Mixed resolution designs as alternatives to Taguchi inner/outer array designs for robust design problems

There has been considerable debate over the contributions made by Genichi Taguchi to robust process and product design. As a result of the numerous debates, there have been many alternative approaches presented that are better suited to the robust design problem. In this paper a combined array design is presented as an alternative to a standard Taguchi design. The mixed resolution design is illustrated in an example involving control and noise variables. Two new variance properties of experimental designs are also presented. Copyright © 2000 John Wiley & Sons, Ltd.     

AN OVERVIEW OF TAGUCHI METHOD AND NEWLY DEVELOPED STATISTICAL METHODS FOR ROBUST DESIGN

Robust Design is an important method for improving product quality, manufacturability, and reliability at low cost. Taguchi's introduction of this method in 1980 to several major American industries resulted in significant quality improvement in product and manufacturing process design. While the robust design objective of making product performance insensitive to hard-to-control noise was recognized to be very important, many of the statistical methods proposed by Taguchi, such as the use of signal-to-noise ratios, orthogonal arrays, linear graphs, and accumulation analysis, have room for improvement. To popularize me use of robust design among engineers, it is essential to develop more effective, statistically efficient, and user-friendly tech niques and tools. This paper first summarizes the statistical methods for planning and analyzing robust design experiments originally proposed by Taguchi; then reviews newly developed statistical methods and identifies areas and problems where more research is needed. For planning experiments, we review a new experiment format, the combined array format, which can reduce the experiment size and allow greater flexibility for estimating effects which may be more important for physical reasons. We also discuss design strategies, alternative graphical tools and tables, and computer algorithms to help engineers plan more efficient experi ments. For analyzing experiments, we review a new modeling approach, die response model approach, which yields additional information about how control factor settings dampen the effects of individual noise factors; this helps engineers better under stand die physical mechanism of the product or process. We also discuss alternative variability measures for Taguchi's signal-to-noise ratios and develop methods for empirically determining the appropriate measure to use.     

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.     

Strategies for planning experiments using orthogonal arrays and confounding tables

Genichi Taguchi has popularized a robust design method which employs experimental design techniques to help identify the levels of design factors to improve the quality of products and manufacturing processes. Experimental design techniques are extremely effective for identifying improved factor levels in problems that involve a large number of factors. Taguchi's success in getting engineers to use experimental design techniques is due, at least in large part, to his use of tools and techniques that simplify the experiment planning process. Recognizing the advantages of this approach, this paper proposes a new set of tools, confounding tables, which offer more guidance to experimenters. Confounding tables provide a clear and systematic representation of confounding relationships. They are simple and useful tools for constructing experiment plans, and they enable users easily to evaluate the confounding patterns of a completed plan. We show how confounding tables provide more information than Taguchi's linear graphs, and are useful for a large class of experiment plans.     

Process optimization using sequential design of experiment: A case study

In practice, engineers seek to find reasonable solutions for complex and unstructured problems, which are common in many areas. The workable solutions for these problems are never a one-shot experiment and data analysis procedure. Rather, the proper solution for these problems requires an inductive-deductive process which involves a series of experiments. To teach engineers the sequential learning strategy in solving complex problems, this article presents a case study on the startup of an ethanol–water distillation column that illustrates the scientific process of response surface methodology. The goal of this experiment is generally to find a good, robust solution that produces high grade concentration of ethanol with maximum profit. This case illustrates the sequential application of response surface methodology and consists of an initial fractional factorial design, a steepest ascent design, a full factorial design, and a central composite face-centered cube design. The analysis of the data in the previous steps gives engineers a guidance about the design of experiment in the next step. This study uses the desirability function approach to obtain a compromise optimization between the concentration of ethanol and the profit, which gives a robust solution to the complex problem. Finally, we conduct appropriate confirmation experiments to verify the optimization results. The case study emphasizes the importance of sequential nature and provides a useful guidance for engineers to solve complex problems.     

基于满意度函数的多响应稳健优化设计研究综述

在21世纪的竞争环境中,满足顾客多样化需求是企业面临的一大挑战。基于此,本文阐述了在产品设计过程中如何同时优化多个质量特性,并使得最终参数符合稳健设计的理念。本文在回顾了响应曲面法、田口三次设计法、满意度函数法的基础上,综合分析了目前多响应稳健优化设计的研究现状,最终提出将信噪比作为衡量多响应稳健性指标的可行性。     

Minimum time collision-free path planning for robotic assembly

Optimum path planning of manipulator arms in assembly applications involves the selection of the optimum combination of the robot control variables under the constraints imposed by the robot's physical capabilities and the condition of the working area. The present paper describes an approach based on numerical optimization techniques to plan collision-free paths, and on Taguchi parameter design methodology to optimize the control parameters of the pick-and-place operation that would yield minimum cycle time     

The construction of robust mixture‐process experimental designs via genetic algorithm

Mixture experiments with the presence of process variables are commonly encountered in the manufacturing industry. The experimenter who plans to conduct mixture experiments in which a process involves the combination of machines, methods, and other resources will try to find condition of design factors which make the product/process insensitive or robust to the variability transmitted into the response variable. We propose the genetic algorithm (GA) for generating robust mixture‐process experimental designs involving control and noise variables. When the noise variables, which are extremely difficult to control or not routinely controlled during the manufacturing process and may change without warning, are considered in a mixture experiment, we propose the robust design setting. When considering a robust design, the design that has a lower and flatter faction of design space curves for all levels of the controllable process variables at varying noise interaction is preferable. We evaluate the designs with respect to these criteria for both the mean model and the slope model. The evaluation demonstrates that the proposed GA designs are robust to the contribution of the interactions involving the noise variables.     

Robust design of assembly and machining tolerance allocations

Tolerancing is one of the most important tasks in product and manufacturing process design. The allocation of design tolerances between the components of a mechanical assembly and manufacturing tolerances in the intermediate machining steps of component fabrication can significantly affect a product's quality and its robustness. This paper presents a methodology to maximize a product's robustness by appropriately allocating assembly and machining tolerances. The robust tolerance design problem is formulated as a mixed nonlinear optimization model. A simulated annealing algorithm is employed to solve the model and an example is presented to illustrate the methodology.     

Robust design of assembly and machining tolerance allocations

Tolerancing is one of the most important tasks in product and manufacturing process design. The allocation of design tolerances between the components of a mechanical assembly and manufacturing tolerances in the intermediate machining steps of component fabrication can significantly affect a product's quality and its robustness. This paper presents a methodology to maximize a product's robustness by appropriately allocating assembly and machining tolerances. The robust tolerance design problem is formulated as a mixed nonlinear optimization model. A simulated annealing algorithm is employed to solve the model and an example is presented to illustrate the methodology     

Robust design with imprecise random variables and its application in hydrokinetic turbine optimization

In robust design, uncertainty is commonly modelled with precise probability distributions. In reality, the distribution types and distribution parameters may not always be available owing to limited data. This research develops a robust design methodology to accommodate the mixture of both precise and imprecise random variables. By incorporating the Taguchi quality loss function and the minimax regret criterion, the methodology mitigates the effects of not only uncertain parameters but also uncertainties in the models of the uncertain parameters. Hydrokinetic turbine systems are a relatively new alternative energy technology, and both precise and imprecise random variables exist in the design of such systems. The developed methodology is applied to the robust design optimization of a hydrokinetic turbine system. The results demonstrate the effectiveness of the proposed methodology.     

Multiresponse optimization using multivariate process capability index

Robust design is an efficient method for product and process improvement which combines experimentation with optimization to create a system that is less sensitive to uncontrollable variation. In this article, a simple and integrated modeling methodology for robust design is proposed. This methodology achieves the robustness objective function and input variables constraints simultaneously. The objective function is written in terms of the multivariate process capability vector (MC_pm) of several competing features of the system under study. The proposed methodology is applicable to general functions of the system performance with random variables. The effectiveness of the methodology is verified using two real‐world examples which are compared with those of other robust design methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust Parameter Design: A Review

Parameter design is an engineering methodology intended as a cost‐effective approach for improving the quality of products and processes. The assumption is that there are both controllable factors (control variables) and uncontrollable/difficult to control factors (noise variables) that operate on the quality characteristic of a process. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic while minimizing the variation imposed on the process via the noise variables. Parameter design was popularized in the mid 1980s by Japanese quality consultant Genichi Taguchi. A panel discussion edited by Nair summarized important responses to Taguchi's ideas and methodology. In the last decade, there have been many applications and new developments in this important area. This review paper focuses largely on the work done since 1992, but a historical perspective of parameter design is also given. Copyright © 2003 John Wiley & Sons, Ltd.     

Product Robust Design and Process Robust Design: Are They the Same? (No.)

Taguchi's ideas of robust parameter design motivated the development of the dual-response approach, where both the mean and the variance of the quality response are modeled in terms of the design parameters and noise factors. These are then used to identify optimal settings that achieve the dual objective of optimizing the signal (the mean) and minimizing variation. While much research has been published recently with regard to how to solve the dual-response problem (DRP), relatively little attention has been given to the unique characteristics of process robust design, like the existence of systematic variation or intercorrelations among the process “controllable” variables. These properties indeed put process robust design in a category of its own (separate from product robust design). In this paper, we first expound these unique properties and develop a general formulation of the DRP as it applies to process robust design. We then report on an implementation to an industrial process in a high-tech corporation.     

基于信噪比的随机设施布局方法

设施布局对于生产需求不确定、产品多样化制造企业十分重要。随机设施布局评价的重要指标就是布局的鲁棒性和稳定性,但这两个特征之间存在一定矛盾,很难同时满足这两个特征。针对布局问题的这两个目标,引入Taguchi稳健设计中信噪比理论,建立了基于信噪比的随机设施布局优化模型,并通过仿真进行验证,实验结果表明新方法在随机设施布局问题中能获得较好的鲁棒性和稳定性。     

On stochastic optimization: Taguchi Methods™ demystified; its limitations and fallacy clarified

The intent of this paper is to clarify and straighten out important misperceptions. Recently, the need for Stochastic Optimization in Design and Manufacturing Engineering has received increased recognition. The only technique belonging in the realm of Stochastic Optimization that has been practiced somewhat in industry is Taguchi Methods™. (Taguchi Methods™ and Robust Design™ are registered trademarks of the American Supplier Institute for Taguchi methodology. In this paper, Taguchi Methods or methodology is used in the singular and without the trademark symbol, and mostly its acronym, TM, is used.) However, Taguchi Method (TM) has been incorrectly promoted by many as THE work process for attaining “a robust design,” thus the use of Robust Design™ to stand for TM! This has caused great confusion since much else is needed for designing a robust product. More serious is that simple mathematical fundamentals behind TM have not been fully clarified so that its limitations and deficiencies would be obvious. Thus even greater confusion exists amongst people who “learn” or hear of TM or are intended practitioners. Because of our extensive work on HPD (Holistic Probabilistic Design), which holistically treats Stochastic Optimization and thus includes comprehensively and rigorously addressing robustness, we have gone beyond TM capabilities. As byproducts, we can now demystify TM in a simple manner, show its limitations clearly, and clarify TM's fallacy which essentially invalidates it as a technique!     

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.     

Computer-Aided Design of Fractional Factorial Experiments Given A List of Feasible Observations

When attributes of experimental units serve as independent variables, locating the units possessing the required combinations of attribute values for an experimental design can be a serious practical problem. Often, however, data sets of observable experimental units exist. A computer-aided design methodology is presented which determines which two-level factorial and orthogonal fractional factorial designs are feasible, given the data set of observable experimental units. Contrary to usual practice, the number of factors to consider is an explicit experiment planning variable in the methodology. All combinations of ten and fewer factors and 2¹⁰ and fewer observations (in steps of powers of 2) are represented by a feasibility matrix. For a given set of observable experimental units, the design methodology attempts to map which cells of the matrix are feasible. Dependency relationships among feasibility matrix cells are stated which allow implicit enumeration of cells. An example taken from highway safety research is used to demonstrate use of the design methodology. Lastly, search times for random data sets indicate seven or fewer factors can be searched at low cost, but the cost for more than seven factors is dependent upon data-set size.     

Optimizing Response Surface Experiments with Noise Factors Using Confidence Regions

One way to improve quality is to reduce the impact of variation. Taguchi emphasized that quality is improved by minimizing the effect of variables that are difficult or impossible to control. In robust design experiments, settings of design variables that are controllable are sought that are insensitive to the effects of the noise factors. A summary of methods for using confidence statements in the optimization of a product or process during the design phase is given. In addition, confidence regions for determining control factor settings that optimize the mean and variance simultaneously are discussed. An example is used to illustrate the advantages of characterizing the uncertainty in the optimal factor settings.     

Multiobjective robust optimization method for drawbead design in sheet metal forming

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.