Restrictions of point estimate methods and remedy

Point estimate methods (PEMs) are widely applied to approximately estimate the moments and uncertainty of a random output variable in reliability evaluation and other engineering applications due to its computational efficiency and satisfactory accuracy. However, as any numerical approximation method, PEMs have their own limitations and should be used with caution. Unfortunately, although a lot of papers on point estimate methods have been published so far, almost none of them mentioned the limitations and restrictions of PEMs. In this paper, the restrictions of PEMs are theoretically analyzed and discussed with illustrative examples. A remedy for the restrictions is presented.