Research on Injection Mould Intelligent Cost Estimation System and Key Technologies

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1 Int J Adv Manuf Technol (2003) 3: Ownership and Copyright 2003 Springer-Verlag London Limited Research on Injection Mould Intelligent Cost Estimation System and Key Technologies H. Wang, X. H. Zhou and X.-Y. Ruan National Die and Mould CAD Research Centre, Shanghai Jiaotong University, Shanghai, P. R. China The manufacturing cost of injection-moulded parts is mainly decided by the cost of the injection mould. Thus if we can ascertain the cost of the injection mould as early as possible, it will be a great contribution to an injection mould cost evaluation system and research on the economics of injected part manufacture. In this paper, related work on injection mould cost estimation has been discussed. A case-based reasoning (CBR) approach is used for evaluating the manufacturing cost of injection moulds. Case indexing, neural network-based case retrieval, knowledge-abundant case-adaptation and knowledge-absent case-adaptation strategies, and case learning are all considered. A comprehensive cost model including mould manufacturing costs, tax costs and general administrative costs is also discussed. The model is valuable for the price estimation of injection moulds. The application of the system is illustrated with an example. Keywords: ANN; Case-based reasoning; Cost estimation; Cost model; Difference; Injection mould 1. Introduction In modern society, plastics are of great importance. As the main forming method of plastic products, injection moulding is the focus of our research project. The cost of an injection part is made up of design, manufacturing, management, transport costs and taxes, etc. The manufacturing cost is a large part of the total injection part cost. The manufacturing costs of injected-moulded parts are made up of mould cost, part material cost, technical cost and auxiliary tooling cost, so, if we know the injection cost, we can establish the cost of injected parts. The main manufacturing tools used for injected parts are dies and moulds. There is a close connection between the cost of an injected part and that of the injection mould. If we can decide the general cost of injected parts as quickly as possible Correspondence and offprint requests to: H. Wang, National Die and Mould CAD Research Center, Shanghai Jiaotong University, Shanghai, , P. R. China. wanghui1977@yahoo.com and set up a comprehensive evaluation system, it will be very valuable. The reason is that it will greatly help the decision making of managers on the one hand, and help the estimation of the injection mould on the other. Human experts have traditionally been used for this work. Unfortunately, due to the personal attitudes to the same problems and the long time for an expert to acquire the necessary experience, this method cannot satisfy the increasing demands for accurate cost estimation. Thus, if modern computer technologies are used to help the cost estimation of injection moulds, and if the evaluation expert system is mature and accurate, we think it will be of great importance to the injection industry. Therefore, in this paper, research on an injection mould cost estimation system is summarised, our research methods are discussed in detail and a prototype system is described. Due to the weak academic aspects of the injection mould cost estimation problem, it is very difficult to obtain the manufacturing cost accurately. Case-based reasoning (CBR) captures the experience of human practitioners and so is suitable for use in the injection mould cost estimation field. In this paper, an artificial neural network and CBR are combined to facilitate the calculation of injection mould cost. 2. Review of Previous Studies Estimating the manufacturing cost of an injection mould is very important. There are many methods in the cost estimation field and most of them use traditional formulae. Chen [1] has done research on injection mould cost estimation and classified its features. There are several stages in the design process, which include conceptual design, preliminary design and detail design. Injection feature evolution in these continuous stages can lead to the modification of costrelated parameters, which include materials, technologies and mould manufacture. By concurrently considering the parameters in advance, and setting up special knowledge bases, improper design can be avoided. Chin [2] set up an injection cost estimation system called ESIMCOST. Research topics include the concurrent relationship among injection parts design, injection mould design and technology decisions concerning mould

2 216 H. Wang et al. manufacture. Rule-based methods are used, which means the system is made up of a series of if then rules. A further system based on ESIMCOST was then set up called DTMOLD- 1[3], which is used in the electronic domain. In DTMOLD-1, decision tables rather than simple if then rules are used to build the system. By setting up a series of complex mathematical formulae, Shing [4] divides general costs into materials, moulds and technology costs according to the different structures. The system is not dependent on the special geometrical modelling, but by confirming a series of special parameters, the cost of injection parts and injection moulds is calculated. Weustink et al. [5] constructed a general framework for product design and cost estimation/control. Hierarchical methods were adopted, including a feature level, a part level and an assembly level. There were geometry, materials, technologies and processing plans attributes at each level. Rosen [6] analysed the features of injection parts, and the effects of these features on injection mould cost estimation. At the same time, a mapping mechanism between part features and mould costs was set up. In the end, a series of valuable conclusions was proposed. Fagade and Kazmer [7] reviewed two kinds of mould cost estimation methods, and provided a comparison and analysis. Yao and Kim [8] proposed a method to solve the problem of multiple qualities and costs optimisation. Injection parts manufacturing costs are the objective of the problem, and qualities are the constraints. By the use of penalty functions, this problem is changed into a single-objective optimised problem. El-Mehalawi [9,10] described an expert system used for estimating the cost of the net shape forming of parts. CBR, which is based on geometry similarity, was used. Attributed graphs of the parts were used to record the geometry information. Component representation is based on the data extracted from its STEP file. The reasoning criteria were based on the similarities of the attributed graphs of the injection parts. Static modelling was developed to evaluate the injection parts costs by Merino [11]. Fourteen variables were used for input, this method being called modified group technology system. Injection costs were divided into capital cost, technology cost, post-technology cost, material cost and set-up cost. The life circle of injection parts was also discussed. Hu and Poli [12] discussed the cost features of injection parts and stamped parts using a cost estimation formula (CEF). General guidelines were given to decide if a component should be injection moulded or stamped, and whether several components should be combined into a single component. The cost evalu- ation and comparison were primarily in terms of the functional equivalence of features, components and assemblies. We found the earliest injection parts cost estimation method in handbooks like that of Ahmad [13]. Ahmad and others developed various methods for estimating tooling costs, material costs, etc., but these methods cannot be applied directly to support product design and redesign decisions. Ulrich and Fine [14] developed a cost estimation system for the design and manufacture of printed wiring boards. Only when the process plan was determined would the cost be estimated. Shah and Hisiao [15] proposed a framework for expressing manufacturing expertise obtained from experts. The framework was used in a feature-based CAD system for the trade-off between redesign and maximum cost gains. Boothroyd et al. [16] developed a method for the selection of possible process/material combinations for components. The process was divided into four steps, namely, geometry input, process selection, material selection and update. The cost-based process/material ranking for different processing was then given. Koch et al. [17] discussed a method to integrate CAD and active-based cost estimation in the design course. 3. The Framework of Injection Mould Cost Estimation System Since most methods are limited to experiential formulae which are unable to support sophisticated realities, a CBR method is adopted here. Currently, the application of CBR in the netshape forming field has appeared only once [9], which is mainly due to part complexity. For many reasons, the reasoning processes are very complex. In this paper, plastic similarity is used in a CBR system, and case adaptation is discussed as the key point. CBR technology is an important division of intelligent reasoning. Similar to human cognitive processes, CBR uses memory organisation to put the reasoning processes into practice. Because of its strong practical features, it is very difficult to use if then rules to obtain accurate cost values. A modular structure of CBR system for injection mould cost estimation is therefore proposed (see Fig. 1). The key technologies are listed as follows: case representation, case indexing, case retrieval, case adaptation and case learning. The application of artificial neural networks in the case retrieval courses is given particular attention. Fig. 1. Modular structure of CBR system for injection mould cost estimation.

3 Injection Mould Intelligent Cost Estimation Case Representation Mechanism and Flow Chart of CBR System A case representation mechanism for a CBR system was set up (see Fig. 2). When the user inputs information of new case features into the CBR system, by case coupling, cases that meet certain similarity criteria are selected. The cases are then adapted and the case library is refreshed. Frame/object descriptive methods are adopted in this system. The case in the case library can be defined as follows: Problems: eight injection part feature factors. Outcomes: (1) The mould features that are independent of the detailed manufacturing conditions of the enterprise (number of cavities per mould, mould base type, cavity material, plating, mould base materials). (2) The mould process factors that are closely related to the individual mould manufacturing factories (labour rate of mould manufacture factory, the equipment used by the manufacturing factory, the price of mould bases and the general cost of standard parts). (3) A pointer leading to other manufacturing and process information. 5. Key Technologies of the CBR System 5.1 Case Indexing Case indexing mainly refers to the organisational method. The main methods of case organisation are linear, concurrent and hierarchical. When CBR is used to estimate the cost of an injection mould, as the main objective is to obtain the cost, to facilitate the reasoning processes, all the cases are classified according to the type of injection parts in the simplest manner, and each single case is organised individually. 5.2 Case Retrieval Case retrieval means to retrieve the most similar case from the case library, and similarity calculation is the core of the case retrieval process. Many researchers have studied retrieval algorithms. Xu [18] uses AHP (analytical hierarchical process) to decide the power of feature value, constructs a fuzzy similarity model and adopts entropy pairs to evaluate the similarity of injection parts, which is a valuable procedure. Fig. 2. Flow chart of CBR system for injection mould cost estimation.

4 218 H. Wang et al. The case retrieval algorithm in this paper is discussed below (see Fig. 3) Retrieval Algorithm The traditional algorithm of case adaptation is to use an AHP algorithm to calculate the weight i of the feature, then use the nearest neighbour (NN) algorithm formula: d s = n i S(f 1 i f k i) i=1 (1) n i i=1 to calculate similarity. Its merit is that it is very simple to calculate; however, it ignores the correlation among cases and the non-linear properties that exist in reality. An artificial neural network is adopted here. The basic concept is as follows: 1. Set up the artificial neural network to calculate the similarity between each case in the case library and the case to be input to the system. 2. Compare each case in the case library with the case to be calculated, and find the appropriate one, which satisfies certain criteria. 3. Stop the retrieval process. The strategies are shown in Fig. 3. Here the key is to train the original samples, assure the standardisation of inputting parameters and decide the weights of the neural network Training the Samples of the Neural Network The inputs of the network are eight injection part feature factors. These factors are first to be coded, then are trained according to the following algorithms: 1. AHP phase. Use the concept of nearest neighbour (NN). AHP is first used to calculate the weight i of input features. The output of the neural network can be represented as d s = n i S(f 1 i f k i) i=1 n i i=1 which is the appropriate value of the key features between the new and old cases. Then go to (3). 2. Human expert adjustive phase. If human experts feel unsatisfied with the results of the sample output, they can adjust the similarity value of the system directly, then go to (3). If the human experts feel satisfied, then the training process is stopped. The appropriate neural network is set up. 3. Use the samples to train the artificial neural network, go to (2). 5.3 Case Adaptation Case adaptation is the bottleneck for CBR systems. The focus of adaptation is on the manufacturing cost of the mould. Fig. 3. Strategies of using an artifical neural network to calculate similarities in a CBR system.

5 Injection Mould Intelligent Cost Estimation 219 Case adaptation can be classified into knowledge-abundant adaptation and knowledge-absent adaptation. In this paper, knowledge-abundant case adaptation models are discussed in detail, although knowledge-absent case adaptation models are also referred Strategies for Knowledge-Abundant Case Adaptation 1. If the similarity between the case to be retrieved and the case in the case library is 100%, then the complexity of the new plastic part is the same as that of the plastic part stored in the case library. Without case adaptation, we get the ultimate effort. 2. If the similarity between the new case and the case in the library is between 80% and 100%, then the ideal modelbased case adaptation method involves three steps: First, determine the difference between the structures of the two plastic parts, and analyse the differences in plastic part structure, which may lead to the alteration of mould structures. According to this mapping mechanism, modify the mould structure. Second, analyse these differences, and estimate the manufacturing cost of the injection mould in the same processing conditions as the old case retrieved from the case library. Third, discuss the variation in manufacturing cost when processing conditions are different from the old case. The final solutions are then obtained. This method requires suggestions from experienced human experts, and it depends greatly on the experiences and the mature mapping mechanism of parts-to-moulds. Thus it is very difficult to use. In this paper, to simplify the case adaptation and use the advantages of other mature cost estimation methods, we adopt the following simplified strategies. In addition to the model-based case adaptation method, there are two kinds of mature cost estimation experiential formulae: (a) (b) Dixon and Poli s (D-P) Method [19]. Adopt a fixed plastic part as a reference disc part. Thus any part that has a relative tooling cost greater than 1 has a higher tooling cost than the reference disc, while a relative tooling cost less than 1 implies a lower tooling cost than for the reference disc. Relative tooling cost C d is defined as: C d = Cost of tooling for designed part Cost of tooling for reference part Boothroyd and Dewhurst s (B-D) Method [20]. This is another method for estimating the manufacturing cost of injection-moulded plastic parts at the design stage. The B-D method uses experiential-derived formulae to estimate the times for different operations carried out in transforming a purchased mould base to a finished mould. The sum of these times is then multiplied by a shop rate R, to obtain an estimate of the tooling cost C tool. This method assumes that the purchase price of the mould base should be doubled to account for the custom work (2) on it: C tool = C mm + C mb (3) C mm = R(T po + T e + T x + T a ) (4) C mb = A m (h d ) 0.4 (5) Here T e is manufacturing hours for the ejector pins system; T x is manufacturing hours associated with part geometrical complexity; T po is manufacturing hours for a cavity and core insert set, for a part with very simple geometry; T a is manufacturing hours due to six additional part characteristics; R is shop average hourly rate; C mm is estimated mould-manufacturing cost for a single set of core and cavity inserts; C mb is cost of a mould base; A m is the area of mould base cavity plate; and h d is combined thickness of cavity and core plates (cm). These two kinds of mature cost estimation methods can be used to calculate the cost difference between the old and new cases. This value can then be used as a modified variable of case adaptation. The following paragraph explains the details. Use D-P/B-D methods to calculate the cost of the new case and the old case in the case library, and then calculate the difference: = (Cost of new case calculated by D-P/B-D methods) (Cost of old case calculated by D-P/B-D methods). The ultimate cost of the old case then equals the sum of and the cost of the old case stored in the case library. 3. If the similarity between the new case and cases in the case library is within the range of 60 80%, then we can adapt the same method. In addition, the cost and complexity of the new part should be adjusted manually. 4. If the similarity is less than 60%, CBR fails. We can only use D-P/B-D methods to calculate the cost of a new case, and adjust the cost by the human expert individually. This case can be added to the case library as a new case. Then we continue to update the training process Our Research Plans Concerning Knowledge- Absent Case Adaptation Strategies For knowledge-absent case adaptation strategies, genetic algorithms are used. During case retrieval, cases whose similarities are less than a certain level are excluded. If the quantity of original samples is less than a certain number, some original samples should be duplicated randomly from cases whose similarities are more than a certain level. Chromosome coding includes four parts, which are injection part features, injection mould features, injection mould process features closely related to the individual mould manufacture factory, and mould manufacturing cost. The special point is the construction of a fitness function f. When the proper cases are adapted, we hope that the ultimate case will satisfy the special requirements of injection part features, injection mould features and process conditions of the mould manufacturing factory. We wish to find when the sum of square of the differences between the chromosome coding corresponding to the special demands and chromosome coding of the current case is the least, this sum being the fitness

6 220 H. Wang et al. value. We are now testing genetic algorithms in the case adaptation phase and will soon put them into practice. It is very promising. 5.4 Case Learning This is the final step of CBR. According to the previous presentation, it can be seen that the CBR method used in this paper is very convenient for case learning and maintenance. The algorithm is as follows: 1. First, set up the original database, utilising the artificial neural network method to calculate the similarity among cases in the case library. 2. If the similarity of old cases is over 90%, these cases can be amalgamated into a lesser number of cases to reduce the total number of cases in the library. 3. If the similarity of the new case is between 60% and 75%, by human experts decision, the new case may be added to the case library. 4. If the similarity of the new case is less than 60%, add the case to case library directly. 6. Expand CBR Algorithm to all the Cost- Related Factors Currently, our research is limited to the manufacturing cost, which includes material fees and processing fees, of the injection mould. The output value of our CBR system is injection mould manufacturing cost. In fact, the total cost of an injection mould must also include taxes, administrative costs, design fees, etc. An injection mould CBR cost estimation system should contain all these factors. We hope to expand the current CBR case library. To each case in the case library, other price-related factors will be added, such as design fees, profits, value-added tax, try-mould fees, packing and carrying fees, administrative costs and sales fees, etc. Thus, when an appropriate case whose similarity meets certain criteria is found, these price-related factors can be considered in the case adaptation phase. By setting up a cost-mapping model between the new case and the similar case in the case library, the ultimate results are obtained. For example, Mould design fees = Design fee coefficient Mould processing fees, and the processing fees can be estimated to be 80% of the mould-manufacturing costs. So, Mould design fees = Design fee coefficient Mould manufacturing cost 0.8. Once the modified mould-manufacturing costs are obtained, the other related costs can be calculated by similar methods. The price and the related factors of the new case can finally be obtained. Table 1. Input of injection part features information, Part number 001 Part material ABS Part name Back cover board of lamp Overall length of part 80 mm Overall width of part 72 mm Overall height of part 28 mm Part maximum thickness 2 mm Number of internal undercuts 1 Number of external undercuts 0 Cavity details Medium Surface finishes SPI 3 Tolerance requirement Standard Parting plane complexity Planar.. use is Microsoft Visual C++ 6.0, and databases are managed by Access DAO. The data used in the system are from the relative documents and industrial parts. The strategies are as follows: 1. Input user information, such as the name, ID and password. 2. Input the injection part feature information (see the features we have discussed; shown in Fig. 4). 3. CBR is used. The old case, which has the highest similarity to the new one, is selected. The mould selected has two cavities. Here we use an artificial neural network. The following is then the case adaptation of the CBR system. 4. When comparing them, we found the difference between the new case and the old case is not great, and as the similarity is 92% we adopt the same cavity type (Fig. 5). There are only tiny convex increases. Here we use the difference B-D method to change the cost value. Finally, we get the modified cost value Y 28,613. When the samples and the retrived case are compared, we can easily modify the 7. An Illustrative Example To demonstrate the theories proposed, an injection mould cost estimation prototype system was developed. The software we Fig. 4. Plastic part input to the CBR system.

7 Injection Mould Intelligent Cost Estimation 221 Fig. 5. The closest case and its mould structure calculated by the retrieval system. mould structures, and give some advice to the downstream processes. The estimated cost value is Y 30,000 by the human expert and the total price is about Y 41, Conclusions Key technologies of the CBR injection mould cost estimation system are discussed. Case representation, case retrieval, case indexing, case adaptation and the case learning mechanism are studied in detail. An artificial neural network is used to facilitate case retrieval and the other mature cost estimation methods are used to facilitate case adaptation. In addition, the genetic algorithm method is referred to and it has great potential. Related research is being carried out. We believe that our work can achieve all the scheduled goals in the future. References 1. Y.-M. Chen and J.-J. Liu, Cost-effective design for injection moulding, Robotics and Computer-Integrated Manufacturing 15, pp. 1 21, K.-S. Chin and T. N. Wong, An expert system for injection mold cost estimation, Advances in Polymer Technology, 14(4), pp , K.-S. Chin and T. N. Wong, Developing a knowledge-based injection mould cost estimation system by decision tables, International Journal of Advanced Manufacturing Technology, 11, pp , O. N. Shing, Design for manufacture of a cost-based system for molded parts, Advances in Polymer Technology, 18(1), 33 42, I. F. Weustink, E. ten Brinke, A. H. Streppel and H. J. J. Kals, A generic framework for cost estimation and cost control in product design, Journal of Materials Processing Technology 103, pp , D. W. Rosen, J. R. Dixon and C. Poli, Features and algorithms for tooling cost evaluation in injection molding and die casting, Computers in Engineering, 1, 1992.

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