4. Emotional factors:

**Figure 17.** Membership values of emotional factors.

5. Satisfaction factors:

**Figure 18.** Membership values of satisfaction factors.

#### *4.4. Evaluating the 'Assembleability' of Design Schemes*

A product design is considered not good enough if it cannot be manufactured and assembled in an efficient way. The implementation of the design for assembly (DFA) approach during product design is to improve the productivity. The application of DFA presents several advantages as follows:


During the first stage, the main task is to determine the minimum number of components. The calculation of the minimum number of components is determined by considering whether the components can deliver the required functions for the product. It is advised to carry out a discussion on the four questions as follows:


If the answer to any of the above questions is yes, the component should exist in a standalone way. During the second stage, the main task is to analyze and measure the manual handling and manual insertion of each component:

10. Manual handling: This deals with the motions including grabbing, transporting and positioning components and their direction.


#### 4.4.1. Structure Tree of Design Schemes

A graphical description is used to build up the assembly sequence of the assembling process. Each design idea is presented in exploded view drawing. The dimensions of each component are marked in the three-view drawing of each component. The sequence is shown in Figures 19–22.

Idea 1:

**Figure 19.** Exploded view drawing of the assembly of Idea 1.

Idea 2:

**Figure 20.** Exploded view drawing of the assembly of Idea 2.

Idea 3:

**Figure 21.** Exploded view drawing of the assembly of Idea 3.

Idea 4:

**Figure 22.** Exploded view drawing of the assembly of Idea 4.

In order to calculate the assembly efficiency, assembly time and assembly cost according to the DFMA table, each component of these four design ideas was displayed separately and its length, width and height are marked in the drawing.

#### 4.4.2. DFMA Analysis of the B and D of Design Ideas

After the dimensions of each component were determined in the exploded view drawing, the data was filled into the DFMA table. At the completion of this table, the total assembly time, total assembly cost and the necessity of each component of each design concept could be determined.

#### *4.5. Analysis of the 'Assemblability' Evaluation Results*

After the assembly time and cost of these four design ideas were determined, the change rate of the component numbers and that of the assembly time are shown in Table 9.


**Table 9.** Comparison of assembly e fficiency of each component.

It is known from Table 9 that the improvement of Idea 2 is the optimal one among these four design ideas and it is more suitable for improvement from the assembly e fficiency. The optimal sequence of the assembly e fficiency of these four design ideas is as follows:

Idea 1 ≥ Idea4 > Idea3 > Idea 2

After that, the next section is to investigate the consideration from the usability aspect. The sequence that was obtained from the engineering aspect is included for a comprehensive investigation.

#### **5. Correlation Between Assembly Design and Usability Operation**

The influence of the items at the upper level on the child levels can be determined from the procedure in the above section. In order to make the weights at the upper level suitable for the decision of the design scheme replacement, the application of βvalue should be discussed as follows [18].

#### *5.1. Definition of* β *Value*

A suitable β value is a ffected by each item's weighting function (*Wi*) and fuzzy probability (*rij*). Therefore, β value often varies with the weighting function (*Wi*) and fuzzy probability (*rij*).

The method of M(\*,<sup>+</sup>,β) is also called the generalized weighted mean method. The definition is as follows:

$$\sigma\_{\vec{\beta}} = \{ \sum\_{i=1}^{m} w\_i \times r\_{i\vec{\beta}} \beta \rangle \times \frac{1}{\beta}, \, \mathbf{j} = 1, 2, \, \dots, \, \text{n.} \tag{5}$$

An additional index β is adopted and the β value is in the range of −∞ to +∞. The β value is determined by the designers according to attribute of each problem.

Under the condition that W1 = 0.15, W2 = 0.15, W3 = 0.25, W4 = 0.175, W5 = 0.275 for the weighting functions, the variation in the membership function can be determined.

#### *5.2. Influence of the Weighting Function*

In order to test the di fference between the weighting functions, the results of these five di fferent weighting functions (W1, W2, W3, W4, W5) were reviewed as follows:


#### *5.3. Fuzzy Average Predicted Values*

In order to make decisions on a single β value, the detailed fuzzy average predicted values can be determined for decision-making. They can be expressed by the following equation [19].

$$S = \int\_{\beta 1}^{\beta 2} ej(\beta) d\beta / \int\_{\beta 1}^{\beta 2} d\beta \tag{6}$$

The β1 and β2 values are the upper and lower limits and a decision is made between these two values. *ej* (β) indicated the membership function of the *j*th design idea. The values are shown in Table 10 as follows.


**Table 10.** Fuzzy average predicted values of four design ideas.

(\* indicated the highest value of correlation).

It is known from the above table that Idea 2 has the highest membership value. Therefore, by strengthening the weighting relationship between five different considerations, it can be observed that Idea 2 is the optimal and the most suitable decision. The overall product is shown in Figure 23 as follows.

**Figure 23.** Idea 2 as the optimal idea.

#### *5.4. Results and Analysis of the Correlation Between Assembly and Usage*

Under the condition of weighting functions of W1 = 0.15, W2 = 0.15, W3 = 0.25, W4 = 0.175, W5 = 0.275, the variation in the membership functions can be determined. It is known from the consideration of usability that, the ranking of the design ideas according to the participants' preference is as follows.

Idea 2 > Idea 1 > Idea3 > Idea4

Moreover, the comparison to the sequence of assembly design is shown in Table 11.

> **Table 11.** Comparison of the correlation between assembly design and usability.


It is known from Table 11 that Idea 1 and Idea 3 are ranked higher from the aspect of engineering and usability. Therefore, if a company is planning to roll out new stereo systems, it is advised to extract some design elements that meet consumer demands from Idea 1 and Idea 3 for the consideration of product innovation.

#### **6. Conclusions and Recommendation**

An evaluation system for assembly design and usability operation complexity was proposed in this study. The problems that are related to product designs were handled by computers. The decision-making on the assembly sequence was assisted by the calculation of matrices according to the principles of assembly design. This approach can reduce the errors and problems due to personal factors of the operators. The potential interference problems between components of a product can also be eliminated by computer-aided analysis during the assembly process.

The fuzzy theory was applied to the decision-making from the concept development stage to sketches and finally to the product mock-ups. The participants were allowed to simulate the mechanical movements of these four di fferent design ideas. From the scores that were given by the participants, the optimal design concept can be determined. The design ideas were ranked from the consideration of usability without considering much of the engineering aspect. Therefore, the engineering evaluation was accomplished by DFA, which can calculate the assembly e fficiency, assembly time and cost of these four design ideas. From the consideration of the DFA engineering aspect, the ranking of these four design ideas can also be determined. This approach can not only improve the usability but can also enhance a product's value from the engineering aspect for the reference of follow-up research.

The development process of each product involves the joint endeavor of many departments. Therefore, when constructing the decision model of a product, it is required to correlate the design logics prior to and after each process. The considerations include the development basis of sketches, the parametric configuration of modeling, the simulation of mechanisms of the assembly and the

questionnaire design. The correlation between weighting functions and the transformation of the questionnaire into engineering parameters for further application are also important and should follow the strict rule.

In order to respond to the rapid changes in market demands, a product designer needs to develop a design and production approach that can adapt to the rapid changes in product styles. Therefore, a product designer is required to create designs that present di fferent ways of using or di fferent appearances in order to satisfy various consumer demands such as various types of co ffee machines and speaker systems. Meanwhile, in order to broaden the usage range for consumers, a product design approach is expected to allow designers to increase or decrease the number of functional components while the product appearance remains the same. Alternatively, a di fferent product style can be created by altering the pattern of one of the internal components such as various types of desktop computers. Under the market mechanism, a product designer needs to carry out the development of product variability in order to enhance a product's competitiveness on the market, by satisfying di fferent consumer usage models or di fferent preferences.

This study aims to connect the manufacturing end to the user end so that a simple and basic assembly planning can be realized during the earlier design stage. Via the concurrent engineering concept, the product design quality and e fficiency can be enhanced. Moreover, via the engineering-oriented assembly consideration and the user-oriented consideration, a designer is allowed to consider design feasibility during the earlier design stage so that the final product can be accepted and recognized by general users.

**Funding:** This work was supported by the Ministry of Science and Technology of the Republic of China under gran<sup>t</sup> MOST 107-2635-E-468-001.

**Conflicts of Interest:** The authors declare no conflict of interest.
