Evaluating the effectiveness of functional decomposition in early-stage design: development and application of problem space exploration metrics

This paper aims to explore metrics for evaluating the effectiveness of functional decomposition methods regarding problem space exploration at the early design stage. Functional decomposition involves breaking down the main purpose of a complex problem or system into a set of more manageable sub-functions, leading to a clearer understanding of the problem space and its various aspects. While various metrics have been used to evaluate functional decomposition outcomes, little literature has focused on assessing its effectiveness in problem space exploration. To address the gap, this research introduces three metrics for problem space evaluation defined by functional models: quantity of unique functions (M1), breadth and depth of the hierarchical structure (M2), and relative semantic coverage ratio of the problem space (M3). An example study is conducted to illustrate the evaluation process, comparing functional analysis with and without explicit human-centric considerations using a power screwdriver as a case product. The analysis in the example study reveals that the breadth of the hierarchical structure (part of M2) is marginally larger in the condition with explicit human-centric considerations (Condition A) compared to the condition without such considerations (Condition B). However, no significant differences are observed in terms of other metrics. The qualitative analysis based on semantic comparisons suggests that Condition A facilitates participants in generating a diverse set of functions supporting user safety requirements more effectively than Condition B. Overall, the example study demonstrates the evaluation process for each metric and discusses their nuances and limitations. By proposing these metrics, this research contributes to benchmarking and evaluating the effectiveness of different methods in promoting functional analysis in engineering design. The metrics provide valuable insights into problem space exploration, offering designers a better understanding of the efficacy of their functional decomposition methods in early design stages. This, in turn, fosters more informed decision-making and contributes to the advancement of functional analysis methodologies in engineering design practices.