Optimization of Dynamic Multi-Response Problems Using Grey Multiple Attribute Decision Making

While many of the previous Taguchi method applications dealt with a state system problem, dynamic multi-response problems have received only limited attention. This study presents a practical and systematic procedure to resolve dynamic multi-response problems based on Taguchi's parameter design. The quality loss function is initially applied to assess the quality performance for each response. The technique for order preference by similarity to the ideal solution (TOPSIS), associated with the multiple attribute decision-making (MADM) method, is then incorporated into the Grey relational model of the Grey system theory. The integrated Grey relational grade (IGRG) relative closeness to the ideal solution is determined as a multi-response performance index for determining the optimal parameter setting. The proposed procedure can not only efficiently determine the optimal parameter setting, but also reduce the conflicts when determining the optimal parameter setting for the multi-response problems. Experimental results obtained from the biological reduction of an ethyl acetoacetate process demonstrate the effectiveness of the proposed procedure.     

MOORA-based Taguchi optimisation for improving product or process quality

In this study a multi-objective optimisation on the basis of ratio analysis (MOORA)-based Taguchi application is used to solve multi-response optimisation problems. In this application, the MOORA method is integrated with the Taguchi method to convert the multi-response problem into a single-response problem. Four examples are considered in this paper for illustrative purposes. The MOORA-based Taguchi method is simple and robust compared to the other MADM methods, such as TOPSIS, VIKOR and GRA. The proposed model reduces the time associated with the amount of calculation steps significantly. We found that solution results of the MOORA-based Taguchi application and other hybrid models in the literature were not significantly different. The MOORA-based Taguchi application offers also a new tool in the optimisation of Taguchi’s multi response problem.     

The use of a grey-based Taguchi method for optimizing multi-response simulation problems

Simulation modelling is a widely accepted tool in system design and analysis, particularly when the system or environment has stochastic and nonlinear behaviour. However, it does not provide a method for optimization. In general, problems contain more than one response, which are often in conflict with each other. This article proposes a grey-based Taguchi method to solve the multi-response simulation problem. The grey-based Taguchi method is based on the optimizing procedure of the Taguchi method, and adopts grey relational analysis (GRA) to transfer multi-response problems into single-response problems. A practical case study from an integrated-circuit packaging company illustrates that differences in performance of the proposed grey-based Taguchi method and other methods found in the literature were not significant. The grey-based Taguchi method thus provides a new option when solving a multi-response simulation-optimization problem.     

The incorporation of the Taguchi and the VIKOR methods to optimize multi-response problems in intuitionistic fuzzy environments

The Taguchi method is a powerful method of solving quality problems in various fields of engineering. However, this method was developed to optimize single-response processes. In many multi-response optimization problems, the important response is determined subjectively, based on knowledge or experience. However, using only exact numbers to represent this importance is problematic, because there is uncertainty and vagueness. The concept of intuitionistic fuzzy sets (IFSs) is a powerful method for characterization, using a membership function and a non-membership function. This paper proposes an efficient VIKOR method that optimizes multi-response problems in intuitionistic fuzzy environments. The importance weights of various responses are evaluated in terms of IFSs. In the proposed method, the similarity measure between IFSs is used to determine the crisp weights of the responses. This scheme eliminates the need for complicated intuitionistic fuzzy arithmetic operations and increases efficiency in solving multi-response optimization problems in intuitionistic fuzzy environments. Two case studies: plasma-enhanced chemical vapor deposition and a double-sided surface mount technology electronic assembly operation are used to demonstrate the effectiveness of the proposed method.     

Characterizing and optimizing multi-response processes by the taguchi method

In this paper we demonstrate the ability of the Taguchi technique accurately to characterize and successfully to optimize complicated multi-response processes with the minimum of experiments, provided one uses simple statistical techniques which can ensure valid, and definitive results. We point out the usefulness of suitable data-transformations, and we suggest a systematic procedure for establishing the optimal operating conditions and for carrying out confirmatory experiments. For the particular case detailed in this paper (which is typical of multi-response processes) the Taguchi technique achieved an improvement in uniformity of a factor of 2, together with optimized process control.     

Optimal design of multi-response experiments using semi-definite programming

Optimal design of multi-response experiments for estimating the parameters of multi-response linear models is a challenging problem. The main drawback of the existing algorithms is that they require the solution of many optimization problems in the process of generating an optimal design that involve cumbersome manual operations. Furthermore, all the existing methods generate approximate design and no method for multi-response n-exact design has been cited in the literature. This paper presents a unified formulation for multi-response optimal design problem using Semi-Definite Programming (SDP) that can generate D-, A- and E-optimal designs. The proposed method alleviates the difficulties associated with the existing methods. It solves a one-shot optimization model whose solution selects the optimal design points among all possible points in the design space. We generate both approximate and n-exact designs for multi-response models by solving SDP models with integer variables. Another advantage of the proposed method lies in the amount of computation time taken to generate an optimal design for multi-response models. Several test problems have been solved using an existing interior-point based SDP solver. Numerical results show the potentials and efficiency of the proposed formulation as compared with those of other existing methods. The robustness of the generated designs with respect to the variance-covariance matrix is also investigated.     

Optimization in CNC end milling of UNS C34000 medimum leaded brass with multiple surface roughnesses characteristics

The present study highlights a multi-objective optimization problem by applying utility concept coupled with Taguchi method through a case study in CNC end milling of UNS C34000 medium leaded brass. The study aimed at evaluating the best process environment which could simultaneously satisfy multiple requirements of surface quality. In view of the fact, the traditional Taguchi method cannot solve a multi-objective optimization problem; to overcome this limitation, utility theory has been coupled with Taguchi method. Depending on Taguchi’s Lower-the-Better (LB) response criteria; individual surface quality characteristics has been transformed into corresponding utility values. Individual utility values have been aggregated finally to compute overall utility degree which serves as representative objective function for optimizing using Taguchi method. Utility theory has been adopted to convert a multi-response optimization problem into a single response optimization problem; in which overall utility degree serves as the representative single objective function for optimization. The study of combined utility theory and Taguchi method for predicting optimal setting. Based on Taguchi’s Signal-to-Noise ratio (S/N), analysis has been made on the overall utility degree and optimal process environment has been selected finally which corresponds to highest S/N Ratio. Optimal result has been verified through confirmatory test. The case study indicates application feasibility of the aforesaid methodology proposed for multiresponse optimization and off-line control of multiple surface quality characteristics in CNC end milling.     

Application of semi-definite programming to the design of multi-response experiments

The need to be able to design experiments with multiple responses is becoming apparent in many real-world applications. The generation of an optimal design to estimate the parameters of a multi-response model is a challenging problem. Currently available algorithms require the solution of many optimization problems in order to generate an optimal design. In this paper, the problem of multi-response D-optimal design is formulated as a semi-definite programming model and a relaxed form of it is solved using interior-point solvers. The main advantage of the proposed method lies in the amount of computation time taken to generate a D-optimal design for multi-response models. The proposed method is tested on several test problems and is shown to be very efficient with optimal designs being found very quickly in all cases. The robustness of the generated designs with respect to the variance-covariance matrix is also assessed for the test problems in order to show how a sensitivity analysis can be performed. The characteristics of the proposed method are also compared with those of other existing methods.     

Robust design for multiple dynamic quality characteristics using data envelopment analysis

The Taguchi method is extensively adopted in various industries to continuously improve product design in response to customer requirements. The dynamic system of the Taguchi method is frequently implemented to design products with flexible applications. However, Taguchi's dynamic system can be employed only for individual quality characteristic, and the relationship between the quality characteristic and the signal factor is assumed to be linear. Because of these restrictions, Taguchi's dynamic system is ineffective for multiple quality characteristics or when the quality characteristic has a nonlinear relationship with the signal factor. This study describes a novel procedure for optimizing a dynamic system based on data envelopment analysis. The proposed procedure overcomes the limitations of Taguchi's dynamic system. Two cases are analyzed to demonstrate the effectiveness of the proposed procedure. The results show that the proposed procedure can enhance multiple dynamic quality characteristics. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of dynamic robust design experiments

Robust design is an important method for improving product or manufacturing process design by making the output response insensitive (robust) to diDcult-tocontrol variations (noise). Most of the robust design research in the literature focuses on problems with static responses. This paper investigates robust design problems with dynamic responses. For analysing robust design experiments with dynamic systems, Taguchi (1986) proposes a two-step procedure to identify the 'optimal' factor settings that minimize the average quadratic loss. In this paper we show that Taguchi's procedure is only appropriate under a multiplicative model. We develop the appropriate two-step procedure for dynamic systems under an additive model. The procedure reduces the dimension of the optimization problem and allows for future changes of the target slope without re-optimization. We illustrate the proposed procedure and Taguchi's procedure with real examples. We also discuss future research and extensions to general classes of models.     

Application of integrated Taguchi and TOPSIS method for optimization of process parameters for dimensional accuracy in turning of EN25 steel

Abstract

The turning process is one of the fundamental machining operations wherein optimization of parameters leads to better machining performance. This study has applied integrated Taguchi and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods to determine the optimum process parameters in turning operation of EN25 steel using coated carbide tools. The process parameters considered are cutting speed, feed rate, and depth of cut. The objective is to minimize circularity and cylindricity simultaneously. An orthogonal array, Signal to Noise (S/N) ratio, and TOPSIS are employed to analyze the effects of input parameters on the output parameters. In this study, a decision matrix is formed using S/N ratios; then the TOPSIS method is used to transmogrify a multi-criteria optimization problem into a single-criterion problem. The result revealed that the proposed method is appropriate for solving multi-criteria optimization of process parameters. Results also showed that cutting speed of 215 m/min, feed rate of 0.07 mm/rev, and depth of cut of 1.5 mm are the optimum combination of process parameters.     

Development of a new multi-criteria optimization method for engineering design problems

In this study, we developed a new multiple criteria optimization method in the context of engineering design. The design of experiment (DoE) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods are combined to identify an objective function of the selected problem by fitting a polynomial to the experimental data in a multiple linear regression analysis. Then, the regression function is incorporated into a mathematical model with the criteria constraints to determine an optimal criteria set. The proposed method can be used to compare the functionality and results provided by different scenario analyses of a building design optimization problem, which represent design solutions. We applied the DoE–TOPSIS model to solve different multi-criteria design optimization problems using two examples from the literature and obtained satisfactory results. In the examples, the results obtained using the combined DoE–TOPSIS model are almost in agreement with those derived from conventional multi-criteria design optimization methods, which demonstrates the simplicity, usability, and flexibility of the proposed method in solving engineering design problems.     

Multi-response optimization of post-fire performance of strain hardening cementitious composite

This paper presents results of an experimental program conducted to optimize the post-fire performance of Strain Hardening Cementititous Composites (SHCC) using Taguchi approach with utility concept. The experiments were first undertaken by determining nine SHCC mixes using a standard L9 (3⁴) orthogonal array of four parameters and each parameter with three levels. The four parameters of SHCC mixes included fly-ash/binder ratio, sand/binder ratio, water/binder ratio and fiber proportions. The responses of SHCC to be optimized were tensile strain capacity, compressive strength and post-fire compressive strength after subjected to 200 °C, 400 °C, 600 °C and 800 °C of isothermal heating. Utility concept was introduced to simplify the multi-response problem into mono-response question together with Taguchi method. The role of different parameters on the composite responses of SHCC was examined. Furthermore, an optimal SHCC mix to maximize multi-responses was determined based on statistical analysis and validated by additional confirmation tests.     

Signal-to-noise ratio development for quality engineering

Dr. Taguchi developed the concept of signal-to-noise (SN) ratio in quality engineering to evaluate the performance of a system. The objective is to develop systems which are robust against noise factors. The SN ratio indicates the degree of the predictable performance of a product or process in the presence of noise factors. Parameter design of the Taguchi method optimizes the SN ratio in the domain of control factors, so that performance could be made insensitive to the noise factors in order to improve product quality. If the domain of the control factors is a continuous space, the problem is a non-linear programming problem. Usually, in practice, there are only a few available levels for the control factors. Thus, experimental design methods can be useful for such problems. The SN ratio for four cases of dynamic characteristic problems is developed in this paper. This paper also gives the method to compute SN ratios for both equispaced and non-equispaced intervals for levels of signal factors. Two examples are presented to illustrate the method.     

Product portfolio planning: a metaheuristic-based simulated annealing algorithm

Product portfolio diversity is prominent for customers, but critical for manufacturers. From the manufacturers’ perspective, diversity must be maintained at a level where engineering costs do not exceed the acquired advantages of increased market share. Therefore, in this paper we consider the problem of product portfolio planning to simultaneously maximise market share and minimise manufacturing engineering costs. Since this problem belongs to the NP-hard class of problems, exact algorithms are incapable of rendering an optimal solution. Therefore, we used metaheuristic-based simulated annealing to deal with the problem. Our proposed algorithm consists of two parts, i.e. a random search and a predetermined rule to generate the next possible neighbours (product portfolio). In order to have a robust algorithm, we calibrated different levels of our problem's parameters using the Taguchi method. This method picks the best levels of different parameters, conducting the least possible experiments. To evaluate the performance of our proposed algorithm, we compared it with a strong algorithm – the genetic algorithm. We used this comparison as the basis of our research. The obtained computational results clearly demonstrate the efficiency and effectiveness of our proposed algorithm.     

Robust design with dynamic characteristics using stochastic sequential quadratic programming

Robust design with dynamic characteristics is an important off-line quality engineering technique for improving product quality over a range of input conditions by reducing variations caused by uncontrolled factors. Since several studies have indicated that there are important limitations to Taguchi's S/N ratio analysis, the solution procedure for dynamic systems deserves further investigation. This paper proposes a stochastic optimization modeling procedure to overcome the difficulty in Taguchi's method to accommodate dynamic characteristics. The main idea underlying the proposed method is to minimize the total variations on quality characteristics while attaining the target performance over a range of input conditions. Due to the nonlinear nature of the stochastic optimization model, two stochastic versions of sequential quadratic programming respectively embedded with a Monte Carlo simulation and numerical approximations are devised to solve the problem. In the robust design of a temperature control circuit often discussed in dynamic problems, the proposed method performs efficiently and effectively. Compared with the Taguchi method, the design solved in this paper has smaller variations, indicating that the proposed method is a promising technique for dynamic-characteristic robust design.     

Particle simulation of spontaneous crack generation problems in large‐scale quasi‐static systems

To extend the application range of the distinct element method from a laboratory scale into a large scale such as a geological scale, we need to deal with an upscale issue associated with simulating spontaneous crack generation problems in large‐scale quasi‐static systems. Toward this direction, three important simulation issues, which may affect the quality of the particle simulation results of a quasi‐static system, have been addressed in details in this paper. The first simulation issue is how to determine the particle‐scale mechanical properties of a particle from the measured macroscopic mechanical properties of rocks. The second simulation issue is that the fictitious time, rather than the physical time, is used in the particle simulation of a quasi‐static problem. The third simulation issue is that the conventional loading procedure used in the distinct element method is conceptually inaccurate, at least from the force propagation point of view. A new loading procedure is proposed to solve the conceptual problem resulting from the third simulation issue. The proposed loading procedure is comprised of two main types of periods, a loading period and a frozen period. Using the proposed loading procedure, the parameter selection problem stemming from the first issue can be somewhat solved. Since the second issue is an inherent one, it is strongly recommended that a particle‐size sensitivity analysis of at least two different models, which have the same geometry but different smallest particle sizes, be carried out to confirm the particle simulation result of a large‐scale quasi‐static system. The related simulation results have demonstrated the usefulness and correctness of the proposed loading procedure for dealing with spontaneous crack generation problems in large‐scale quasi‐static geological systems. Copyright © 2006 John Wiley & Sons, Ltd.     

CovSel: Variable selection for highly multivariate and multi-response calibration: Application to IR spectroscopy

Variable selection is of major interest for NIR calibration, either as a feature selection or for the design of multi-wavelength devices. Some dedicated methods have been developed in chemometrics, but a few of them addresses explicitly the case of multi-response calibration. Variable selection for NIR spectroscopy must face two problems: (1) the huge number of variables yields a very large solution space; (2) variables are highly correlated, and if no special attention is paid the model built on the selection may be ill-conditioned. This article presents a new method, CovSel, which tackles these two problems by following this procedure: (1) variable selection step by step on the basis of their global covariance with all the responses; and (2) projection of the data orthogonally to the selected variable. CovSel was applied on three problems: the first one concerns a single response MIR calibration (Brix degree content in apricot), the second one concerns a multi-response NIR calibration (4 main constituents in corn) and the last application concerns the NIR discrimination of 3 wine grape varieties.     

Study of friction welding characteristics of Al/SiC composite and application of grey-based TOPSIS

The present work investigates the possibility of producing friction welded joints with an advanced material like Al/SiC (aluminum–silicon carbide) composite. The study also discloses the multi response optimization in the process of continuous drive friction welding using a hybrid algorithm of grey-based TOPSIS (technique for order of performance by similarity to ideal solution). The friction welding parameters (frictional pressure, upset pressure, burn off length and rotational speed) were optimized considering the multiple performance characteristics such as proof stress, tensile strength, and microhardness. Taguchi’s L₂₇ orthogonal array was used for conducting the welding trials. The confirmation test was conducted at the optimal setting, to sort out the effectiveness of the proposed hybrid algorithm. The macro photographs of the joints and optical micrographs of the weld zone were studied. The scanning electron microscope images of the fractured surface were also examined to identify the failure mode of joints. The significant improvements in the performance characteristics prove the effectiveness of the grey-based TOPSIS method in experimental welding optimization.     

A methodological concept for phase change material selection based on multiple criteria decision analysis with and without fuzzy environment

Selection of proper phase change material (PCM) plays an important role towards the development of a latent heat thermal energy storage system. Selection of the phase change material is a difficult and restrained task due to the immense number of different available materials having different characteristics. One has to select such PCM which will give the desired thermal performance at minimum cost. This study deals with two Multiple Attribute Decision-Making (MADM) methods to solve PCM selection problem. These two methods are technique for order preference by similarity to ideal solution (TOPSIS) method and fuzzy TOPSIS method that uses linguistic variable presentation and fuzzy operation. Both the methods use an analytic hierarchy process (AHP) method to determine weights of the criteria. TOPSIS and fuzzy TOPSIS methods are used to obtain final ranking. A problem to evaluate the best choice of PCM used in solar domestic hot water system is considered here to demonstrate the effectiveness and feasibility of the proposed model. Empirical results showed that the proposed methods are viable approaches in solving PCM selection problem. TOPSIS is suitable for the use of precise performance ratings while the fuzzy TOPSIS is a preferred technique when the performance ratings are vague and inaccurate.