This work proposes an uncertainty metric to capture and encode parametric uncertainty information that will enable engineering decision analyst to combine and compute probabilities of expected outcomes through mathematical constructs of joint probability functions. Its integration in a mechanical design system can be expected to facilitate simulation-based design under uncertainty. Specifically, the proposed technique helps to study the impact of the probabilistic nature of the input design or state variables and by applying the concept of failure probability aims to generate the corresponding probabilistic information of the output performance function. This work is based on evaluating a series of probabilities that the output cannot exceed a certain value for a given perturbed value of the design point. In this context, this paper reviews the First Order Second Moment (FOSM) reliability theory where the random parameters influencing the design appear only through their means and co-variances. Building on these works, an alternate approach is presented taking into account the fact that the system output is all the more influenced by functional constraints in the system, which if ignored can lead to inaccurate or irrelevant error estimation and could seriously affect subsequent posterior decision analysis. This work includes a reliable and efficient error estimation procedure to identify design points that violate boundary conditions through methodical constraint evaluations and subsequent adjusting of output estimation values. The proposed method is illustrated with the aid of a constrained optimization case study and an I-beam design problem.

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