Modern computational techniques for reliability estimation

The Monte Carlo method and its refinements can deal with quite general reliability problems. Thus the random variables may each have any appropriate probability density function, the limit state functions need not be linear and there may be many of them. The brief overview of some of the Monte Carlo possibilities given here will indicate the significant advantages they can have over other techniques. For problems which involve load processes, it is necessary, usually, to solve a stochastic load combination problem. A more direct approach is to use the concept of vector process outcrossing. Although difficult to solve analytically, recent progress has been made in using simulation techniques and this will be outlined. This type of approach is being explored at present also for use in problems in which there is time or load-cycle deterioration of material strength.