# A Trimming Design Method Based on Bio-Inspired Design for System Innovation
## 3 Theoretical Method
### Analysis before Trimming the System  
The analysis performed before trimming the system involves several specific steps to help designers make wise decisions when formulating the trimming plan based on the function-oriented analysis of the product system. This process comprises three specific steps. Step A1: Analyzing system functions. Function analysis mainly relies on functional decomposition to analyze the known product by revealing the causal relations between all function carriers within the product system. Each function of the product system plays one of four roles, depending on how it affects the ideality of the system: a useful function is able to increase the ideality of the system; a harmful function leads to a decrease in system ideality; an insufficient function produces lower ideality than required; an excessive function reduces the ideality level of the system, even though its useful effect exceeds requirements. This paper uses a method from a previous study [13] to calculate scores of the function levels of components. For example, \"5\" is used to indicate a useful function, \"\(-\)5\" denotes a harmful function, \"3\" is an insufficient function, and \"\(-\)3\" indicates an excessive function. Step A2: Identifying the main design problem. The previous step defines harmful and excessive functions in the product system. Subsequently, this step applies CECA to analyze and identify the main design problem in the product system. CECA reveals the causal relations between design problems and physical components that serve as function carriers in the product system with harmful, excessive or inefficient functions. Figure 2 illustrates how CECA is used to identify design problems of a water heater with two causal relations, that is, \"or\"/\"and\". The causality between components and functions is established based on CECA. In Figure 2, the causal relations between two components and harmful, excessive and insufficient functions are represented by \"or\"/\"and\", which are the premise for calculating the function values for components in the product system. Step A3: Determining trimming priorities. After CECA has revealed causal relations between product components and their functional roles in the product system, the function value for every component in the product can be calculated based on weights according to their roles. CECA includes approaches  
Figure 2: Function tree of a water heater product design problem based on CECA. to tackling \"or\"/\"/\"and\" relations. Specifically, each factor in the \"and\" connection has an equivalent weight in the function unit. For example, in the illustrative case shown in Figure 2, the heater and water tank components work together through the \"and\" relation and have the harmful function of \"increase the costs of energy/material\" with a score of \"\(-5\) \", so the functional values of the heater and water tank are \"\(-2.5\)\". \[V_{\text{i}}=\sum_{i=1}^{n}F_{i}\cdot L_{i}\cdot T_{i} \tag{1}\]  
Formula (1) represents the calculation of the system component's function value based on the results of CECA. In Formula (1), \(V_{\text{i}}\) denotes the value for component \(i\), \(F_{\text{i}}\) is the function weight, \(L_{\text{i}}\) is the weight of the causal relation in CECA, and the value of \(T_{\text{i}}\) is assigned by the position of the function in the whole function tree in CECA. The values of harmful and excessive functions located at the root of the CECA-based system function tree are higher than those located at the top because these types of functions are the foundation of the whole causal chain that leads to design problems. For the section containing useful and insufficient functions, the top-level useful function has a lower function value because it is directly related to the requirements of the system. The case of the water heater in Figure 2 is used as a simple example to explain how to calculate the function value of a product component based on Formula (1).