The high-dimensional model decomposition method is an effective approach for solving the reliability of engineering structures or composite materials with a large number of uncertain parameters. The multiplicative dimensionality reduction method is a high-dimensional model decomposition technique that decomposes a high-dimensional function into a combination of low-dimensional functions and approximates the overall response of the high-dimensional function by solving the responses of these low-dimensional functions. This paper begins by discussing the extrema of functions based on the multiplicative dimensionality reduction method. Then, by combining it with Taylor series expansion, a method for approximating the extremum of a high-dimensional function was proposed. Furthermore, based on the multiplicative dimensionality reduction method, first-order reliability method, and Taylor series expansion, the functional relationship between upper and lower bounds of failure probability and interval variables was derived. Finally, using the algorithm proposed in this paper, the extrema of high-dimensional functions can be calculated to solve the upper and lower bounds of failure probability under random-interval hybrid uncertainty. This paper presents two engineering structures and a numerical example to demonstrate the efficiency and accuracy of the proposed method.
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