3.3 Failure cause analysis of machine tools

2.6 Coefficients of similarity and dissimilarity

per Eqs. (8) and (9).

selected case studies are as follows.

extensively vital.

124

3.2 Selection of industrial robot

3.1 Machinability evaluation of work materials

The calculation is being performed for similarity and dissimilarity coefficients as

3. Case studies on graph theory: a view on real-life problem solving

Computer Architecture in Industrial, Biomechanical and Biomedical Engineering

There are so many investigations that have been carried out by the numerous researchers throughout the globe in the domain of graph theory and its allied approaches to study and analyze the method's applicability and reliability. The further optimization of the process under the study can also help the investigator to attain better and effective research outcomes [1, 14]. The discussion has also been explored by incorporating the possibilities to use the artificial intelligence-inspired logics in collaboration with the established graph theory approach. In this way, some case studies are reviewed and presented below to provide an overview which can explore about the major findings of the researches persuaded and the stateof-the-art representation of past investigations in the best conclusive manner. The

Rao and Gandhi [8, 9] have presented a graph theory-based methodology with a view to evaluate the machinability of work materials for a given machining operation. They have proposed a universal machinability index that evaluates and ranks work materials for a given machining operation. The development of a digraph was also conducted to reflect the machinability attributes and their relative importance for the operation considered. The coefficients of similarity and dissimilarity and the identification sets have also been proposed. Disparate the traditional methods which adopt only one of the machinability assessment criteria, their proposed method has considered all of the criteria simultaneously and gives the correct and complete evaluation of the machinability of work materials. They have concluded that their proposed universal machinability index evaluates and ranks work materials for the considered machining operation. When it comes to taking the combined advantages of the features of artificial intelligence with the graph theory approach, the process moderation always becomes more crucial to consider. The requirements of the end customer regarding the produced goods further become

Rao and Padmanabhan [15] have conducted a research study based on graph theory method for the evaluation of alternative industrial robots. They have attained a robot selection index that evaluates and ranks robots for a considered industrial application. The calculated index was obtained from a robot selection attribute function, obtained from the robot selection attribute digraph. They have reported that the obtained similarity index from robot selection attribute function which was quite useful for easy storage and retrieval of the data. The proposed study was a general methodology, and there can be any number of quantitative and qualitative robot selection attributes simultaneously and offers a more objective, simple, and consistent robot selection approach. Their proposed robot selection index has been utilized to evaluate and rank the robots for the selected robot selection problem. In addition, the expectation of the end user of the robotic system

Rao and Gandhi [8, 9] have analyzed the failure reasons of a machine tool by means of digraph and matrix approaches. The machine tool failure causation digraph has been modeled a failure reason taking into deliberation its failurebacking actions and their contact in terms of the reason—consequence relationship. After that, they have determined machine tool failure causation function from the machine tool failure causation matrix. The said matrix was attained through the digraph, which is distinctive of the failure root. The obtained function was not only convenient for failure reason analysis but likewise for comparison and appraisal of the failure reason. In addition, the machine tool failure causality index, derived from the machine tool failure causality function, had also been proposed, which evaluated and ranked the failure causes of a machine tool.

The attained machine tool failure causation function has identified the backing failure occasions of a machine tool that were decisive for minimization of the failure root and also supports in contrast and assessment of the failure source of a machine tool. The arithmetical value of the machine tool failure causation function has also been computed and named as the machine tool failure cause index. This index has been concluded as a measure of the severity of the failure cause. Furthermore, an artificial intelligence-inspired fuzzy logic-based system can properly help to make the problem more realistic, and the causes of the tool failures can be resolved out or eliminated [18, 19]. The AI-based process optimization is another domain where the failure reduction and the overall performance improvement can be settled out.

### 3.4 Selection of rapid prototyping process

Rao and Padmanabhan [20] have employed a graph theory-based methodology for selection of a rapid prototyping (RP) process that best suits the end use of a given product or part. The "rapid prototyping process selection index" has been also anticipated to estimate and rank the RP progressions for constructing a given product. The index was gained from an RP procedure assortment attribute function, acquired from the RP course selection attribute digraph. The digraph is established considering RP method assortment attributes and their relative importance for the deliberated application. The projected process reflects RP process variety attributes and their interrelations, and the RP process assortment index evaluates and ranks RP processes for a given RP procedure collection problem. The projected method was observed as a broad technique and capable to deliberate any number of measurable and qualitative RP course assortment attributes concurrently and proposes a more objective and modest RP method selection approach.

#### 3.5 Performance evaluation of carbide compacting die

Jangra et al. [21, 22] conducted a study to assess the concert of carbide compacting die by means of graph theory approach (GTA). Factors influencing the die performance and their relations were analyzed by evolving a mathematical model by employing the digraph-based matrix method. The die performance index was attained through the matrix model established from the developed digraphs. This index value has compared and ranked the factors distressing the die

performance. They have considered several process output errors such as dimensional inaccuracy, large surface craters, deep recast layers, etc. that have been minimized during die manufacturing which further helps to achieve better die performance. They have formed a group of factors upsetting the presentation of carbide compacting die into major five factors, viz., machine tool, work material, the geometry of die, tool electrode, and processing operation. The GTA procedure revealed that the machine tool had the maximum value of the index. Consequently, they have considered it as the utmost persuading factor influencing the die performance. Furthermore, they have also reported that in the event of die material, low cobalt concentration and lesser grain size harvest decent surface finish, while in machine tool, low discharge energy and high dielectric flow rate yield good surface finish. In the case of die geometry, large workpiece thickness and small taper angles result in lesser geometrical deviations.

Through this methodology, they have quantified the weak and strong factors which help in efficient process planning during die manufacturing, consequently. The GTA practice revealed that the machine tool had an uppermost value of the computed index. Therefore, it was considered as the most influencing parameter affecting the die performance.

While in respect of the die material, small grain size and low cobalt concentration yielded decent surface finish; however, in the case of the machine tool, low discharge energy and high dielectric flow rate yielded good surface finish and hence favors the good die performance. In the case of die geometry, large workpiece thickness and small taper angles reported in slighter geometrical deviances hence aid to attain better die performance. Die performance was articulated in terms of an index. This index value was depending on the inheritance of main factors which was further depending on their sub-factors. Therefore, a suitable combination of the sub-system and their sub-factors could easily be selected for the required die performance.

3.6 Analysis and evaluation of product design

Triangular membership functions of fuzzy system.

DOI: http://dx.doi.org/10.5772/intechopen.82011

selected as the finest one.

127

Figure 3.

Paramasivam and Senthil [1] have explored that the product design evaluation is essential for all manufacturing industries to explore the soundness and effectiveness of the product design. In their study, they presented a mathematical model for evaluating and analyzing the product design alternatives using graph theory and matrix approach. The different contributing factors were identified, and their relative importance was considered. A digraph model was constructed to represent the abstract information of the product design which takes into account all the factors. The digraph model was then transformed into a matrix form, which further was employed for computer processing. A permanent index was attained from the product design appraisal function, consequent from the matrix for all product design substitutes, and it showed the effectiveness of the product design. The indices were also deliberated for all the alternatives under study, and they were graded in rising order, and the product design analogous to the first rank was

Decision-Making in Real-Life Industrial Environment through Graph Theory Approach

Their proposed practice was quite adaptable from the opinion that it incorporates all factors of the product design. The GTM method was explored as pertinent to any product design entailing of any number of variables. The utility of matrix algebra was found to be expedient both for pictorial and computer analysis. The product design assessment index has represented the product design features and was useful in positioning the several product models based on the design facets. It was also concluded that the GTM method can be applicable to various problems of incompatible nature and to the problems, where the measurable data are not obtainable, i.e., machine cell layout analysis, material handling system evaluation, vehicle routing optimization, supplier selection problem, etc. Furthermore, the

Singh et al. [23] have reported the optimization of the process inputs while processing composite material using ultrasonic machining using fuzzy logic-based smart decision- and rule making. The overall fuzzy system possesses the basic elements particularly fuzzy sets, fuzzy rulings, fuzzy inference, membership functions, and defuzzification [24–26]. The basic fuzzy logic system is illustrated in Figure 2. They have also explored the utility of the fuzzy logic-based ruling for the proper implementation of the human neural system logics. Figure 3 is describing the employed triangular membership functions for the composite problem [23].

Figure 2. The fuzzy logic system.

Decision-Making in Real-Life Industrial Environment through Graph Theory Approach DOI: http://dx.doi.org/10.5772/intechopen.82011

#### Figure 3.

performance. They have considered several process output errors such as dimensional inaccuracy, large surface craters, deep recast layers, etc. that have been minimized during die manufacturing which further helps to achieve better die performance. They have formed a group of factors upsetting the presentation of carbide compacting die into major five factors, viz., machine tool, work material, the geometry of die, tool electrode, and processing operation. The GTA procedure revealed that the machine tool had the maximum value of the index. Consequently, they have considered it as the utmost persuading factor influencing the die performance. Furthermore, they have also reported that in the event of die material, low cobalt concentration and lesser grain size harvest decent surface finish, while in machine tool, low discharge energy and high dielectric flow rate yield good surface finish. In the case of die geometry, large workpiece thickness and small taper angles

Computer Architecture in Industrial, Biomechanical and Biomedical Engineering

Through this methodology, they have quantified the weak and strong factors which help in efficient process planning during die manufacturing, consequently. The GTA practice revealed that the machine tool had an uppermost value of the computed index. Therefore, it was considered as the most influencing parameter

While in respect of the die material, small grain size and low cobalt concentration yielded decent surface finish; however, in the case of the machine tool, low discharge energy and high dielectric flow rate yielded good surface finish and hence favors the good die performance. In the case of die geometry, large workpiece thickness and small taper angles reported in slighter geometrical deviances hence aid to attain better die performance. Die performance was articulated in terms of an index. This index value was depending on the inheritance of main factors which was further depending on their sub-factors. Therefore, a suitable combination of the sub-system and their sub-factors could easily be selected for the required die

Singh et al. [23] have reported the optimization of the process inputs while processing composite material using ultrasonic machining using fuzzy logic-based smart decision- and rule making. The overall fuzzy system possesses the basic elements particularly fuzzy sets, fuzzy rulings, fuzzy inference, membership functions, and defuzzification [24–26]. The basic fuzzy logic system is illustrated in Figure 2. They have also explored the utility of the fuzzy logic-based ruling for the proper implementation of the human neural system logics. Figure 3 is describing the employed triangular membership functions for the composite problem [23].

result in lesser geometrical deviations.

affecting the die performance.

performance.

Figure 2.

126

The fuzzy logic system.

Triangular membership functions of fuzzy system.

#### 3.6 Analysis and evaluation of product design

Paramasivam and Senthil [1] have explored that the product design evaluation is essential for all manufacturing industries to explore the soundness and effectiveness of the product design. In their study, they presented a mathematical model for evaluating and analyzing the product design alternatives using graph theory and matrix approach. The different contributing factors were identified, and their relative importance was considered. A digraph model was constructed to represent the abstract information of the product design which takes into account all the factors. The digraph model was then transformed into a matrix form, which further was employed for computer processing. A permanent index was attained from the product design appraisal function, consequent from the matrix for all product design substitutes, and it showed the effectiveness of the product design. The indices were also deliberated for all the alternatives under study, and they were graded in rising order, and the product design analogous to the first rank was selected as the finest one.

Their proposed practice was quite adaptable from the opinion that it incorporates all factors of the product design. The GTM method was explored as pertinent to any product design entailing of any number of variables. The utility of matrix algebra was found to be expedient both for pictorial and computer analysis. The product design assessment index has represented the product design features and was useful in positioning the several product models based on the design facets. It was also concluded that the GTM method can be applicable to various problems of incompatible nature and to the problems, where the measurable data are not obtainable, i.e., machine cell layout analysis, material handling system evaluation, vehicle routing optimization, supplier selection problem, etc. Furthermore, the
