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A modified method to compute the reliability with arbitrary independent random variables

For reliability problems with arbitrary independent random variables, the variables are always transformed into normal variables for the convenience of reliability analysis. Usually, the probability density function (PDF) of normal variables do not always well reflect the real probability feature of the tail of the original PDF. Hence, non-negligible equivalent normalization error affects the accuracy of the computed reliability results, especially when the original probability of failure of the reliability problem is quite low. In order to tackle this problem, the paper introduces a modified estimation of the unified form of the maximum entropy PDF (MEPDF) of these variables. Since the modified MEPDF brings the benefits for getting a better approximation in the tails of the original PDF, during the reliability analysis, the paper uses the MEPDFs as the surrogate of the original ones and exploits the first and second order moment approach by resorting to facilitation brought by the unified form of the MEPDF. Lastly, the presented examples show that the proposed method achieves better accuracy of the computed reliability results.