# Application of Quality Function Deployment for Product Design Concept Selection
## 3 Materials and Methods
Then, divide the summation of values in row \(i\) by \(C^{1}_{ik}\) to yield another column vector (Equation (4)),  
\[\overline{C}=\left[ \begin{array}{cccc}\overline{C}^{1}_{1k}\\ \vdots\\ \overline{C}^{1}_{nk}\end{array} \right]=\left[ \begin{array}{cccc}\frac{ \left(C^{1}_{1k}a_{11}+C^{1}_{2k}a_{12}+\cdots+C^{1}_{nk}a_{1n}\right)}{C^{1} _{ik}}\\ \vdots\\ \frac{\left(C^{1}_{1k}a_{11}+C^{1}_{2k}a_{12}+\cdots+C^{1}_{nk}a_{nn}\right)}{ C^{1}_{nk}}\end{array} \right] \tag{4}\]  
where \(\overline{C}\) refers to a weighted sum vector. (e) Compute the averages of values in vector \(\overline{C}\) to yield the maximum eigenvalue of matrix A (Equation (5)),  
\[\lambda_{max}=\frac{\sum_{i\in R}\overline{C}^{1}_{1k}}{n} \tag{5}\]  
(f) Compute the consistency ratio (Equation (6)),  
\[CI=\frac{\lambda_{max}-n}{n-1} \tag{6}\]  
where RI(\(n\)) is a random index of which the value is dependent on the value of n. If CR is greater than 0.10, then go to step (a). Otherwise, go to step (g). (g) Compute the importance rating of each stakeholder requirement  
where S denotes the set of company stakeholders, that is, S = {1, 2, \(\ldots,\,m\)}, and \(pk\) denotes the proportion of customers \(k\). After calculating the final assessment scores, we conduct a quadrant analysis to categorize the new design concepts into four groups. We analyse the relative position of each design concept versus the current design through quadrant analysis. Figure 1 depicts the detailed procedures of the proposed framework. Step A: Determining new design alternatives  
In this step, we apply the traditional QFD method to select the ES from CR and demonstrate the relative importance. These selected specifications and their relative importance can be crucial for designers to generate new design concepts. Then, we determine the candidates for design concept selection. This QFD analysis is also linked to the next evaluation step. Step B: Evaluating new design concepts  
In the second step, we assess the relative concept competitiveness and design development efficiency of the new design concept versus the current design concept. We suggest an integrated analysis with QFD and AHP for concept competitiveness. The AHP scores (V\({}_{comp}\)) represent a relative concept competitiveness among the candidates. As shown in Figure 1, first, we determine the evaluation criteria which correspond to the CR in the QFD. Second, we conduct a pair-wise comparison of the criteria to decide the weighted values. Third, the relative competitiveness levels of the new design concept  
Figure 1: Framework of the proposed method. Source: made by authors. versus the current design concept are determined in advance. We calculate the concept competitiveness scores by multiplying the weighted values and rating scores and then normalize these scores by dividing each original score by the AHP score of the current design concept. Furthermore, the super-SBM scores (V\({}_{\textit{eff}}\)) represent the relative design development efficiency. We identify the input and output criteria to evaluate the efficiency in advance. Then, we gather the quantitative and qualitative data and adjust the direction of the data. Thus, we calculate DEA scores through the super-SBM and then normalize the scores by dividing each original score by DEA score of the current design concept. Step C: Selecting the best new design concept  
In the last step, we calculate the combined scores for B2B firms to determine the best design concept. We conduct group decision making using an AHP pair-wise comparison between the concept competitiveness and the development efficiency to determine weighted values (wt\({}_{\textit{comp}}\),wt\({}_{\textit{eff}}\)). From the combined scores, we rank the design concepts and select the best one. Then, we carry out the quadrant analysis to recognize the relative position of new concepts versus the current design concept. This step completes the proposed method.