Confidence bounds on component reliability in the presence of mixed uncertain variables

Uncertainties in a physical system can be modeled and analyzed by using probability theory or possibility theory, depending on the amount of information available. In probability theory, uncertain variables are modeled using probability density functions (PDFs) and then propagated through the system to obtain its reliability. In the absence of sufficient data to model a PDF, possibility theory, in which variables are represented using fuzzy membership functions, can be used to propagate uncertainty. However, when dealing with a combination of both probability distributions and fuzzy membership functions, the computational cost involved in estimating the membership function of reliability increases exponentially because one reliability analysis, which is a computationally expensive procedure, is performed at each possibility level to obtain the bounds on the reliability of the structure. To improve the computational efficiency, a technique that uses response surface models and transformations of possibility functions is presented in this paper. The efficiency and accuracy of the proposed methodology is demonstrated using numerical examples.