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In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but is also dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. One of the most efficient statistical approaches used to model the multistage problems is the response surface method (RSM). However, it is necessary to optimize each response in all stages so to achieve the best solution for the whole problem. Robust optimization can produce very accurate solutions in this case.

In order to model a multistage problem, the RSM is often used by the researchers. A classical approach to estimate response surfaces is the ordinary least squares (OLS) method. However, this method is very sensitive to outliers. To overcome this drawback, some robust estimation methods have been presented in the literature. In optimization phase, the global criterion (GC) method is used to optimize the response surfaces estimated by the robust approach in a multistage problem.

The results of a numerical study show that our proposed robust optimization approach, considering both the sum of square error (SSE) index in model estimation and also GC index in optimization phase, will perform better than the classical full information maximum likelihood (FIML) estimation method.

To the best of the authors’ knowledge, there are few papers focusing on quality-oriented designs in the multistage problem by means of RSM. Development of robust approaches for the response surface estimation and also optimization of the estimated response surfaces are the main novelties in this study. The proposed approach will produce more robust and accurate solutions for multistage problems rather than classical approaches.

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 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.

The Taguchi method is the conventional approach used in off‐line quality control. However, most previous Taguchi method applications have dealt only with a single‐response problem. The multi‐response problem has received only limited attention. Proposes an effective procedure on the basis of the quality loss of each response so as to achieve the optimization on multi‐response problems in the Taguchi method. The procedure is a universal approach which can simultaneously deal with continuous and discrete data. Evaluates a plasma‐enhanced chemical vapour deposition (PECVD) process experiment and a case study, indicating that the proposed procedure yields a satisfactory result.

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.

Looks at the Taguchi method, a traditional approach that seeks to obtain the best combination of factors with the lowest societal cost solution to achieve customer requirements, and also principal component analysis (PCA). States that the Taguchi method can only be used to optimize single response problems and not multi‐response problems and that PCA, although it has been considered to solve multi‐response problems, itself has shortcomings. Proposes a data envelopment analysis ranking (DEAR) approach as an effective means of optimizing the multi‐response problem. Includes a series of steps from the proposed approach which are capable of decreasing uncertainty caused by engineering judgement in the Taguchi method and overcoming the shortcomings of PCA. Concludes that the DEAR approach is more powerful for practical applications.

This paper aims to examine an investigation of high-pressure coolant (HPC) drilling process with regard to experimental models of output parameters, effect of input parameters on output parameters and simultaneous optimization of the output parameters.

Experimental plan was designed using response surface method and experiments were conducted on HPC drilling set up. Measurements for output parameters were carried out and mathematical models were obtained. Multi response optimization using a composite desirability function approach was used to obtain optimum values of input parameters for simultaneous optimization of output parameters.

Optimal value of input parameters for optimization of HPC drilling process were obtained as; coolant pressure: 21 bar, spindle speed: 3,970 rpm, feed rate: 0.084 mm/rev and peck depth: 5.50 mm. The composite desirability obtained is 0.9412, which indicates that the performance of HPC drilling process was significantly optimized. Developed mathematical models of the output parameters accurately represent the entire design space under investigation.

This is the first study that involves variation of higher coolant pressure and investigation of HPC drilling process using response surface methodology and multi response optimization technique with desirability function.

This paper discusses multi‐response robust parameter design problems based on response surface method. Most research effort on multi‐response parameter design problem focuses much on finding out optimal parameters based on certain criteria or objectives. Research shows that optimal solution in terms of some criteria may not be robust. To achieve robust solution we should consider how sensitive the solution is when the factors change around it. A comparative study of methods for multi‐response robust parameter design is conducted. Solution with consideration of robustness and optimality is proposed with applications of the example.

This paper aims to present a multi-response robust design (RD) optimization approach for U-shaped assembly cells (ACs) with multi-functional walking-workers by using operational design (OD) factors in a simulation setting. The proposed methodology incorporated the design factors related to the operation of ACs into an RD framework. Utilization of OD factors provided a practical design approach for ACs addressing system robustness without modifying the cell structure.

Taguchi’s design philosophy and response surface meta-models have been combined for robust simulation optimization (SO). Multiple performance measures have been considered for the study and concurrently optimized by using a multi-response optimization (MRO) approach. Simulation setting provided flexibility in experimental design selection and facilitated experiments by avoiding cost and time constraints in real-world experiments.

The present approach is illustrated through RD of an AC for performance measures: average throughput time, average WIP inventory and cycle time. Findings are in line with expectations that a significant reduction in performance variability is attainable by trading-off optimality for robustness. Reductions in expected performance (optimality) values are negligible in comparison to reductions in performance variability (robustness).

ACs designed for robustness are more likely to meet design objectives once they are implemented, preventing changes or roll-backs. Successful implementations serve as examples to shop-floor personnel alleviating issues such as operator/supervisor resistance and scepticism, encouraging participation and facilitating teamwork.

ACs include many activities related to cell operation which can be used for performance optimization. The proposed framework is a realistic design approach using OD factors and considering system stochasticity in terms of noise factors for RD optimization through simulation. To the best of the authors’ knowledge, it is the first time a multi-response RD optimization approach for U-shaped manual ACs with multi-functional walking-workers using factors related to AC operation is proposed.

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.