A fuzzy expected value-based goal programing model for product planning using quality function deployment

Product planning is one of four important processes in new product development using quality function deployment (QFD), which is a widely used customer-driven approach. In this article, a hierarchical framework for product planning using QFD is developed. To tackle the fuzziness in functional relationships between customer requirements and engineering characteristics (ECs) in product planning, the least squares method is incorporated into fuzzy regression to investigate those functional relationships, by which a more central tendency can be obtained. Furthermore, a fuzzy expected value-based goal programing model is proposed to specify target values of ECs. Different from some fuzzy product planning approaches for QFD, the proposed programing model has unambiguous interpretations. An illustrated example of a quality improvement problem of emulsification dynamite-packing machine design is given to demonstrate the application and performance of the proposed approach.     

Assessing the relative importance weights of customer requirements using multiple preference formats and nonlinear programming

Quality function deployment (QFD) is a methodology to ensure that customer requirements (CRs) are deployed through product planning, part development, process planning and production planning. The first step to implement QFD is to identify CRs and assess their relative importance weights. This paper proposes a nonlinear programming (NLP) approach to assessing the relative importance weights of CRs, which allows customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats. The proposed NLP approach does not require any transformation of preference formats and thus can avoid information loss or information distortion. Its potential applications in assessing the relative importance weights of CRs in QFD are illustrated with a numerical example.     

A novel fuzzy linguistic model for prioritising engineering design requirements in quality function deployment under uncertainties

Quality function deployment (QFD) is a planning and problem-solving tool gaining wide acceptance for translating customer requirements (CRs) into the design requirements (DRs) of a product. Deriving the priority order of DRs from input variables is a crucial step in applying QFD. Due to the inherent vagueness or impreciseness in QFD, the use of fuzzy linguistic variables for prioritising DRs has become more and more important in QFD applications. Existing approaches make use of the associated fuzzy membership functions of linguistic labels based on the fuzzy extension principle. However, an inherent limitation of such fuzzy linguistic approaches is the information loss caused by approximation processes, which eventually implies a lack of precision in the final results. This paper proposes an alternative approach to prioritising engineering DRs in QFD based on the order-based semantics of linguistic information and fuzzy preference relations of linguistic profiles, under random interpretations of customers, design team and CRs. Ultimately, this approach enhances the fuzzy-computation-based models proposed in the previous studies by overcoming the mentioned limitations. A case study taken from the literature is used to illuminate the proposed technique and to compare with the previous techniques based on fuzzy computation.     

Hesitant fuzzy integrated MCDM approach for quality function deployment: a case study in electric vehicle

Quality function deployment (QFD) is a product planning management instrument which has been used in a broad range of industries. However, the traditional QFD method has been criticised much for its deficiencies in acquiring experts’ opinions, weighting customer requirements (CRs) and ranking engineering characteristics (ECs). To overcome the limitations, an integrated analytical model is presented in this study for obtaining the importance ratings of ECs in QFD by integrating decision-making trial and evaluation laboratory (DEMATEL) technique and Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method under hesitant fuzzy environment. In particular, the hesitant fuzzy DEMATEL is used to analyse the interrelationships among CRs and determine their weights, and the hesitant fuzzy VIKOR is utilised to prioritise ECs. Finally, the feasibility and practicality of the proposed method are verified by an example regarding the product development of electric vehicle.     

Costing-based coordination between mt-iPSS customer and providers for job shop production using game theory

The industrial product-service system for Computer Numerical Control machine tool (mt-iPSS) has drawn much interest. Under the new paradigm of functional result-oriented mt-iPSS, mt-iPSS customer (i.e. owner of the workshop) pays for time or results of mt-iPSS providers. The present problem for mt-iPSS customer is how to timely identify the optimal machine tools, sequence and cutting parameters of operation to finish the jobs while mt-iPSS providers try to maximise their benefit in a non-cooperative game structure. In this paper, a Stackelberg game model is put forward to solve the coordination problem based on the costing of different job shop scheduling solutions under the result-oriented mt-iPSS paradigm. Then, to solve the established bi-level programming model of the Stackelberg game, a solution procedure based on hierarchical particle swarm optimisation is proposed. Finally, a case from a printing machinery enterprise is analysed to validate the proposed model. This research is expected to improve the quality and effectiveness of coordination for scheduling and process planning decision between mt-iPSS customer and multi-providers.     

Quantification for the importance degree of engineering characteristics with a multi-level hierarchical structure in QFD

Quantification for the importance degree of engineering characteristics (ECs) is an essential problem in quality function deployment. In real-world scenario, it is sometimes difficult to directly evaluate the correlation degree between ECs and customer requirements (CRs) as ECs are too abstract. Thus, the target ECs have to be further decomposed into several more detailed basic ECs and organised by a multi-level hierarchical structure. The paper investigates the quantification problem for the importance degree of such target ECs and tackles two critical issues. The first issue is how to deal with the uncertainties including fuzziness and incompleteness involved during the evaluation process. A fuzzy evidential reasoning algorithm-based approach is proposed to tackle this issue and derive the correlation degree between each of the basic ECs and the whole CRs. The second issue is how to deal with the interactions among the basic ECs decomposed from the same target EC during the aggregation process. A λ-fuzzy measure and fuzzy discrete Choquet integral-based approach is proposed to tackle this issue and aggregate these basic ECs. Final importance degree of the target ECs can then be obtained. At the end of this paper, a case study is presented to verify the feasibility and effectiveness of the method we propose.     

Methods for processing and prioritizing customer demands in variant product design

In the current highly competitive marketplace, customer demand is a major factor in the product design process. Many methods, such as quality function deployment and House of Quality (HoQ), provide a powerful process for translating and mapping customer demands into technical requirements. In the HoQ process, the customers' perceptions and expectations should be evaluated together in order to identify desirable product features. Moreover, in variant product design, the priority of each feature needs to be determined based on the customers' ratings of both the feature importance and customers' satisfaction. Although many methods such as quality attribute ranking, potential gain in customer value index and the analytic hierarchy process have been previously used to determine the relative importance of customer demands, they do not offer specific methods to determine a revised priority for product redesign. To address this issue, this research focuses on not only determining, but also revising the priority of customer demands for a variant product design based on new customer surveys. Two methods are proposed in this research. The first method classifies customer demands using natural language processing techniques in order to obtain customer expectations. Once comprehensive customer demands are obtained, the second method determines the revised priority of the customer demands using a fuzzy logic inference. These methods are implemented by two computerized systems, a customer demand decomposition and a classification system, and a customer demand priority rating system, with user-friendly interfaces. An example for car redesign is used to demonstrate the proposed methods. With the use of these two systems, the collection and revision of prioritization of the customer demands can be accomplished effectively.     

Systematical decision-making approach for quality function deployment based on uncertain linguistic term sets

A systematical decision-making approach is constructed for quality function deployment (QFD) in uncertain linguistic situations. The mathematical expression and operation of linguistic terms play important roles in the proposed approach in terms of customer requirements (CRs) and design requirements (DRs) in QFD. First, hesitant fuzzy linguistic term sets are designed to conveniently express uncertain linguistic terms and compute with words after the data derived from customers are pretreated and integrated in the decision-making process. Second, the tolerance deviation is defined to restrict innovatively the deviation range of fuzzy linguistic terms in the assessment stage of relative importance for CRs. Third, information entropy is originally designed to determine the final importance of DRs. Moreover, an empirical study on the research project called vortex recoil hydraulic retarder is conducted to demonstrate the performance of the systematical decision-making approach. The proposed approach can be applied to a wide variety of new product development problems in uncertainty settings.     

Fuzzy regression approach to process modelling and optimization of epoxy dispensing

Epoxy dispensing is one of the popular processes to perform microchip encapsulation for chip-on-board (COB) packages. However, determination of proper process parameters setting for optimal quality of the encapsulation is difficult due to the complex behaviour of the encapsulant during dispensing and the uncertainties caused by fuzziness of epoxy dispensing systems. In conventional regression models, deviations between the observed values and the estimated values are supposed to be in probability distribution. However, when data is irregular, the obtained regression model has an unnaturally wide possibility range. In fact, these deviations in some processes such as epoxy dispensing can be regarded as system fuzziness that can be dealt with properly using fuzzy regression method. In this paper, a fuzzy regression approach with fuzzy intervals to process modelling of epoxy dispensing for microchip encapsulation is described. Two fuzzy regression models relating three process parameters and two quality characteristics respectively for epoxy dispensing were developed. They were then introduced to formulate a fuzzy multi-objective optimization problem. A fuzzy linear programming technique was employed to formulate the optimization model. By solving the model, an optimal setting of process parameters can be obtained. Validation experiments were conducted to evaluate the effectiveness of the proposed approach to process modelling and optimization of epoxy dispensing for microchip encapsulation.     

A manufacturing resource allocation method with knowledge-based fuzzy comprehensive evaluation for aircraft structural parts

Manufacturing of aircraft structural parts has the characteristics of multiple varieties, complex structures and small batches, which make the manufacturing resource allocation highly difficult. This paper proposes a manufacturing resource allocation method with knowledge-based fuzzy comprehensive evaluation, considering multiple manufacturing resources including process planners, machine tools and cutting tools, as well as manufacturing process schemes of aircraft structural parts. Knowledge in terms of experts’ experience and historical data is used for fuzzy comprehensive evaluation. A manufacturing resource allocation model is proposed based on the analysis of manufacturing processes of aircraft structural parts. The capability of planners, the complexity of structural parts, the reliability of machine tools, the reliability of cutting tools and the correlations between manufacturing resources and structural parts are evaluated using the fuzzy comprehensive evaluation method. Multiple manufacturing resources are allocated based on the fuzzy comprehensive evaluation results. A prototype system has been implemented and a case study is used to validate the proposed approach.     

Determining the Importance Weights for the Customer Requirements in QFD Using a Fuzzy AHP with an Extent Analysis Approach

In the Quality Function Deployment (QFD) process, determining the importance weights for the customer requirements is an essential and crucial process. The Analytic Hierarchy Process (AHP) has been used to determine the importance weights for product planning, but this has occurred mainly in crisp (non-fuzzy) decision applications. However, human judgment on the importance of customer requirements is always imprecise and vague. To make up for this deficiency in the AHP, a fuzzy AHP with an extent analysis approach is proposed to determine the importance weights for the customer requirements. In the method, triangular fuzzy numbers are used for the pairwise comparison of a fuzzy AHP. By using the extent analysis method and the principles for the comparison of fuzzy numbers, one can derive the weight vectors. The new approach can improve the imprecise ranking of customer requirements inherited from studies based on the conventional AHP. Furthermore, the fuzzy AHP with extent analysis is simple and easy to implement to prioritize customer requirements in the QFD process compared with the conventional AHP. This paper uses an example of a hair dryer design to illustrate the proposed approach.     

A genetic programming based fuzzy regression approach to modelling manufacturing processes

Fuzzy regression has demonstrated its ability to model manufacturing processes in which the processes have fuzziness and the number of experimental data sets for modelling them is limited. However, previous studies only yield fuzzy linear regression based process models in which variables or higher order terms are not addressed. In fact, it is widely recognised that behaviours of manufacturing processes do often carry interactions among variables or higher order terms. In this paper, a genetic programming based fuzzy regression GP-FR, is proposed for modelling manufacturing processes. The proposed method uses the general outcome of GP to construct models the structure of which is based on a tree representation, which could carry interaction and higher order terms. Then, a fuzzy linear regression algorithm is used to estimate the contributions and the fuzziness of each branch of the tree, so as to determine the fuzzy parameters of the genetic programming based fuzzy regression model. To evaluate the effectiveness of the proposed method for process modelling, it was applied to the modelling of a solder paste dispensing process. Results were compared with those based on statistical regression and fuzzy linear regression. It was found that the proposed method can achieve better goodness-of-fitness than the other two methods. Also the prediction accuracy of the model developed based on GP-FR is better than those based on the other two methods.     

Improved approach to quality function deployment based on Pythagorean fuzzy sets and application to assembly robot design evaluation

Quality function deployment (QFD) is an effective method that helps companies analyze customer requirements (CRs). These CRs are then turned into product or service characteristics, which are translated to other attributes. With the QFD method, companies could design or improve the quality of products or services close to CRs. To increase the effectiveness of QFD, we propose an improved method based on Pythagorean fuzzy sets (PFSs). We apply an extended method to obtain the group consensus evaluation matrix. We then use a combined weight determining method to integrate former weights to objective weights derived from the evaluation matrix. To determine the exact score of each PFS in the evaluation matrix, we develop an improved score function. Lastly, we apply the proposed method to a case study on assembly robot design evaluation.     

基于状态空间模型的机床加工精度分析

伺服进给系统的机电耦合特性直接影响数控机床的加工精度，单独针对伺服系统或机械系统建立的模型不足以准确分析系统参数对机床整机加工精度的影响。因此，综合考虑机床伺服系统与机械结构之间的耦合关系，建立伺服进给系统机电耦合动力学模型具有重要意义。首先，为保证伺服进给系统建模精度，利用状态空间法建立了机床机电耦合状态空间方程。其次，建立了伺服进给系统机电耦合Simulink模型，在此基础上采用复合控制提高系统的响应速度和加工精度。随后，利用多体动力学软件建立机床进给系统的刚柔耦合动力学模型，添加摩擦、阻尼等非线性因素，并导入Simulink与伺服系统建立耦合关系。最终，建立了卧式加工中心伺服进给系统的刚柔-机电耦合仿真加工平台，通过模拟机床加工轨迹以验证机电耦合状态空间模型的可靠性。结果表明：该状态空间模型能准确描述系统内部参数和系统输入输出的耦合关系；采用复合控制结构能有效提高系统的响应速度和加工精度。研究结果为数控机床的仿真建模和提高加工精度提供理论依据，为机床机电系统的设计提供有效指导。     

Fuzzy expected value modelling approach for determining target values of engineering characteristics in QFD

Quality function deployment (QFD) is a planning and problem-solving tool that is renowned for translating customer requirements into the technical attributes of a product. To deal with the imprecise elements in the development process, fuzzy set theory is incorporated into QFD methodology. A novel fuzzy expected value operator approach is proposed in this paper to model the QFD process in a fuzzy environment, and two fuzzy expected value models are established to determine the target values of engineering characteristics in handling different practical design scenarios. Analogous to stochastic programming, the underlying philosophy in the proposed approach is based on selecting the decision with maximum expected returns. Furthermore, the proposed approach considers not only the inherent fuzziness in the relationships between customer requirements and engineering characteristics, but also the correlation among engineering characteristics. These two kinds of fuzzy relationships are aggregated to give the fuzzy importance of individual engineering characteristics. Finally, an example of a quality improvement problem of a motor car design is given to demonstrate the application and performance of the proposed modelling approach.     

Optimal process planning for a combined punch-and-laser cutting machine using ant colony optimization

A machine that performs both punching and laser-cutting operations is referred as combined punch-and-laser machine. Such a machine has been in the market for about two decades. Although process-planning tools have been used on such a combined machine, the optimization of process planning dedicated to combined machines, based on our literature search results, has never been directly studied. This work addresses the process-planning problem for the combined punch-and-laser machine by integrating knowledge, quantitative analysis, and numerical optimization approaches. The proposed methodology helps making decisions on following issues: (i) which type of operation should be applied to each feature, and (ii) what is the optimal operation sequence (tool path) to achieve the maximum manufacturing efficiency. The ant colony optimization (ACO) algorithms are employed in searching the optimal tool path. Sensitivities of control parameters of ACO are also analysed. Through applications, the proposed method can significantly improve the operation efficiency for the combined punch-and-laser machine. The method can also be easily automated and integrated with the nesting and G-code generation processes. Some issues and possible future research topics have also been discussed.     

Passive estimated state feedback fuzzy controller design for discrete perturbed fuzzy systems with multiplicative noises

This article presents an estimated state feedback fuzzy controller design method for uncertain passive discrete-time nonlinear stochastic systems with multiplicative noises. The nonlinear stochastic systems considered in this article are represented by Takagi–Sugeno (T–S) fuzzy models. For describing stochastic behaviors, stochastic differential equations are used to structure the stochastic T–S fuzzy model for representing nonlinear stochastic systems. Besides, the uncertainties of the controlled system are considered for dealing with molding errors and varying parameters. The concept of parallel distributed compensation is employed in this article to construct the estimated state feedback fuzzy controllers. Applying the Lyapunov and passivity theories, the sufficient stability conditions are derived in terms of linear matrix inequality. Finally, a numerical example is provided to show the effectiveness and applicability of the proposed fuzzy controller design approach.     

基于RIR-MOO的定制产品优化设计方法研究

大规模定制是未来产品制造的发展方向,以低成本快速响应客户的个性化需求是定制产品设计的关键。以往对定制产品设计的研究缺少从个性化需求到产品参数的流程化设计指导方法,无法从定制产品个性化的客户需求出发,快速地关联设计目标并指导产品参数的设计。为此,提出了基于RIR-MOO （relative importance ratings and multi-objective optimization,相对重要性等级-多目标优化）的定制产品优化设计方法,从客户需求出发,将关键需求映射到相关的设计目标,再通过多目标优化（multi-objective optimization,MOO）方法快速求解产品参数,实现定制产品的快速响应和优化设计。首先,针对模糊、动态变化的客户需求,利用加权区间粗糙集分析方法对客户需求进行客观分析,排除争议性大的模糊需求,同时计算不同客户需求的相对权重,得到其相对重要性等级（relative importance ratings,RIR）;然后,提出一种基于转换矩阵的客户需求与设计目标关联的方法,根据关键需求与设计目标的关联度以及关键需求的RIR,对关键需求与设计目标进行匹配,实现关键需求到设计目标的转换;最后,基于MOO方法对设计目标对应的产品参数进行优化设计,实现约束条件下定制产品的多目标优化。以汽车发动机活塞机构优化设计为例,对基于RIR-MOO的优化设计方法的可行性进行验证。结果表明,所提出的方法可以快速响应定制产品的客户需求并指导其优化设计,可为定制化产品制造企业提供指导。