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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.

In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment times, but also reduces the fitting accuracy of the response surface. In addition, the uncertainty of the optimal variables and their boundary conditions makes the optimal solution difficult to obtain. The purpose of this paper is to propose a method of fuzzy optimization design-based multi-level response surface to deal with the problem.

The main optimal variables are determined by Monte Carlo simulation, and are classified into four levels according to their sensitivity. The linear membership function and the optimal level cut set method are applied to deal with the uncertainties of optimal variables and their boundary conditions, as well as the non-fuzzy processing is carried out. Based on this, the response surface function of the first-level design variables is established based on the design of experiments. A combinatorial optimization algorithm is developed to compute the optimal solution of the response surface function and bring the optimal solution into the calculation of the next level response surface, and so on. The objective value of the fourth-level response surface is an optimal solution under the optimal design variables combination.

The results show that the proposed method is superior to the traditional method in computational efficiency and accuracy, and improves 50.7 and 5.3 percent, respectively.

Most of the previous work on optimization was based on single-level response surface and single optimization algorithm, without considering the uncertainty of design variables. There are very few studies which discuss the optimization efficiency and accuracy of multiple design variables. This research illustrates the importance of uncertainty factors and hierarchical surrogate models for multi-variable optimization design.

There are process uncertainties and material property variations during laminated steel sheet forming, and those fluctuations may result in non-reliable forming quality issues such as fracture and delamination. Additionally, the optimization of sheet forming process is a typical multi-objective optimization problem. The target is to find a multi-objective design optimization and improve the process design reliability for laminated sheet metal forming. The paper aims to discuss these issues.

Desirability function approach is adopted to conduct deterministic multi-objective optimization, and response surface is used as meta-model. Reliability analysis is conducted to evaluate the robustness of the multi-objective design optimization. The proposed method is implemented in a step-bottom square cup drawing process. First, forming process parameters and three noise factors are assumed as probability variables to conduct reliability assessment of the laminated steel sheet forming process using Monte Carlo simulation. Next, only two forming process parameters, blank holding force and frictional coefficient, are considered as probability variables to investigate the influence of the forming parameter deviation on the variance of the response using the first-order second-moment method.

The results indicate that multi-objective design optimization using desirability function method has high efficiency, and an optimized robust design can be obtained after reliability assessment.

The proposed design procedure has potential as a simple and practical approach in the laminated steel sheet forming process.

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.

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 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.

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 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 study is to provide a method for Lean Six Sigma (LSS) improvement projects that may aid LSS practitioners to plan and conduct robust and lean product/process optimization studies for complex and constrained products, such as those encountered in food industry operations.

The technique is to be used for replicated LSS product experimentation on multiple effects elicited on several product traits. The authors compress replicated information reducing each response to simpler lean and robust median and range response components. Then, the desirability method is utilized to optimize concurrently location and dispersion contributions.

The suggested method is demonstrated with a case study drawn from the area of food development where cocoa-cream filling for a large-scale croissant production operation undergoes a robust screening on two crucial characteristics – viscosity and water activity – that influence product and process performance as well as product safety.

The proposed method amalgamates concepts of fractional factorial designs for expedient experimentation along with robust multi-factorial inference methods easily integrated to the desirability function for determining significant process and product effects in a synchronous multi-characteristic improvement effort. The authors show that the technique is not hampered by ordinary limitations expected with mainstream solvers, such as MANOVA. The case study is unique because it brings in jointly lean, quality and safety aspects of an edible product. The showcased responses are unique because they influence both process and product behavior. Lean response optimization is demonstrated through the paradigm.

The purpose of this paper is to propose a manufacturing product‐screening methodology that will require minimal resource expenditures as well as succinct improvement tools based on multi‐response prioritisation.

A six‐step methodology is overviewed that relies on the sampling efficiency of fractional factorial designs introduced and recommended by Dr G. Taguchi. Moreover, the multi‐response optimisation approach based on the super‐ranking concept is expanded to the more pragmatic situation where prioritising of the implicated responses is imperative. Theoretical developments address the on‐going research issue of saturated and unreplicated fractional‐factorial designs. The methodology promotes the “user‐friendly” incorporation of assigned preference weights on the studied responses. Test efficiency is improved by concise rank ordering. This technique is accomplished by adopting the powerful rank‐sum inference method of Wilcoxon‐Mann‐Whitney.

Two real‐life case studies complement the proposed technique. The first discusses a production problem on manufacturing disposable shavers. Injection moulding data for factors such as handle weight, two associated critical handle dimensions and a single mechanical property undergo preferential multi‐response improvement based on working specification standards. This case shows that regardless of fluctuations incurred by four different sources of response prioritisation, only injection speed endures high‐statistical significance for all four cases out of the seven considered production factors. Similarly, the technique identifies a single active factor in a foil manufacturing optimisation of three traits among seven examined effects.

This investigation suggests a technique that targets the needs of manufacturing managers and engineers for “quick‐and‐robust” decision making in preferential product improvement. This is achieved by conjoining orthogonal arrays with a well‐established non‐parametric comparison test. A version of the super‐ranking concept is adapted for the weighted multi‐response optimisation case.