The point estimate method (PEM) is an alternative to Monte Carlo Simulation (MCS) and First Order Second Moments (FOSM) for evaluating the moments and probability distribution of the system or component performance. Although PEM is a powerful and simple method, it is often limited by the need to make 2n or even 3" evaluations when there are n random variables, which is unaffordable for many engineering applications. In the previous paper by the authors [15], a variable-point PEM method was proposed to improve the efficiency and accuracy of the existing approaches. However, when it applied to the problems with large number of design variables (number of design variables > 10), the method still requires hundreds or thousands of simulation runs. This paper further improves the efficiency of the variable-point PEM based upon two fundamental concepts: 1) The Pareto principle; and 2) The Central Limit Theorem of Statistics, i.e., under common engineering conditions, a linear combination of random variables can be approximated to first order by a normal distribution. The efficiency and accuracy of the proposed method are validated with three benchmark problems.
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