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It is common to give assurance in terms of the probability of success in satisfying some performance criteria and the probability of success is estimated from the mean value and variance of the performance function. The mean value and variance of the performance function is further estimated from the propagation of the input uncertainties. Therefore, it becomes a fundamental challenge to accurately estimate the uncertainty propagations from given input randomness in the probabilistic design process. Better approximation of the performance function is a key factor in enhancing the approximation quality of the mean value and the standard deviation. However, higher order approximations for the performance increase the computational cost associated. This paper presents an improved approximation method for the prediction of the mean and variance without increasing the number of function evaluations.