## Publication Date

8-1-2024

## Abstract

In engineering designs, we usually need to make sure that the values of some characteristics y do not exceed a certain threshold y0 – e.g., that the stress at each location does not exceed a certain critical value. Usually, we know how each of these characteristics y depends on the design parameters x1, . . . ,xn, i.e., we know the function y= f (x1, . . . ,xn). However, it is not enough to use the nominal values of the design parameters in our analysis, since the actual values are, in general, somewhat different from the nominal values. Often, the only information that we have about the actual values of the parameters xi are tolerance intervals [xi,xi]. It is therefore possible to compute the range [y,y] of the function f (x1, . . . ,xn) on these intervals. The problem is that the resulting worst-case interval is too wide, it includes many value y that are not practically possible – since it is highly improbable that all parameters attain their extreme values at the same time. Using this too-wide interval would lead to unnecessarily complicated and expensive design. It is therefore desirable to come up with a narrower interval. In this paper, we first provide a recommendation for computing such a narrower interval based on heuristic fuzzy-logic-based ideas. We also describe an alternative mathematically justified approach and show that it leads to exact same recommendations.

## Comments

Technical Report: UTEP-CS-24-42