## 3 Quantitative Analysis by the Analytic Hierarchy Process (AHP)  
Evaluating the efficiency of a process qualitatively with respect to various criteria for finding the optimum solution is not an easy task; however, using quantitative analysis, such as the analytic hierarchy process (AHP) [12; 13], provides a good solution to satisfy this objective. In the present case study of the assembly of a brake disc, the considered evaluation criteria are productivity, human fatigue, safety, and quality. While the comparative solutions are one that employs a human-only system and one that is based on a human-robot collaboration system, AHP analysis is used as the evaluation methodology. The four criteria of productivity, human fatigue, safety, and quality were considered the most important by both the factory managers and the expert personnel involved in this activity; other criteria were ignored since they would not significantly affect this human-robot collaboration procedure. To implement this activity, three expert personnel participated in decision-making and planning, and they support the author's choice of the AHP method to evaluate the efficiency of the human-robot collaboration. The AHP analysis proposed by References [14; 15; 16; 17; 18] is defined in eight general steps, as follows:  
1. Identify the problem and define the goals. 2. Construct the general framework of the AHP analysis in a hierarchically descending order; this means that the objective set at the highest level is followed by the criteria set at the intermediate levels, and then solutions, which are set at the lowest levels. 3. Use the pair-wise comparison scale for AHP preference from References [14; 15; 16; 17; 18], ranging from 1-9 (intensity of importance) as shown in Table 1. In this scale, 1 expresses the equally-preferred status and 9 expresses the extremely-preferred status. 4. Construct the pair-wise comparison matrix for the four criteria, as in Tables 2 and 3. Figure 1: Brake disc elements for assembly operation. (**a**) First step; (**b**) Second step; (**c**) Third step; (**d**) Fourth step; (**e**) Fifth step. Figure 2: The sequence steps of the manual brake disc assembly on the production line. (**a**) First step; (**b**) Second step; (**c**) Third step; (**d**) Fourth step; (**e**) Fifth step. Construct the pair-wise comparison matrices of alternatives for each specific criterion; this means that if there are n criteria and m alternatives available in the procedure, there should be n matrices with the size of m \(\times\) m, as in Tables 4-7. 6. Construct the synthesized comparison matrices of alternatives for each specific criterion to calculate the priority vectors; each value of the synthesized matrix is calculated by dividing the same element in Tables 4-7 by the summation of its column. Each priority vector is then calculated as the average of the new matrix row, as shown in Tables 4-7. 7. Calculate the consistency ratio for the pair-wise matrix of the four criteria to check the consistency of the analysis comparisons. 8. Construct the priority matrix of alternatives (solutions), as in Table 8.  
The pair-wise comparison matrix of the four criteria, as reported in Tables 2 and 3, aims to show the importance of one criterion over the others [18]. In this research, the intensity and importance of each criteria was chosen through a group decision. This sorted out that (see the columns of Table 2) the safety factor has the highest importance intensity, followed by productivity and quality factors, while the human fatigue factor has the lowest importance intensity. The pair-wise comparison of alternatives with respect to each criterion is evaluated at steps 4 and 5 based on the actual system operation. The use of a human-robot collaboration design can give a greater importance to productivity and quality factors so that they have, comparatively, the same intensity and importance to reach the goal in the assembly of the brake disc (Tables 4 and 5).