خانه اندازه گیری فازی کیفیت و گسترش کارکردکیفیت برای مشکل برآورد رگرسیون فازی

In present competitive environment, it is necessary for companies to evaluate design time and effort at the early stage of product development. However, there is somewhat lacking in systemic analytical methods for product design time (PDT). For this end, this paper explores an intelligent method to evaluate the PDT. At the early development stage, designers are short of sufficient product information and have difficulty in determining PDT by subjective evaluation. Thus, a fuzzy measurable house of quality (FM-HOQ) model is proposed to provide measurable engineering information. Quality function deployment (QFD) is combined with a mapping pattern of “function → principle → structure” to extract product characteristics from customer demands. Then, a fuzzy support vector regression machine (FSVRM) model is built to fuse data and realize the estimation of PDT, which makes use of fuzzy comprehensive evaluation to simplify structure. In a word, the whole estimation method consists of four steps: time factors identification, product characteristics extraction by QFD and function mapping pattern, FSVRM learning, and PDT estimation. Finally, to illustrate the procedure of the estimation method, the case of injection mold design is studied. The results of experiments show that the fuzzy method is feasible and effective.

As global competition increases and product life cycle shortens, companies try to employ effective management to accelerate product development. However, product development projects are often suffered with schedule overruns. In most cases, problems of overruns were due to poor estimations. That is coincident with the saying “you cannot control what you do not measure” (DeMarco, 1998). In the whole product development process (PDP), product design is an important phase. The control and decision of product development is based on the pre-estimation of product design time (PDT). Nevertheless, PDP always means the brand-new or modified product design. Thus the cycle time of design process cannot be measured directly. Much attention has been focused on reducing the time/cost in product design, but little systematic research has been conducted into the time estimation. Traditionally, approximate design time is determined empirically by designers in companies. With the increase of market competition and product complexity, companies require more accurate and creditable solutions. Recently, a small number of researches have dealt with the estimation of design time and effort. These existing approaches all belong to the factor analytical method. Using traditional regression analysis, Bashir and Thomson (2001) propose two types of parametric models: a single-variable model based on product complexity, and a multivariable model based on product complexity and severity of requirements. As other factors have not been considered in these two models, the practicability and accuracy are suspectable. Griffin, 1997a and Griffin, 1997b relates the product development cycle time to factors of project, process and team structure with a statistical method, and quantitatively analyzes the impact of the project novelty and complexity on cycle time. Nevertheless, he does not present an effective method for estimating the design time. Jacome and Lapinskii (1997) present a model for estimating effort for electronic design which takes into account three major factors: size, complexity and productivity. However, this model is applicable only for effort estimation for electronic design. Therefore, there is a demand for more systematic and general methods, which can be applied to a wide range of engineering design projects. For those nonlinear systems that have many uncertainties, there are no precise mathematic models. Fortunately, adopting intelligent technologies, such as neural network and fuzzy logic, is sometimes a good choice. Jahan-Shahi, Shayan, and Masood (2001) use multivalued fuzzy sets to model the activity time/cost estimation in flat plate processing. Based on neural networks, Seo, Park, Jang, and Wallace (2002) present an approximate method to provide the product life cycle cost in conceptual design. Recently, a novel machine learning technique, called support vector machine (SVM), has drawn much attention in the fields of pattern classification and regression estimation. SVM was first introduced by Vapnik (1995). It is an approximate implementation to the structure risk minimization (SRM) principle in statistical learning theory, rather than the empirical risk minimization (ERM) method. This SRM principle is based on the fact that the generalization error is bounded by the sum of the empirical error and a confidence interval term depending on the Vapnik–Chervonenkis (VC) dimension. By minimizing this bound, good generalization performance can be achieved. Compared with traditional neural networks, SVM can obtain a unique global optimal solution and avoid the curse of dimensionality. These attractive properties make SVM become a promising technique (Acır et al., 2006, Bergeron et al., 2005, Colliez et al., 2006, Frias-Martinez et al., 2006, Goel and Pal, 2009, Huang et al., 2005, Mohammadi and Gharehpetian, in press, Osowski and Garanty, 2007, Samanta et al., 2003, Übeyli, 2008, Vong et al., 2006 and Wu, 2009). SVM was initially designed to solve pattern recognition problems (Acır et al., 2006, Frias-Martinez et al., 2006, Mohammadi and Gharehpetian, in press, Samanta et al., 2003 and Übeyli, 2008). Recently, with the introduction of Vapnik’s ε-insensitive loss function, SVM has been extended to function approximation and regression estimation problems ( Bergeron et al., 2005, Colliez et al., 2006, Goel and Pal, 2009, Huang et al., 2005, Osowski and Garanty, 2007, Vong et al., 2006 and Wu, 2009). In many real applications, the observed input data cannot be measured precisely and usually described in linguistic levels or ambiguous metrics. However, traditional support vector machine (SVM) method cannot cope with qualitative information. It is well known that fuzzy logic is a powerful tool to deal with fuzzy and uncertain data. For this end, this paper develops a time estimation method for the product remodeling design, which is based on fuzzy logic and support vector regression machine. There is a kind of nonlinear mapping relationship between engineering factors and PDT. SVRM can perform this mapping well. Fuzzy inference theory is introduced to handle the fuzzy input variables. Product characteristics are important parts of engineering factors. As the product characteristics are not available before a product design project begins, this paper attempts to extract product characteristics from customer demands using quality function deployment (QFD) and function mapping methodology. Therefore, the whole estimation method includes three steps: characteristic extraction, support vector machine learning and time estimation. The proposed FSVRM can solve the estimating problem of uncertain fuzzy system. The input and output of the proposed FSVRM are fuzzy numbers. In this paper, we put forward a new fuzzy inference theory. Based on the fuzzy inference theory and Fν-SVRM, an estimation method for product design time is proposed. The rest of this paper is organized as follows: in Section 2, PDT factors are identified firstly; Section 3 describes a new house of quality (HOQ) model and introduces a mapping methodology to extracting product characteristics; in Section 4, fuzzy support vector regression machine is presented to realize the estimation of PDT; Section 5 presents an example to illustrate the estimation method; and Section 6 is the conclusion.

The control and decision of product development is based on the pre-estimation of PDT. However, this PDT estimation problem is always overlooked because of the insufficiency of quantitative methods. This research attempts to develop an intelligent estimation method. In order to find out product characteristics at the early stage of product development, a fuzzy measurable house of quality (FM-HOQ) model is established. This model is applied to measure and map characteristics from customer’s technical demands, with the decomposition idea of QFD. For customer’s functional demands, a mapping pattern of “functions-principle-structure” is taken on. The data of product characteristics having been obtained, a new Fv-SVRM model is presented to fuse data and realize the estimation of design time. The application of the FM-HOQ model and Fv-SVRM -based intelligent estimation method to the design of injection molds indicates that the model and method are feasible. This estimation method can be used for the remodeling products at the early stages of development. The known characteristics of existing products are used to train the Fv-SVRM. Thus this trained Fv-SVRM can be approximated to the design time for a new product. For a certain kind of product, the accuracy of this method will be enhanced while more samples are added to the training set. On the other hand, there are some limitations in this estimation method. For the brand-new products, this PDT estimation method will be inapplicable. The influencing weights of linguistic variables obtained by experience or experiment are important for the Fv-SVRM model. If all influencing weights of linguistic and numerical variables are used as the connection weights between the input layer and fuzzifization layer, and optimized by the Fv-SVRM learning, then the Fv-SVRM model will be more reliable and these influencing weights will have further applicable value. This is a problem for future research. Anyway, the main contributions of this research can be shown as follows: (1) Develop a time estimation method that is helpful for product development. (2) Propose a kind of fuzzy measurable HOQ for mapping and analysis of product characteristics. (3) Provide a Fv-SVRM model for the MISO system with high-dimensionality and mixed-type inputs.