A Comprehensive Design for a Manufacturing System using Predictive Fuzzy Models

Today, the design factors of manufacturing systems are still an active research topic and the predictive models are highly interested by the scholars. Design and manufacturing costs are some of the key issues for determining the competitive product in the global market. During current research a guideline to estimate mechanical cost of developing and manufacturing processes presented. The anticipated equation embeds both engineering factors and cost management contributors that could be applied to estimate, predict, control, and reduce costs. Applicable cost factors have been determined by designers using any suitable method for weighing and ranking in the related industries. The cost design model has been established by comparing the target cost of design and design real cost. The target cost of design should be experimentally nominated based on the product’s cost and profit in the context. The manufacturing cost-based design cost forecasting model then validated using an effective fuzzy statistical method. The proposed model creates economical manufacturing of an affordable design in line with the design capability for manufacturing in terms of cost & price.


Introduction
In a competitive environment, it is necessary that the design process and cost engineering are combined for calculating the cost of design with the definition and selection of cost-effective factors.
Cost estimation in the early stages of design projects involves a great deal of uncertainty. Therefore, there is a great demand for an effective way to reduce uncertainty in the product's cost estimation. An effective-cost prediction method can be the process of identifying and measuring cost-effective factors in design for manufacturing (DFM). Optimization and cost reduction in the manufacturing process must begin with the design process and the prerequisite of this is to identify all the aspects of the design cost.
These factors must be general, functional, flexible and integrated to be able to illuminate all the design cost perspectives regardless of product type and scope for the designer and manufacturer. The design cost factors should also cover all stages of the design, and the more these criteria are in the early stages of design, the more efficient it will be to control and optimize them. Our method can be used to predict manufacturing costs based on the cost of mechanical design.
Before 1980, the cost estimation and determination of design and manufacturing projects has been accomplished by two methods: (1) feasibility study and (2) use of cost data in similar projects. Since artificial intelligence became popular in the 1980s, a new approach to estimating design costs has been introduced, while several studies have used different methods to estimate costs across a wide range of industrial applications. Later, in the 1990s, neural networks (NNs) were introduced as a branch of artificial intelligence as an alternative method of estimating manufacturing costs. (Anderson, 2017) presented a report on the design and engineering cost analysis of minerals processing. The use of neural networks for cost product packaging modeling was developed by (Zhang et al. 1996;Shtub and Versano, 1999) compared to neural network performance and regression analysis when estimating the cost of constructing a steel pipe bending process. (Cavalieri, et al. 2004) compared parametric models and neural networks to estimate production costs and concluded that the neural network performs better and is more reliable. (Verlinden, et al. 2008) developed MRA and ANN-based models to estimate the cost of a sheet metal production. (Bo LI, et al. 2017) Researched on Design Innovation Approaches: product form, decoration materials, brand image building cost control& product promotion for Enhancing Product Value Based on Cost Control. (Arabzadeh and Niaki, 2018) estimated the cost of spherical storage tanks by artificial neural networks and hybrid regression. (Chan , 2002) introduced an expert system for manufacturability and cost evaluation. (Izadi et al. 2020) presented a review and cost structure models and cost factors of road freight transportation.
The early stages of product development have uncertainties and factors such as the design time and the manufacturing process, and this directly affects the cost estimation of the product and design project (Xu et al. 2012). (Kolbachev, 2017) suggested that the cost of manufacturing a machine early in the engineering process can be estimated. Such an estimate is based on its parametric information integration index. Design processes are a structural index entropy-based approach.
The most important reason for doing this research is the need to have a flexible way of accurately calculating the design cost to predict the manufacturing cost with actual cost data in the design process regardless of the type, shape and raw material used in making the product. It provides an applied flexible method for identifying & selecting design cost factors based on a mechanical designed product.
Determination and calculation of design costs are existed by these factors for providing in a competitive market. The monitoring of cost-effective factors helps to optimize the price of the designed products.
Calculated design costs as outputs can be used to predict manufacturing costs as a criterion of design for manufacturing and cost feasibility study. In the following, you will find out how to design cost factors, how to choose the most effective factors, and the design cost model and its application environment. The manufacturing cost forecasting function is also presented using the design cost in two linear-numerical and fuzzy-regression methods using real data.
The rest of this paper is followed by four sections. Section 2 addresses the materials and methods of this paper to study the background as well as the comprehensive method. Section 3 is the results of the analyses on the proposed method. Section 4 performs the validation, comparison and sensitivity of the method. Finally, the conclusion and future works are drawn in Section 5.

Materials and methods
This model offers a comprehensive, flexible, and proactive approach that is based on the collection of frequently used operational data on the cost of designing or estimating them and makes it possible to predict and estimate the cost of manufacturing based on a fuzzy regression method for a product or set designed and it will develop the DFM method. Figure 1 illustrates a comprehensive view to the proposed method. According to the flowchart the following steps must be taken:

Start
Step 1: Determine the market product price(MPP) Step 2: Determine the profit designed product(PDP) Step 3: Calculate the target cost design(TCD)

TCD=MPP-PDP
Step 4: Determine and verify the best performance conditions Step 5: Identify and define the cost factors/criteria (CFs) Step 6: Specify the usable cost of applicable factors/criteria Step 7: Calculate the design real cost(DRC) by collecting the usable cost factors/ criteria Step 8 Step 14: Manufacturing can be implemented

Yes
Step 11 : Predict & determine the cost of Mfg. a designed product / Previous products made of the similar design Step 10 : Start the design process Step 12 Step 13: Determine the function of predicting mfg. cost based on design cost

5
Step 1 & 2: Determination of market product price (MPP) & profit designed product (PDP): Designer organizations can consider the designed product as a marketable product and determine the selling price based on the information related to the market and also consider the amount of profit from this sale based on their market strategies.
The MPP and PDP should be determined by reliable data through the systematic market surveys and feasibility study.
Step 3: Calculation of target cost of design (TCD): This model has two inputs from the internal environment (Design Real Cost) and external environment (Target Cost of Design). This step delivers the target cost of design (TCD) so it is needed to analyze all of the stages in the product design process and the cost is calculated by determining effective factors. The TCD is predicted by the PMP and PDP. The DRC should be calculated before starting the design process as proactive action. So a database for recording the DRC's results is required to compare this information with the TCD. Analyzed information must have a target, trend, comparison, cause, and scope.
At the beginning, this process in designer companies documented procedure is recommended.
Step 4: Determining and verification the best performance conditions: Based on their strategic plans, design and manufacturing organizations should determine the conditions of the product presentation environment in terms of product price and the desired profit margin.
For identifying the best condition, the following issues should be considered: The market price of product (MPP) should be presented as higher than average in the desired market.
The design real cost (DRC) could be occurred in the low and medium level. Profit designed product (PDP) could be had two levels between medium and high.
Step 5: Identification and definition of cost factors (CFs): This step gives the design real cost (DRC) that helps for determining the affordable product's manufacturing volumes and it is used for estimating the returned capital of the product design.
The new contributive method is based on researches, studies, technical interviews and audit results of several companies so this general practical model is applicable for determining cost in engineering design for economic manufacturing.
The DRC formula has been generated by the effective design cost factors with a general application for all of the design & manufacturing organizations.
The following set of factors is used to calculate the DRC by applicable factors with notification to the rate of usability. The data related to the factors have been recorded by designers during the suitable stages of design activities.
The following factors are used in the stages of mechanical design process regardless of product type, product application, and product complexity but the applicability level of these factors should be determined based on the scoring method through the knowledge of designers and designer's qualifications.

CF1: Cost of the design feasibility study
This mechanical feasibility study will address the current mechanical system and suggest an alternative approach for mechanical system design. The design feasibility study is proactive teamwork that is providing evidence of capability for designing of the desired product as needed design inputs. This cost covers all of the dimensions of the feasibility study to product's definition, written of engineering performance, tolerances review, adequate capacity, required tools and equipment, such as FMEA, risk analysis, life cycle analysis. (Nonami et al. 2005) CF2: Human cost (Designers) The human cost could be defined as salary, bonus, gifts and it is applicable for full time/ part-time personals which are in a design team. (Li et al. 2018) CF3: Software cost (General, Technical & Special) All of the costs related to software and applications that used in the design process for creating design outputs, design reviews, calculations and re-calculations, simulation and solving methods and operational testing could be specified. (Sánchez et al. 2017) CF4: Cost of customer's verification/ user's validation Sometimes designers need to get verification or validation for more confidence and the cost of these activities should be calculated for adding to design cost. (Maropoulos et al. 2010) CF5: Cost of design's references Designers need to use books, standards, journals, technologies, knowledge, seminars, training workshops, specialized exhibitions, technical consulting. (Silva et al. 2019) CF6: Cost of documented researches Collection of data and creation information related to design and development of products could be a contented descriptive model of a design process, a respective model of design, computer-based 7 models, languages, representations, and environments of design, analysis of design such as DFM, reliability, & serviceability. (Finger et al. 1989) CF7: Cost of design's benchmarking Cost of activities for comparing a product in current and past such: similar designs, idea, sketch, technologies, patents. (Nick et al. 2010) CF8: Cost of design review between inputs & outputs A structured approach is described to analyze the design of mechanical systems and equipment which includes the design specification, and system, functional unit & component levels of design. The design review considers maintainability, reliability and all other factors which contribute to the total performance of a plant. Specific analysis techniques are described with respect to their applicability to different stages in a design review exercise. It covers all of the activities which be included comparison reports, structured meetings, and completion of review checklists, force analysis, DFM's reports, and client's review. (Thompson et al. 2007) CF9: Cost of prototype building/Product Modeling One of the tangible costs in the design process is prototype building and this cost should be determined in operational condition for more effectiveness. (Jones et al. 1996;Otto et al. 2000) CF10: Cost of necessary tools, gages & equipment for verifying/validating If designers use some tools for measuring, control and verification, these costs will be added to the cost of design projects. (Ertas et al. 1992) CF11: Cost of time-consuming for design Design is one of the operations that is based on time planning / duration and could be affected by cost of design. This factor shall be measured by the monetary unit. (Xu et al. 2006;Holliman et al. 2019) CF12: Cost of design changes Each change in design stages shall be passed through review, verification and validation steps and all of these activities can increase the cost. It could change the design outputs in conjunction with design inputs so. (Ullah et al. 2016) CF13: Cost of specific environmental condition as applicable This is the cost of design for an environment such as material purification, less material variety, avoidance of toxins, use of recycled materials and includes eco-design, raw materials selection and use, manufacturing, material handling, installation and maintenance, use and end of life. (Sahiti et al. 2016) CF14: Cost of re-calculations/testing /inspections Includes the cost of calculations with other design methods such as design verification, cost of laboratory tests, operational testing, durability testing, design of experiments calibration & measurement system analysis. (Hwang et al. 2004) Applicability of the cost factors for mechanical design stages are shown in Table 1. This table shows the importance of CFs with a number of applications for measuring and monitoring. After the definition and measurement of CFs, as it can be seen CF2, CF3 & CF10 must be measured and monitored continuously. The CF12 & CF13 should be controlled in planned intervals. Other CFs is used for increasing cost-effectiveness.
Engineering design process is a specialized process that after achieving design costs, a decisionmaking process and team action formation must be done.
Step 6: Specification of cost applicable factors: The applicability coefficients of cost factor could be determined based on recognition and experience competent designers by surveys, interviews or Focus on group studies. At this point, design experts are scoring each of the cost factors with a scoring method based on product recognition. This stage can be done individually or in the form of a scoring team. It helps the designers who collect the most applicable cost factors for fast calculation of the real design cost.
Step 7: Calculation of design real cost (DRC) by collecting cost factors: Based on the available factors, the design team will be able to anticipate and determine each of the cost factors that have been selected as the applicable factor in the previous step and calculate the DRC by summing all the factors. Also, if the organization has already had experience in the previous similar design project, it can use its cost data at this stage.
Step 8: Comparison of the DRC & the cost of similar previous designs (Where appropriate): If possible, the organization has had successful design projects in the past and its cost records are available, these results can be used to confirm the results of the new design costs.
Step 9: Relating the DRC and TCD: Comparison of the DRC and TCD for making an optimum decision for conducting design process: (1) TCD-DRC ≥ 0 → Design Operation could be done.
TCD-DRC < 0 → Design process will be reviewed according to the cost management approach. It may be replaced with another option such as: outsourced design, change of design inputs, use of cheaper technology, elimination of unnecessary product specifications, and Customer agreement on reducing additional expectations.
Also, the analyzed data from this model for each designed product could be used as benchmarked information for designing of other similar products. Comparing these results in designed products/projects could help managers/leaders for getting factual decision making for increasing the design effectiveness.
Step 10: Implementing the design process: The design process should be realized in conjunction with to design plan within any focus to eliminate non-value-added costs through design stages.
Step 11: Predicting & determining the cost of manufacturing of a designed product/ previous products made of the similar design: Cost of design data and cost of manufacturing data is collected through the design and manufacturing processes. The cost of raw material could be excluded of these data because the Cost of materials is very different for different products. Accurate recording of design and manufacturing cost data is very effective in subsequent analyzes, and this data may be generated from an operational design and manufacturing process or a process of predicting and feasibility design and manufacturing.
Step 12: Converting manufacturing costs to suitable fuzzy data: Since manufacturing costs are not always accurate during the design process, manufacturing cost data is converted to fuzzy data by mentioned fuzzy sets and suitable membership functions.
Step 13: Determining the function of predicting manufacturing cost based on design cost: When numerical design data and fuzzy manufacturing data are generated into an appropriate number and acceptable accuracy in a product or collection, with known statistical method, the function of predicting manufacturing cost based on design cost or estimated design cost could be found by using the regression equation method. The value of the dependent variable for different values of the independent variable is estimated by the regression line. In order to estimate the appropriate factors for the model, an attempt is made to select the model that has the least error based on the available data.
This manufacturing prediction function can be considered as basic criteria in design methodology for manufacturing, which is the concern of most organizations.
Step 14: Manufacturing: After estimating the manufacturing cost based on the function obtained from the previous stage and being acceptable, the manufacturing implementation can be started.

Results
In this section, to illustrate the performance of the design cost estimation to determine or predict the manufacturing cost, an attempt is made to use tangible numerical examples or illustrative examples and the results of these steps are analyzed and discussed Without any emphasis on the type of methods used such as Shannon entropy, Taguchi, etc.
For the determination of the MPP and PDP, Table 2 shows an illustrative example of steps 1 and 2 data with a simple calculation for three types of manufacturing i.e. Refrigerators, Hydraulic Cylinder and Waste Containers (sample industry). The target cost of the design (TCD) is calculated according to step 3. At the stage 4, the best performance conditions could be validated by using Taguchi method (Zhang et al. 2009;Parameshwaranpillai et al. 2011). In this situation for example, it will get 2 factors (DRC& PDP) with two levels, it will be 4 experiments and the Taguchi's method introduces L4. Recording of trial conditions for the above definition are shown in Table 3. In order to better illustrate, we have defined the low, medium and high operating ranges in the range of zero and one as follows: Low (0, 0.3], Medium (0.3, 0.7], High (0.7, 1] Results of Taguchi's method (Table 4) shows the best S/N ratio is in nominal QC type for trial#3. Which means The Profit designed product (PDP) & Design real cost (DRC) should be in high range or the more cost-effective the design is, the more successful the product is in sales and profit. In step 5, all the effective factors of the design cost were defined, and in order to introduce an illustrative numerical example, we first present the factors that can be used according to step 6, using the average score of the three independent design groups (Table 5), and then return to step 5. These data are based on a simple scoring method between 1 to 10, which means that the score moves from point one to point ten, the usability decreases. It is needed to specify the usability factor for each factor by using a matrix with (m) rows (number of options) and (n) columns (number of indicators/factors). Each element of this matrix; is called as decision-making matrix data and the data matrix values have been normalized using equation 1 and the entropy of the probability distribution; has been calculated. After calculating the degree of deviation , the weight rate has been specified. The level of the construct's approximating to the optimum condition may be presented as a level of the construct's entropy which is evaluated by using Shannon's methodology (Ghasemzadeh et al. 2018) Lowering the entropy level gets the construct's conditions closer to the optimum and formulated by equation. The last row of Table 6 (Wj) is shown as percentage in Table 7 and used for ranking of cost factors, in which shows that the cost factors 2, 8, 9&10 have the most impact or importance in comparison with other factors. This means that approximately 20% of the cost factors estimate 80% of the design cost. In step 7, the design cost of a stationary hydraulic cylinder (Jack) at different tonnages is provided in Table 8 by illustrative example.  CF3  CF4  CF5  CF6  CF7  CF8  CF9  CF10  CF11  CF12  CF13  CF14   2 Ton  196  3920  539  1392  343  882  578  2450 2548 2871  902  735  270  1568  5 Ton  196  3920  539  1392  343  882  578  2450 2548 2871  902  735  270  1568  10 Ton 200  4000  550  1420  350  900  590  2500 2600 2930  920  750  275  1600  15 Ton 218  4360  600  1548  382  981  843  2725 2834 3194 1003  818  300  1744  20 Ton 228  4560  627  1620  399  1026  673  2850 2964 3340 1049  855  314  1824 The data of Table 8 should be specified for each part of hydraulic cylinders exactly as following Table  9.  Table 10 has been formed by TCD (the last column of Table 2) and DRC (the sum of rounded values of Table 9 in accordance to steps 8 and 9 in which the difference of these amounts are positive showing the design implementation could be done according to step 10; since the design process is affordable.  When the amount of the 4 th column of the Table 10 is positive, the implementation of design will be affordable and the design process could be started. The results are shown that implementation of design will be more economic when the capacity of the hydraulic jack is high. As mentioned in step 11, at this stage, the numerical data related to the manufacturing (mfg.) cost are determined or predicted in the same structure as the design cost in Table 11. Since manufacturing costs are not always accurate during the design process, manufacturing cost data is converted to fuzzy data by triangle membership functions. The Fuzzy set and membership functions are shown in Table 12.  In this part, the data on manufacturing costs have been converted to fuzzy data and fuzzy data have been specified in Table 13 as illustrative fuzzy example. In the following, with the help of this example, we will analyze fuzzy regression and validate the results for further transparency. After studying the cost of design for hydraulic cylinders in a variety of capacities in Table 9, Fig. 3 could be considered. The cost of manufacturing for hydraulic cylinders in a variety of capacities as given in Table 11, could be shown in Fig. 4  The neuro-fuzzy hybrid system is a learning mechanism that utilizes the training and learning neural networks to find parameters of a fuzzy system based on the symptoms created by the mathematical model. Adaptive learning is an important characteristic of neural networks. Adaptive Neuro-Fuzzy Inference System (ANFIS) is used for system identification based on the available data (Loganathan et al. 2013), this modeling approach is based on data classification and then applying activation functions or so-called membership functions.

The function of manufacturing cost based on design cost
The purpose of this is to move data from scalar space to a higher dimension so that data can be easily processed. One of the most important functions used in this field is the Gaussian activation function which gives good accuracy in modeling. In summary, the data is first given to the network and based on input and output it generates an elementary model by membership and clustering functions using the fuzzy clustering means (FCM). In the following, this basic model is optimized by a hybrid or error propagation algorithm, and we present the fuzzy and final learning model. The data presented after sorting and removing the additional columns have 4 columns (see the Table13, 1 of the columns is that design and another 3 columns are fuzzy mfg.) As such, the first column being the input and the next three columns the output of the fuzzy model. The method is such that the data is first divided into two subsets by a random separator function.
The first subset contains 85% of the data used to train fuzzy networks. The second subset contains 15% of the data used for fuzzy model validation and testing. The fuzzy converter is therefore trained by 85% of the data and then tested with the remaining 15% to ensure the correct model performance. It is necessary to explain that the modeling process is performed 3 times to model all three outputs with the input of the first column. Inputs are the design's costs and outputs are manufacturing's cost.
Results of analysis have been drawn for 3 variable outputs such as coefficient of determination(R), R squared (R 2 ), mean squared error (MSE), root mean squared error (RMSE) and mean absolute error (MAE) in Table 14.  The coefficient R 2 indicates the dominance of the model in estimating the output data .Therefore, by studying the coefficient of R 2 , in Table 14, it is specified that variables 2 is acceptable because it has a lower error rate so.

Conclusion
The proposed model presented is a scientific and practical one that has high applicability in designing and manufacturing organizations also it is applicable for making a factual decision in a design for the manufacturing process and it provides monitoring applied dashboard for managing, controlling and improving desired results of the design process.
We have developed a comprehensive method for determining cost-effective factors during the design and development process to predict and realize the real cost of design (DRC) in the framework of the target cost of design (TCD) and have evolved it with the suitable method for ranking and selecting effective applicable factors. These cost factors can help improve the integrity of the design and improve the performance of the designers as criteria for the design process.
The real cost of design also enables companies to evaluate the future of the designed product form (features, types, complexities, characteristics, and limitations). Design cost is a key feature of determining the final product's selling price and achieving profit in a competitive market. One of the most important things to pay attention to is that in this way the designed product can be considered as a final product to be delivered, meaning that this method will be applied to solely designer companies. Another benefit of this approach is that to reduce the cost of manufacturing, which is one of the most important issues of an organization today, it is necessary to rely on the design cost, and by focusing on design cost centers, organizations can achieve an effective design to reduce manufacturing costs. This achievement can enable design and manufacturing organizations to consider the cost of design and manufacturing as one of the key criteria in DFM's evaluation method for their products. This method allows designers to choose the best design at affordable costs from the proposed designs and it can be a mechanism for deciding cost-based design.it is a novel fuzzy approach to predict manufacturing cost based on optimal design cost that is adaptable to the nature of different design and manufacturing organizations. Also, studying the cost and value of the design for the manufacturing process based on measuring cost efficiency can be considered in further researches as its productivity indicator.