.1) requires that all its components perform satisfactorily to allow satisfactory performance of the entire system. Similarly, for a single-component system involving […]

As mentioned previously, the reliability of a system depends on the component reliabilities and interactions and configurations of components. Consequently, computation of system reliability requires knowing what constitutes the system being in a failed or satisfactory state. Such knowledge is essential for system classification and dictates the methodology to be used for system reliability determination. […]

7.1 Introduction Most systems involve many subsystems and components whose performances affect the performance of the system as a whole. The reliability of the entire system is affected not only by the reliability of individual subsystems and components but also by the interactions and configurations of the subsystems and components. Many engineering systems involve multiple […]

Note that the Monte Carlo simulation described in preceding sections is con­ducted under the condition that the probability distribution and the associated population parameters are known for the random variables involved in the system. The observed data are not used directly in the simulation. In many statistical estimation problems, the statistics of interest often are […]

The basic idea behind the control-variate method for variance reduction is to take advantage of the available information for the selected variables related to the quantity to be estimated. Referring to Eq. (6.91), the quantity G to be estimated is the expected value of the output of the model g(X). The value of G can […]

The Latin hypercube sampling (LHS) technique is a special method under the umbrella of stratified sampling that selects random samples of each random variable over its range in a stratified manner. Consider a multiple integral involving K random variables G = g (x) fx (x) d x = E [g (X)] (6.91) J xeE where […]

The stratified sampling technique is a well-established area in statistical sam­pling (Cochran, 1966). Variance reduction by the stratified sampling technique is achieved by taking more samples in important subregions. Consider a prob­lem in which the expectation of a function g (X) is sought, where X is a random variable with a PDF fx(x), x є […]

Correlated-sampling techniques are especially effective for variance reduction when the primary objective of the simulation study is to evaluate small changes in system performance or to compare the difference in system performances between two specific designs (Rubinstein, 1981; Ang and Tang, 1984). Consider that one wishes to estimate