A Statistical Approach to Ranking Similarities of Three Function Structure Groups Using Directed Graphs

Abstract

Prior efforts in the study of engineering design employed various approaches to decompose product design. Design engineers use functional representation, and more precisely function structures, to define a product’s functionality. However, significant barriers remain to objectively quantifying the similarity between two function structures, even for the same product when developed by multiple designers. For function-structure databases this means that function-structures are implicitly categorized leaving the possibility of incorrect categorization and reducing efficacy of returned analogous correlations. Improvements to efficacy in database organization and queries are possible by objectively quantifying the similarity between function structures. The proposed method exploits fundamental properties of function-structures and design taxonomies. We convert function-structures into directed graphs (digraphs) and equivalent adjacency matrices. The conversion maintains the directed (function → flow → function) progression inherent to function-structures and enables the transformation of the function-structure into a standardized graph. For design taxonomies (e.g. D-APPS), graph nodes represent flows in a consistent (but arbitrary) ordering. By exploiting the directional properties of function-structures and defining the flows as the graphical nodes, the objective and standardized comparison of two function-structures becomes feasible. We statistically quantify the association between digraphs using the Pearson Product Moment Correlation (PPMC) for both within-group and between-group comparisons. The method was tested on three product types (ball thrower, food processor, and an ice cream maker) with function-structures defined by various designers. The method suggested herein is provided as a proof-of-concept with suggested verification and validation approaches for further development.