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The purpose of this paper is to propose a simple methodology in solving multi‐response optimisation problems by employing Taguchi methods and a non‐parametric statistical technique.

There is a continuous interest in developing effective and statistically sound multi‐response optimisation methods such that they will provide a firm framework in global product and process improvement. A non‐parametric approach is proposed for the first time in a five‐step methodology that exploits Taguchi's fractional factorial designs and the concept of signal‐to‐noise ratio in data consolidation. The distinct feature of this method is the transformation of each response variable to a single rank variable. The subsequent incorporation of the squared ranks for each of the investigated responses issues a single master‐rank response suitably referred to conveniently as a “Super Rank” (SR) response, thus collapsing all dependent product characteristic information into a single non‐dimensional variable. This SR variable is handled by standard non‐parametric methods such as Wilcoxon's two‐sample, rank sum test or Mann‐Whitney's test eliminating at the same time multi‐distribution effects and small‐sample complications expected for this type of experimentation.

The proposed methodology is tested on already published data pertaining a design problem in the electronic assembly technology field. The case study requires six‐factor simultaneous optimisation of three response variables. A second example is analyzed by the proposed method focusing on the optimisation of a submerged arc‐welding process problem due to a group of five factors. The Mann‐Whitney's test contrasts the effects of factor settings one‐to‐one on the SR response in order to assign statistical significance to the optimal factor settings.

The application of this methodology is tested at the same time in a real three‐response optimisation case study where each response belongs to different optimisation category.

The methodology outlined in this work eliminates the need for sophisticated multi‐response data handling. In addition, small‐sample considerations and multi‐distribution effects that may be inherent do not restrict the applicability of the method presented herein by this type of experimentation.

This investigation provides a new angle to the published methods of multi‐response optimisation by supporting Taguchi's design of experiments methods through a multi‐ranking scheme that leads to non‐parametric factor resolution.

The aim of this paper is to circumvent the multi‐distribution effects and small sample constraints that may arise in unreplicated‐saturated fractional factorial designs during construction blueprint screening.

A simple additive ranking scheme is devised based on converting the responses of interest to rank variables regardless of the nature of each response and the optimization direction that may be issued for each of them. Collapsing all ranked responses to a single rank response, appropriately referred to as “Super‐Ranking”, allows simultaneous optimization for all factor settings considered.

The Super‐Rank response is treated by Wilcoxon's rank sum test or Mann‐Whitney's test, aiming to establish possible factor‐setting differences by exploring their statistical significance. An optimal value for each response is predicted.

It is stressed, by example, that the model may handle simultaneously any number of quality characteristics. A case study based on a real geotechnical engineering project is used to illustrate how this method may be applied for optimizing simultaneously three quality characteristics that belong to each of the three possible cases, i.e. “nominal‐is‐best”, “larger‐is‐better”, and “smaller‐is‐better” respectively. For this reason, a screening set of experiments is performed on a professional CAD/CAE software package making use of an L₈(2⁷) orthogonal array where all seven factor columns are saturated by group excavation controls.

The statistical nature of this method is discussed in comparison with results produced by the desirability method for the case of exhausted degrees of freedom for the error. The case study itself is a unique paradigm from the area of construction operations management.

The aim of this paper is to examine product formulation screening at the industrial level in terms of multi‐trait improvement by considering several pertinent controlling factors.

The study adopts Taguchi's orthogonal arrays (OAs) for sufficient and economical sampling in a mixture problem. Robustness of testing data is instilled in this method by employing a two‐stage analysis where controlling components are investigated together while the slack variable is tested independently. Multi‐responses collapse to a single master response has been incurred according to the Super Ranking concept. Order statistics are employed to provide statistical significance. The slack variable influence is tested by regression and nonparametric correlation.

Synergy among Taguchi methodology, super ranking and nonparametric testing was seamless to offer practical resolution to product component activeness. The concurrent modulation of two key product traits due to five constituents in the industrial production of muffin‐cake is invoked. The slack variable, rich cream, is strongly active while the influence of added amount of water is barely evident.

The method presented is suitable only for situations where industrial mixtures are investigated. The case study demonstrates prediction capabilities up to quadratic effects for five nominated effects. However, the statistical processor selected here may be adapted to any number of factor settings dictated by the OA sampling plan.

By using a case study from food engineering, the industrial production of a muffin‐cake is examined focusing on a total of five controlling mixture components and two responses. This demonstration emphasizes the dramatic savings in time and effort that are gained by the proposed method due to reduction of experimental effort while gaining on analysis robustness.

This work interconnects Taguchi methodology with powerful nonparametric tests of Kruskal‐Wallis for the difficult problem of non‐linear analysis of mixtures for saturated, unreplicated fractional factorial designs in search of multi‐factor activeness in multi‐response cases employing simple and practical tools.

To provide a good insight into solving a multi‐response optimization problem using neuro‐fuzzy model and Taguchi method of experimental design.

Over the last few years in many manufacturing organizations, multiple response optimization problems were resolved using the past experience and engineering judgment, which leads to increase in uncertainty during the decision‐making process. In this paper, a four‐step procedure is proposed to resolve the parameter design problem involving multiple responses. This approach employs the advantage of both artificial intelligence tool (neuro‐fuzzy model) and Taguchi method of experimental design to tackle problems involving multiple responses optimization.

The proposed methodology is validated by revisiting a case study to optimize the three responses for a double‐sided surface mount technology of an electronic assembly. Multiple signal‐to‐noise ratios are mapped into a single performance statistic through neuro‐fuzzy based model, to identify the optimal level settings for each parameter. Analysis of variance is finally performed to identify parameters significant to the process.

The proposed model will be validated in future by conducting a real life case study, where multiple responses need to be optimized simultaneously.

It is believed that the proposed procedure in this study can resolve a complex parameter design problem with multiple responses. It can be applied to those areas where there are large data sets and a number of responses are to be optimized simultaneously. In addition, the proposed procedure is relatively simple and can be implemented easily by using ready‐made neural and statistical software like Neuro Work II professional and Minitab.

This study adds to the literature of multi‐optimization problem, where a combination of the neuro‐fuzzy model and Taguchi method is utilized hand‐in‐hand.

The purpose of this paper is to originate a statistical model for delamination factor, surface roughness, machining force and also to determine and compare the effects of machining parameters (spindle speed, fiber orientation angle, helix angle and feed rate) on the output responses during end-milling of glass fiber reinforced polymers (GFRP) by using desirability functional analysis (DFA) and grey relational analysis (GRA).

Based on Taguchi’s L27 orthogonal array, milling experiments were carried on GFRP composite plates employing solid carbide end mills with different helix angles. The machining parameters were optimized by an approach based on DFA and GRA, which were useful tools for optimizing multi-response considerations, namely, machining force, surface roughness and delamination factor. A composite desirability index was obtained for multi-responses using individual desirability values from DFA. Based on this index and grey relational grade the optimum levels of parameters were identified and significant contribution of parameters was ascertained by analysis of variance.

Fiber orientation angle (66.75 percent) was the significant parameter preceded by feed rate (15.05 percent), helix angle (7.76 percent) and spindle speed (0.30 percent) for GFRP composite plates.

Multi-objective optimization in end-milling of GFRP composites using DFA and GRA has not been performed yet.

Micro-EDM is an important process in the field of micro-machining. Especially, the μEDM is one of the technologies widely used for manufacture of micro-parts, micro-tools and micro-components, etc. The accuracy and repeatability of the μEDM process is still highly dependent on the μWEDG process. The electrode generation and regeneration is considered a key enabling technology for improving the performance of the μEDM process. Many engineers considered the Taguchi technique as engineering judgment during multiple response optimizations. This paper aims to focus on the use of micro-WEDG process to generate a micro-tool (electrode) with minimum surface roughness and higher metal removal rate (MRR).

In this research work, the Taguchi quality loss function analysis is used to examine and explain the influences of three process parameters (feed rate, capacitance and voltage) on the output responses such as MRR and surface roughness. Further, the optimized machining parameters were determined considering the multiple response objective using Taguchi multi-response signal-to-noise ratio.

Based on the experimental result, it was concluded that the Taguchi technique is suitable for the optimization of multi-response problem.

This paper presents an alternative approach using Taguchi's quality loss function. In most of the modern technological situations, more than one response variable is pertinent to the success of an industrial process. In this research work, the influence of feed rate, capacitance and voltage on the MRR and surface roughness (multiple responses) is investigated.

The purpose of this paper is to investigate the influence of turning parameters such as cutting speed, feed rate and depth of cut on tool flank wear and machined surface quality of AISI 304 stainless steel during environment friendly turning under nanofluid minimum quantity lubrication (NMQL) conditions using PVD-coated carbide cutting inserts.

Turning experiments are conducted as per the central composite rotatable design under the response surface methodology. ANOVA and regression analysis are employed to examine significant cutting parameters and develop mathematical models for VB (tool flank wear) and R_a (surface roughness). Multi-response desirability optimization approach is used to investigate optimum turning parameters for simultaneously minimizing VB and R_a.

Optimal input turning parameters are observed as follows: cutting speed: 168.06 m/min., feed rate: 0.06 mm/rev. and depth of cut: 0.25 mm with predicted optimal output response factors: VB: 106.864 µm and R_a: 0.571 µm at the 0.753 desirability level. ANOVA test reveals depth of cut and cutting speed-feed rate interaction as statistically significant factors influencing tool flank wear, whereas cutting speed is a dominating factor affecting surface roughness. Confirmation tests show 5.70 and 3.71 percent error between predicted and experimental examined values of VB and R_a, respectively.

AISI 304 is a highly consumed grade of stainless steel in aerospace components, chemical equipment, nuclear industry, pressure vessels, food processing equipment, paper industry, etc. However, AISI 304 stainless steel is considered as a difficult-to-cut material because of its high strength, rapid work hardening and low heat conductivity. This leads to lesser tool life and poor surface finish. Consequently, the optimization of machining parameters is necessary to minimize tool wear and surface roughness. The results obtained in this research can be used as turning database for the above-mentioned industries for attaining a better machined surface quality and tool performance under environment friendly machining conditions.

Turning of AISI 304 stainless steel under NMQL conditions results in environment friendly machining process by maintaining a dry, healthy, clean and pollution free working area.

Machining of AISI 304 stainless steel under vegetable oil-based NMQL conditions has not been investigated previously.

The purpose of this paper is to optimise the process parameters, namely, fibre orientation angle, helix angle, spindle speed, and feed rate in milling of glass fibre-reinforced plastic (GFRP) composites using grey relational analysis (GRA) and desirability function analysis (DFA).

In this work, experiments were carried out as per the Taguchi experimental design and an L27 orthogonal array was used to study the influence of various combinations of process parameters on surface roughness and delamination factor. As a dynamic approach, the multiple response optimisation was carried out using GRA and DFA for simultaneous evaluation. These two methods are best suited for multiple criteria evaluation and are also not much complicated.

The process parameters were found optimum at a fibre orientation angle of 15°, helix angle of 25°, spindle speed of 6,000 rpm, and a feed rate of 0.04 mm/rev. Analysis of variance was employed to classify the significant parameters affecting the responses. The results indicate that the fibre orientation angle is the most significant parameter preceded by helix angle, feed rate, and spindle speed for GFRP composites.

An attempt to optimise surface roughness and delamination factor together by combined approach of GRA and DFA has not been previously done.

Taguchi's technique is best suited to optimize a single performance characteristic yielding an optimal setting of process parameters. A single setting of process parameters may be optimal for one quality characteristics but the same setting may yield detrimental results for other quality features. Thus the purpose of this paper is to describe simultaneous optimization of multi‐characteristics.

The multi‐machining characteristics have been optimized simultaneously using Taguchi's parameter design approach and the utility concept. The paper used a single performance index, utility value, as a combined response indicator of several responses.

A simplified model based on Taguchi's approach and utility concept is used to determine the optimal settings of the process parameters for a multi‐characteristic product. The model is used to predict optimal settings of turning process parameters to yield the optimum quality characteristics of En24 steel turned parts using TiC coated carbide inserts. The optimal values obtained using the multi‐characteristic optimization model have been validated by confirmation experiments. The model can be extended to any number of quality characteristics provided proper utility scales for the characteristics are available from the realistic data.

The proposed methodology can be applied to those industrial situations where a number of responses are to be optimized simultaneously.

The paper discusses a case study on En24 steel turned parts using titanium carbide coated tungsten carbide inserts. The material, En24 steel, has wide applications in aerospace, machine tools, automobiles, etc. The proposed algorithm is easy to apply.

The purpose of this paper is to propose a new method of robust parameter design for dynamic multi‐response system. The objectives are to resolve the correlations among multiple responses and the uncertainty of system with incomplete information.

First, desirability function is used to measure dynamic system sensitivity and system variation, and principal component analyses on the two indices are conducted. Second, the grey relational grade (GRD) between principal component sequences of the two indices and their respective ideal sequences, gained by grey relational analysis, is converted to an integrated GRD (IGRD) index by means of TOPSIS method, and then the optimal level combination of controllable factors is identified based on the IGRD index.

It was found that the optimal factor level combination obtained by the proposed method is nearest the ideal solution and farthest from the negative ideal solution. The validity and superiority of the proposed method are confirmed through two illustrative examples.

It should be noted that the proposed method fails to consider the interaction effects between controllable factors and noise factors.

The method proposed in the paper effectively integrates several common methods to optimize a dynamic multiple responses system based on Taguchi's robust parameter design. These methods do not involve complicated mathematical theory, and are therefore easy for practitioners to use in engineering practice.