Tree-Based Dependency Analysis in Decomposition and Re-decomposition of Complex Design Problems

We have developed a formal method for decomposition of complex design problems in two phases: dependency analysis and matrix partitioning. Of the most distinct characteristic in this method is the support of cost-effective re-decomposition (as is often required in decomposition solution synthesis), where dependency analysis serves as a platform for the enabling of re-decomposition. Yet, this requires that the result of the dependency analysis be robust and thus reusable for re-decomposition. In this paper, after revealing the deficiency in the current practice of dependency analysis, we present an enhanced dependency analysis method that is built on ordinary tree structure (instead of binary tree structure). This new approach, which is more systematic, ensures robust dependency analysis, whose result is insensitive to the arrangement of a tree structure in tree-based dependency analysis. A complete set of tree-based algorithms is also provided, along with their applications to two design examples