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Abdi and Labib 8 contributed an overall approach of grouping products into families based on operational similarities, when machines are still not identified. Scholz-Reiter et al. Shneor 10 presented the design and implementation of modular machine subsystems that enables various machining processes on the same computer numerical control CNC vertical milling machine.

Aguilar et al. Padayachee and Bright 12 focused on aspects of the mechanical design and the development of a control system that supported the modularity and reconfigurability of the mechanical platform and presented a modular electronic system that is characterized by a plug-and-play approach to control scalability.

Son et al. Dhupia et al. Adamietz et al. Modular design was studied as the main method for RMS reconstruction. Mpofu 16 proposed a hierarchical classification mechanism for machine structures, these structures derive from module combinations where symbology is utilized to represent the machines and these symbols can be used in the configuration process.

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Sibanda et al. The framework provides a guide for designers and manufactures of sheet metal machines in developing the new machine. Xia et al. Mpofu and Tlale 20 presented an effective method that uses multi-level fuzzy decisions to create dynamic optimal configurations of machine structures with respect to a given part geometry. Gadalla and Xue 21 introduced an optimization approach for the design of an RMT based on evaluations to both the different machine configurations and the reconfiguration processes to change between machine configurations.

Strasser et al. Ashraf and Hasan 23 proposed a framework for configuration selection for a manufacturing flow line and demonstrated using non-dominated sorting genetic algorithm-II NSGA-II. Huang et al. Jiang et al. Different methods of analysing, evaluating and optimizing RMS have also been proposed. Mittal and Jain 27 focused on the performance measures and the way to find the best configuration for RMS among various performance measures like ramp-up time, cost, reliability, availability, lead time and reconfiguration time that affect the performance of the RMS.

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Liao and Lee 28 introduced a methodology for designing a reconfigurable prognostics platform which can be easily and effectively used to assess and predict the performance of machine tools. Lorenzer et al. Goyal et al. Youssef et al. Yu et al. The design schemes of the RMS need to be evaluated to obtain the best results. The evaluation involves the following two aspects: evaluation indicators and evaluation algorithms. Due to the criteria multiplicity and information uncertainty evaluations, the evaluation of machine tool design schemes has been examined to quantify the indicators and address the uncertainties in the evaluation process; furthermore, schemes have been evaluated, calculated, sorted and optimized.

For this reason, a multi-attribute decision-making MADM method based on VIKOR for evaluating the reconfiguration schemes of a machine tool is proposed, and the best design proposal is obtained through the quantitative evaluation of three evaluation indicators including the module chain MC similarity, module interface complexity and reconfiguration cost. The similarity between reconfiguration module RM and prototype module PM shows the module utilization in the process of machine tool reconfiguration, including the similarities in layout, function, quantity and physics of the module.

Layout similarity means that the layouts of RM and PM, such as the positional relationship, the connection mode and the arrangement mode, are similar. Functional similarity means that the functional properties of RM and PM, such as the machining speed and the acceleration, load and torque, are similar. The quantity similarity relationship refers to the similar relationship between the number of components in the RM and the PM, such as adding or deleting components in the module when modifying the module. Quantity similarity means that the number of internal parts of RM and PM is similar.

Physical similarity means that the transfer mode of internal energy, information or material flows between RM and PM is similar. The following three aspects in the reconfiguration evaluation should be considered: the degree of similarity between RMT and PMT, the complexity of the module interface and the cost of the reconfiguration. The chain structure of machine tool modules to accomplish a certain function is defined as an MC. Module interface complexity is an important indicator that affects the assembly and disassembly characteristics of RMT.

Non-destructive methods should be adopted as far as possible for module disassembly in the reconfiguration process to increase the module reloading efficiency and reuse probability.

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Entropy, as an effective concept for expressing the amount of information, can be used to measure the interface complexity between modules. In the assembly and disassembly process, the smaller the information entropy of the module interface complexity, the less the difficulty of the assembly and disassembly.

According to the assembly and disassembly characteristics of the module, an interface number relation matrix R M as shown in equation 3 is constructed, where element N M p , q represents the number of interfaces between module p and module q.

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According to the concept of information entropy, the module interface complexity relationship is defined as shown in equation 4. The reconfiguration costs of a machine tool mainly include auxiliary costs, demand costs and module reconfiguration losses. Auxiliary costs include labour costs and resource costs, of which labour costs are used to disassemble and assemble modules in the process of machine reconfiguration, and resource costs are used for the purchase, rental and energy consumption of auxiliary tools needed for reconfiguration. Demand costs are used for module purchases, leases and other expenses resulting from production changes.

Module reconfiguration losses refer to the value loss caused by damage to the module structure, performance and so on during the reconfiguration process. G i j is calculated as shown in equation 6. Step 1. For decision alternatives A 1 , A 2 , … , A m , build a standardized decision matrix D based on evaluation attributes X 1 , X 2 , … , X n such as MC similarity, interface complexity and reconfiguration cost as in equation 8. Step 2. Profitable attributes are the MC similarity, and cost attributes are the interface complexity and reconfiguration cost.

Step 3. Calculate group benefit S i and individual regret Q i. Equation 11 shows that when p is small e. As p increases, individual regrets gradually gain more attention; thus, min i S i is used to maximize group interests. Equation 12 represents individual regret, and min i Q i focuses on minimizing individual regrets. Step 4. Calculate the comprehensive index R i generated by each scheme.

Step 5. Sort the alternatives in ascending order of R i , S i and Q i and determine the compromise solution, where the solution that satisfies both C1 and C2 and in which R i is the minimum is the optimal solution. Equation 14 is a necessary condition for the first scheme to be significantly better than the second scheme, and the schemes are compared in turn when there are multiple schemes. After sorting according to R values, the value of S or Q of the first scheme must be better than that of the second scheme, and the schemes are compared in turn when there are multiple schemes.

If C1 and C2 cannot be satisfied at the same time, a compromise set is obtained. If the relationship between the first scheme and the second scheme only satisfies C2, both schemes are considered to be optimal schemes. If C1 is not satisfied between the first scheme and other schemes, and only C2 is satisfied, then these schemes are considered to be the optimal schemes close to the ideal scheme.

Based on the module composition of the PMT and the machining feature of the part to be machined, five process plans are obtained for the part. The RM of each programme is shown in Table 1. The MC similarity and interface complexity of the RMT are determined by the structure position and the connection mode of the modules. The risk-free interest rate of the reconfiguration cost is calculated using the 1-year fixed deposit interest rate of 3. The expected discount rate is. The above five process schemes are evaluated according to the three evaluation criteria including the MC similarity, interface complexity and reconfiguration cost, and the obtained values are standardized as shown in Table 2.

Table 2. Decision indicator attribute value after normalization. The MC similarity is an efficiency index, and the interface complexity and the reconfiguration cost are cost indicators, which can be obtained according to Table 2. The values of R , S and Q for each alternative are calculated according to equation 16 , and the results are shown in Table 3.

Table 3. The group benefit of A 1 is the greatest, but the individual regret is slightly insufficient; the individual regret of A 4 is the smallest, and the group benefit is second only to A 1. Comprehensively comparing the two solutions, the gap between the advantages and of the two solutions is not obvious, so both are selected as the optimal solution. To compare the effectiveness of the proposed method, simple average weighting SAW and technique for order preference by similarity to an ideal solution TOPSIS are used to evaluate the alternatives. SAW is a weighted linear combination or scoring technique, which is based on the weighted average and an evaluation score is measured by multiplying the normalized value of each criteria for the objectives with the importance of the criteria.

The objectives could be ranked and objective with the highest score is selected as the preferred one. The comparison results of the three methods are shown in Table 4. Table 4.

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From Table 4 , it can be seen that the ranking results obtained by the three methods are basically the same. Therefore, the proposed method is reasonable and feasible for evaluating the performance of the RMT reconstruction scheme. In addition, the decision value obtained by the proposed method is more distinct than the value obtained by SAW and TOPSIS, which can provide more accurate evaluation information for decision makers. This result is also consistent with the research conclusions of Opricovic and Tzeng.