Expression an Effective Method in Generation of Random Samples to Calculate the Failure Probability of Structures With MCS Method

Reliability theory is a part of the general theory of probability that earned a special place in engineering science over recent decades. This theory has a logical framework. It provides the actual safety assessment possibility of a system by analyzing the uncertainties using mathematical methods. These uncertainties are caused by the statistical nature of engineering problems. Reliability is a scale that can measure the probability of failure or safety of a system. So far, various methods have been proposed to estimate the probability of failure of a phenomenon. MCS is one of the most important and most widely used approaches in this field. Many steps will be removed by providing a simple and effective method. The data generated in this method is based on the histogram. SGH, there is no need to curve fitting test. This method is very useful in case data on the studied phenomenon be available in sufficient number, and continuous histograms could be created. The general performance of SGH is passing the histogram of uniform data scattered in three-dimensional space and select samples in the diagram area. As well as, it provided three practical examples. The first one is estimating the failure probability of a concrete beam under moment load with four random variables. The second example expressed failure probability of a steel beam, and the third one is about sliding and overturning failure of SHAFAROUD concrete gravity dam. Results were compared with the usual method of sample generation and indicated the effectiveness and accuracy of the responses of the proposed method.