To represent input variability accurately, input distribution model for random variables should be constructed using many observations or data. However, for certain input variables, engineers may have only their bounds which represent input uncertainty. In practical engineering applications, both random and interval variables could exist at the same time. For the applications, to consider both input variability and uncertainty, inverse reliability analysis should be carried out considering the mixed variables and their mathematical correlation in performance measure. In this paper, an iterative most probable point (MPP) search method has been developed for the mixed variable problem. The random and interval variables update procedures are developed considering the features of mixed variable in the inverse reliability analysis. Both variable update methods proceed one iteration simultaneously to consider the mathematical correlation. An interpolation method is introduced to find better candidate MPP without additional function evaluations. Mixed variable design optimization (MVDO) has been formulated to obtain cost effective and reliable design in the presence of the mixed variables. In addition, the design sensitivity of probabilistic constraint has been developed for effective and efficient MVDO procedure. Using numerical examples, it is found that the developed MPP search method finds accurate MPP more efficiently than generic optimization method. In addition, it is verified that the developed method enables MVDO process with small number of function evaluations.

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