Assessment of the Design for Assembly processes using fuzzy logic

The paper presents methodology for designing the production process of a new product from the point of view of the assembly operations technology criterion (Design for Assembly DFA) in the conditions of high-volume production. Mentioned are DFA methods and techniques used in the implementation of a new product. Author presents a new method for assessing design for manufacturability based on fuzzy variables based on fuzzy variables. An example was given to illustrate the proposed course of action


Introduction
In today's market conditions, the company introducing new products to the production, use different methods and techniques to rationalize actions that make up the concept of pre-production. The issue has a rich literature, different philosophies are presented there to rationalize the production process sequences, for example. Six Sigma, Lean, WCM, Target Costing [1,15,23].
In the conditions of high production volume, when implement new products, less attention is due to the ever-wider technological possibilities of contemporary workplaces, workshop aids, automation, the high performance achieved and relatively low costs, devoted to the processing of elements, components of final products. Hence reported in literature advanced evaluation methods of products design manufacturability tailored to evaluate the implementation of a new product in the conditions of high volume mass production and are directed to processes for assembly. This is due to the high proportion of manual work compared to machining, which is associated with high labour intensity and high costs of assembly processes.
In the production of individual and small-batch main attention is paid to the issue of the possibility to implement in the plant, the possibility of cooperative companies, as well as the determinants of the logistic flow of resources. Therefore, much attention is paid to the performance of the production cost target, taking into account investments in new production lines and positions, defined in terms of having to be carried out also other products and vision of the future production program [7,9,17].

Production preparation process
In the automotive industry, proposals for the use of design-oriented assessment methods for assembly. "Design for Assembly" -DFA, was described by G. Boothroyd and P. Dewhurst in the work "Design for Assembly, A Designers Handbook" in 1983. The concept of "Design for Assembly" can be defined in various ways, from the narrow meaning of "product design from the point of view of manufacturability criterion" to the broader term associated with "product and process design from the cost-effective criterion point of view and reliable manufacturing to ensure the state of customer satisfaction " [18]. Many DFA methods are presented in the literature. The chronology of these methods and their brief characteristics are presented in Table 1. [16]. The method is based on determining the costs associated with the manual or automatic assembly process and has three criteria to limit the number of components.

5.
Integrated The first and the second method are presented in the paper, due to the largest application in practice. Market conditions have forced companies to rationalize a comprehensive approach to the design and marketing of a new product [2,4,5,23]. The need for a broader look at the assessment of the technology of the structure, including this problem, take into account many other aspects, this way of design is illustrated in Fig. 1. In the design process under the aforementioned philosophies have been used methods such as QFD (Quality Function Deployment) [1,10,13] use in processes of implement products customer requirements, FMEA (Failure Mode and Effect Analysis) [19] -related to the prediction and prevention of problems at the product design stage, DFX (Design for X) [23] -e.g. Design for Manufacturing (DFM) regarding the shaping of the design process of components and the product itself [6]. Decisions taken at the product design stage have a significant impact on production costs, efficiency and quality of production. Supporting methods such as modelling, simulation and animation of production processes and systems as well as stimulating innovation such as brainstorming, TRIZ is of great importance in carrying out these works.

Methods of assembly manufacturability assessment
This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation as well as the experimental conclusions that can be drawn.

Lucas DFA method
The method was developed in 1980 by Lucas and University of Hull research teams. The method is used for manual or automatic assembly analysis. The method includes aims to reduce the number of components of the final product, the use of shape the structure of components to facilitate assembly. In the Lucas DFA method, three indicators determine the measure of mounting difficulty. [21] The procedure is as follows. The prepared project is subjected to functional analysis, which determines whether individual components are needed and what their functions are - fig. 2. The project efficiency index based on functional analysis is determined by the formula where: Wep -project efficiency index, LkA -number of A components (fulfill product functions), LkB -number of B components (characterized by lack of fulfill product functions, e.g. rivets, washers). Based on the analysis carried out in this way, it is possible to combine some separate components into one whole, thus reducing the number of individual components that make up the final product, change the design solutions that eliminate components that do not fulfill the function of the product. Then, an analysis is carried out consisting of an analysis of the displacement of the mounted components, their maneuvering and the method of assembly itself. [21] The maneuvering assessment of the assembled product components is determined on the basis of fig. 8.
The Wman maneuvering factor is given by the formula: where: Wman -maneuvering coefficient, Iman -maneuvering index, LpA, LpB, LpC, LpD -values read from tables related to the size and weight of parts, difficulty with maneuvering, assembly orientations.
The formula describing the results of the analysis of the Was feasibility factor according to the Lucas DFA method is:

The Boothroyd Dewhurst method
The method was developed in the late 1970s. by prof. Geoffrey Boothroyd at the University of Massachusetts in Amherst in cooperation with the University of Salford in UK. The method, like the previous one, aims to: reduce the number of components, eliminate rework, use self-positioning and self-embedding components, provide adequate access and unrestricted field of view, ensure ease of assemble parts with looseness, minimizing the need for reorientation during assembly, eliminating parts, which cannot be installed incorrectly, maximizing symmetrical parts, if possible, or if not asymmetrical. The method assumes that the part is a permanent or non-permanent element of the assembly process. A subassembly is considered a part of it is added during assembly. Each part has two parameters -thickness and size (adhesives, fluxes, fillers, etc., used to connect parts are not considered parts) - Fig. 3. Thickness is the length of the shortest side of the smallest cuboid that surrounds the element. If the element has a cylindrical or regular polygonal shape, e.g. a section with five or more sides, the thickness is defined as the radius of the smallest cylinder that surrounds the element. The size is the length of the longest side of the smallest cuboid that can surround the part.  Determining alpha and beta angles [5] BETA is the symmetry of the part relative to the insertion axis, i.e. the smallest rotation angle for correct insertion. ALFA is the symmetry of the part about the axis perpendicular to the insertion direction -the smallest angle between alternative insertion directions [5] (G. Boothroyd, 1983). After determining the thickness, size, BETA and ALFA angles, the method is shown in Fig. 5.

Figura.5. Proceedings in the Boothroyd-Dewhurst for Assembly method
The indexes for handling time and insertion (assembly) time of individual elements are determined. A special table prepared by Boothroyd and Dewhurst serves this purpose. By specifying the time index of element manipulation, you can specify whether the manipulation can be performed: with one hand, one hand with an auxiliary handle, two hands, two hands with mechanical assistance. Knowing the assembly times, you can proceed to process analysis, e.g. whether the number of assembled parts should be reduced, replace them other more complex. This method is used to analyze manual assembly, separate variants of the method are used to analyze automatic assembly. The final step is to calculate the sum of the number of operations, the total operation time, the total cost of the operation, the theoretical minimum number of parts and the DFMA index.
where: Lo -number of operations, loi -assembly operation where: To -the total operation time, toi -operation time, Ima -time index manipulation operations, Imo -time index assembly operations where Ko -cost of the process; loi -an index (number) process operations; koi -average individual process treatment cost where: Ct -the theoretical minimum number of elements; Cpe -number of elements before the elimination analysis; Cae -the number of parts eliminated in the analysis of elimination where: DFMAindex -DFMA index; A -the number of parts necessary for the functioning of the product for a large number of parts it can be assumed that: Lo = A, (the study assumes that Lo = A = Ct); ta -assembly time of basic ideal part (based on Boothoroyd ta = 3s); To -the total assembly time of the product).

Assumptions for the new DFA method
The justification for the emergence of a new fuzzy method for assessing the technology of the structure results from the observed lack of flexibility of the described methods of Boothroyd-Dewhurst and Lucas. These methods were created in the 1980s in the conditions of needs of the economy focused on serial and mass production. The current development of the economy and technology means that the modern economic system is characterized by a much greater need for flexibility in terms of production methods: high volume, low volume and unit. The need to create a more flexible method adaptable to the type of production is noticeable [3].
The design process should be determined from the point of view of various usability criteria - Fig. 6. The assessment should take into account many other various factors, sales, service, spare parts availability, production series, types of equipment, available assembly techniques, level of automation, cooperative services, possibilities of application commercial components, crew technical culture, etc. In small-lot and serial production conditions, the design process of new product production is based on simplified production documentation [9]. Due to the low production series, production data result from the project are rarely verified at the production stage, while the experience gained from this stage is used in the production projects of new products. In relation to mass production and mass production, particular attention from the point of view of cost criterion is paid to: the possibility to use unified and standardized elements included in the final product, the use of work stations and workshop aids for processing and assembly of various elements included in the products making up the program production and introduction of group machining processes, process phases, group operations for various elements [22]. The newly proposed method use fuzzy inference is characterized by such flexibility [11,20]. Experts determine to use method tables, e.g. Boothroyd or Lucas, in accordance with the order of the process for each component of the product design, make an assessment on a scale of 0 to 100. Then the process of the machining process and the assembly process are evaluated. The method was developed on the basis of the proposed General Scheme of Technology Assessment and consists of three stages: assessment of machining efficiency, assessment of assembly efficiency, assessment of production organization efficiency [14].
The assessment is related to the set of linguistic variables Vi = {V1, ..., Vn}, and ∊N -{0}, defining the input and output criteria of technology. The linguistic variable Vi is described by a quadrangle: The assessment of machining processability and subsequent assembly technology assessment correspond to the prototype stage during product design and development, and the assessment of production organization technology corresponds to the plot series and production series during validation and then serial production. The applied variables V1, V2, V3, V4, V5, V6 in the scope of machining technologies, assembly, production organization are shown in Fig. 8. The assessment, depends on the scope of information obtained, can be carried out for individual components of the product, groups of elements, its assemblies or also in a holistic way [12].

Input assumptions
Based on the analyzes of the above methods of assessment the product's producibility, an improved proprietary approach was proposed in the process of shaping the product's productiveness. The illustration of the presented proposals is presented on the example of a singlestage gear in Fig 9. General purpose gearboxes are designed in the form of a series of types from the point of view of market demand, production costs and delivery time to the customer. The gearbox shown in Fig. 9 was designed in a traditional way (welded body, a large number of bolted joints, etc.).

Fuzzy assessment of design for assembly technology
According to the order of evaluation (Fig. 7), experts assess the efficiency of the process for each stage of the process (on a scale of 0 to 100). To illustrate the course of the procedure, the assessment was carried out for sub-step 1 of the design for assembly efficiency assessment - Fig. 8. The remaining stages and assessments were used to compare the results of the proceedings. The example is presented for one group of elements mounted together -body and cover [8,20].

Assessment of Design for Assembly Technology -sub-step 1
The component's technology, assuming that it depends on two factors, which are: access, assemblage has been set by experts for: "Access" = 20, "Number of workshop aids" = 55. The membership functions of linguistic variables for the given factors are given in Table 2 and 3, the bases of rules for them are presented in Table 4 and 5. The area has limited access, but some can be removed without damage 60 The area is easy to assemble, lots of hands/tools 100   For the body, for the values "Access" = 20 and "Maneuverability" = 55 on the basis of Fig. 9, according to the "min" inference rule described above, the following rules are active: - (medium technology) After taking into account rules 10, 11, 14 and 15, in Mamadani's inference there is a maximum operation as an operator of the aggregation of inference results obtained on the basis of individual rules, therefore rules 10 and 15 which have the same "medium-low" rating, we choose MAX so we activate rule 15. Aggregation of rules for assembly technology in sub-step 1 is given in Fig. 10.
Deffuzified Center of Gravity value)  The technology assessment for the 1st stage assumes for the adopted access assessment -20 and the number of workshop aids -55 value ~ 40.

Assessment of Design for Assembly Technology -sub-step 2
The component's technology is determined, assuming that it depends on two factors, which are: orientation, manoeuvrability. The expert group made the following assessment: orientation -10, manoeuvrability = 35. Requires a tool to capture 60 Requires two people 100 Requires service equipment 100

Assessment of Design fo Assembly Technology -sub-step 3
The 3 component technology is determined, assuming that it depends on two factors, which are: Assemblability, Processes. The expert group made the following assessment: assemblability = 20, processes = 35.   The technological assessment for the 3rd stage takes for the adopted assessment of Montability -70 and Joining processes -10 equal to -36.

Comparison of the use of methods on the example of a gear fragment -a drive shaft set
In the study, the indicators of the assessment of the constructionality of the structure were determined for the sample product presented in Fig. 9. As a result of the analysis after the proposed changes, the new form of the gear structure change is illustrated in Fig. 13.   Figure 13. Construction form of the gearbox after the changes have been made

Conclusions and comments
In standard technology analyzes according to B&D and Lucas DFA, it is associated with a reduction in the number of components that have no significant effect on the product's functions or their change consisting in improvement in terms of assembly time and costs. In the traditional arrangement of the above mentioned the methods are oriented towards mass production. The proposed proprietary method based on the analysis of the obtained values of the parameters of the assessment of the efficiency of the entire process enables -unification of components, application of group processing methods, standardization of machining and assembly operations, and thus saving of investment in machines and shorter overall assembly time, shortening of times, elimination of errors, reduction of process costs -taking into account, in addition to assembly, many other various factors, e.g. availability of spare parts, production seriality, production conditions in the form of equipment types, available assembly techniques, level of automation, scope of external cooperation orders -the method can be used for smaller series of manufactured products, -assessment of technology in the form of given indicators and coefficients should be carried out by experts with extensive production experience, -arousing designers' creativity when designing new products, rationalizing works at the stage of improving and expanding the range of implemented production.
The presented method is universal. The use of fuzzy logic gives the opportunity to express incomplete and uncertain information in natural language, in a simple way for humans based on expert knowledge and empirical data. The method takes into account the analysis of the production process in a holistic way.