Often in engineering design selection there is no one design alternative that is better in terms of all attributes, and the preferred design(s) is dependent on the preferences of the Decision Maker (DM). In addition, there is always uncontrollable variability, which is mainly of two types, that has to be accounted for. The first type, preference variability, is caused due to the DM's lack of information on end users' needs. The second type, attribute variability, is caused due to uncontrollable engineering design parameters like manufacturing errors. If variability is not accounted for, the preferred design(s) found might be erroneous. Existing methods presume an explicit form for the DM's "value function" to simplify this selection problem. But, such an assumption is restrictive and valid only in some special cases.

The objective of this research is to develop a decision making framework for product design selection that does not presume any explicit form for the DM's value function and that accounts for both preference and attribute variability.

Our decision making framework has four research components. In the first component, Deterministic Selection, we develop a method for finding the preferred design(s) when the DM gives crisp preference estimates, i.e., best guess of actual preferences. In the second component, Sensitivity Analysis, we develop a method for finding the allowed variation in the preference estimates for which the preferred design(s) do not change. In the third component, Selection with Preference Variability, we develop a method for finding the preferred design(s) when the DM gives a range of preferences instead of crisp estimates. Finally, in our fourth component, Selection with Preference and Attribute Variability, we develop a method in which the DM gives a range of values for attributes of the design alternatives in addition to a range for preferences.

We demonstrate the methods developed in each component with two engineering examples and provide numerical experimental results for verification. Our experiments indicate that the preferred design(s) found in our first, third, and fourth components always include the actual preferred design(s) and that our second component finds the allowed variation in preference estimates efficiently.