Compound Noise: Evaluation as a Robust Design Method

This paper evaluates compound noise as a robust design method. Application of compound noise as a robust design method leads to a reduction in experimental effort. The compound noise strategy was applied to two types of situation: the first type has been described with active effects up to two‐factor interactions and the second type has been described with effects up to three‐factor interactions. These two situations are illustrated with help of case studies. The paper provides theoretical justification for the effectiveness of the compound noise strategy as formulated by Taguchi and Phadke. For example, we found that the compound noise strategy is very effective for systems which exhibit effect sparsity. This paper gives an alternative procedure to formulate a compound noise, distinctly different from Taguchi's formulation. The alternative method requires less information to formulate compound noise as compared to Taguchi's formulation. Overall, the paper studies the effectiveness of such an alternative formulation, outlines scenarios where compound noise as a robust design method can be effectively used and gives alternative strategies for the systems on which compound noise cannot be effective. Copyright © 2006 John Wiley & Sons, Ltd.     

A Robust Design Method in Product Quality Applications

1　IntroductionThe 1980bookletbyTaguchiwaswrittenatatimewhentheinitialsignal to noiseratioswerebeingdevel opedandhisthinkingwasbeingtranslatedfromJapaneseforthefirsttime.Histhinkingandourunder standingofhisthinkinghaveevolvedagreatdealduringtheensuing 2 1years.Taguchi′sapproachestooff linequalityimprovementhavegeneratedmuchinterestanddebateduringthelast2 1years.Foranaccountofthesetechniques ,seeTaguchiandWu( 1980 ) .Thishasinturnledresearcherstocloselyexaminehismeth odsandsuggestvariousimpr…     

Using geometric mean to compute robust mixture designs

Mixture experiments involve developing a dedicated formulation for specific applications. We propose the weighted optimality criterion using the geometric mean as the objective function for the genetic algorithms. We generate a robust mixture design using genetic algorithms (GAs) of which the region of interest is an irregularly shaped polyhedral region formed by constraints on proportions of the mixture component. When specific terms in the initial model display unimportant effects, it is assumed that they are removed. The design generation objective requires model robustness across the set of the reduced models of the design. Proposing an alternative way to tackle the problem, we find that the proposed GA designs based on G- or/and IV-efficiency are robust to model misspecification.     

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.     

Optimizing the parameters of multilayered feedforward neural networks through Taguchi design of experiments

The size and training parameters of artificial neural networks have a critical effect on their performance. This paper presents the application of the Taguchi Design of Experiments (DoEs) off‐line quality control method in the optimization of the design parameters of a neural network. Being a ‘parallel’ approach, the method offers considerable benefits in time and accuracy when compared with the conventional serial approach of trial and error. The use of the Taguchi method ensures that the quality of the neural network is taken into account at the design stage. The interpretation of the experimental results is based on the statistical technique known as analysis of variance (ANOVA). The signal‐to‐noise ratio (S/N) is used in designing a robust neural network that is less sensitive to noise. The effect of design parameters and neural network behaviour are also revealed as a result. Although a Wood Veneer Inspection Neural Network (WVINN) is the particular application presented here, the design methodology can be applied to neural networks in general. Copyright © 2000 John Wiley & Sons, Ltd.     

A methodology for planning experiments in robust product and process design

Robust design is an important method for improving product manufacturability and life, and for increasing manufacturing process stability and yield. In 1980 Genichi Taguchi introduced his approach to using statistically planned experiments in robust product and process design to U.S. industry. Since then, the robust design problem and Taguchi's approach to solving it has received much attention from product designers, manufacturers, statisticians and quality professionals. Although most agree on the importance of the robust design problem, controversy over some of the specific methods used to solve the problem has made this an active research area. Although the answers are not all in yet, the importance of the problem has led to development of a four-step methodology for implementing robust design. The steps are (1) formulate the problem by stating objectives and then listing and classifying product or process variables, (2) plan an experiment to study these variables, (3) identify improved settings of controllable variables from the experiment's results and (4) confirm the improvement in a small follow-up experiment. This paper presents a methodology for the problem formulation and experiment planning steps. We give practical guidelines for making key decisions in these two steps, including choice of response characteristics, and specification of interactions and test levels for variables. We describe how orthogonal arrays and interaction graphs can be used to simplify the process of planning an experiment. We also compare the experiment planning strategies we are recommending to those of Taguchi and to more traditional approaches.     

Robust optimal-parameter design approach for tolerance design problems

A robust optimal-parameter design method, henceforth called the TGAOA, to solve tolerance design problems has been investigated. Tolerance affects system performance and leads to violation of design constraints. The TGAOA approach conducts global exploration by using a genetic algorithm and exploits optimal offspring via the Taguchi method. It is able to effectively reduce the impact of parameter variations in reaching robust optimal-solutions as allowed by the tolerance. Two design examples are employed to evaluate the performance of the new method. The first is for a mixed H₂/H_∞ optimal PID controller under varying PID component specifications, plant uncertainty, and other external unknown disturbance. The second involves a 13-variable test function, which includes quadratic, linear, and polynomial forms to illustrate the general robustness and computational efficiency, for which comparisons are also made with its predecessors of genetic algorithm and hybrid Taguchi-genetic algorithm.     

基于满意度函数的新型逃生管道多目标稳健性设计

新型逃生管道参数具有不确定性且单目标优化存在局限性，为了实现新型逃生管道多目标稳健性设计，结合田口稳健性设计方法与满意度函数，提出了一种基于满意度函数的多目标稳健性设计方法。该方法将产品质量特性的信噪比转换为具有田口稳健性设计的望大特性的满意度，然后通过加权几何均值实现结构的多目标稳健性设计。通过使用Hypermesh和LS-DYNA建立新型逃生管道的有限元模型，并对该有限元模型进行验证，然后运用所提出的方法对新型逃生管道进行多目标稳健性设计。结果表明，稳健性设计后新型逃生管道的信噪比提升了5.3%，说明管道抵抗噪声因子的干扰能力增强，结构更稳健；新型逃生管道质量降低了9.6%，实现了管道轻量化的目的。研究结果对提高新型逃生管道的稳健性具有一定的理论和工程意义。     

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.     

Tough customers: good designs

Good design and successful innovation have been shown repeatedly to be intimately linked to early and close consultations between design and representative customers. What has not been highlighted, and should be, is that the tougher and more demanding the customers are in their equirements, the better and more robust the designs will be, along with their probability of reinnovation and propensity for successful longterm commercial exploitation. To demonstrate this point the history of a number of innovations based on good (commercially successful) designs is examined in two rather diffent industrial sectors — aerospace and agricultural machinery.     

Analysis of Ordered Categorical Data Using Expected Loss Minimization

Robust design is a strong method for the quality improvement of processes (or products). Two main techniques for data analysis in robust design process are the S/N ratio technique and accumulation analysis developed by Taguchi. Accumulation analysis is developed for the study of ordered categorical data. In this article, the current techniques are studied. Then, a new method that is more accurate than other methods is developed and introduced. In the next phase, an example from literature solved by the methods and the new method's optimality against other methods is shown.     

结构动力鲁棒优化设计方法综述

如何提高结构动力学性能的鲁棒性,以减小各种不确定性因素对设计结果的影响是当前学术界和工程界研究和关注的热点问题之一。该文阐述了结构动力鲁棒优化设计的基本概念,从基于Taguchi的方法、基于多目标优化的方法和基于响应面建模的方法三个方面对结构动力鲁棒优化设计的研究进行了综述。以双转子为例,从结构的动力响应要求出发,采用响应面建模、多目标优化的方法进行了设计并与采用Taguchi方法得到的结果进行比较。结果表明,基于响应面建模、多目标优化的方法能够获得多个具有鲁棒性的设计方案,在处理具有不确定性的结构动力学问题时有着很大的应用潜力。最后,对当前方法和后续研究内容作了简要总结和展望。     

微机电器件的稳健设计

微机电系统（MEMS）是一个新兴的跨学科研究领域,成本和可靠性是MEMS商品化的关键。与传统的机械加工和IC加工相比,MEMS加工的尺寸偏差比较大,而且很难控制,因此需要在设计过程中充分考虑加工的不确定性。稳健设计可以在不提高制造成本的前提下提高设计方案的稳健性。稳健优化设计方法主要包括 Taguchi方法和基于容差模型的方法,后者特别适合于处理带约束的优化设计问题。以微加速度计和微阀为例给出了稳健设计在MEMS设计中的应用,验证了稳健设计可以显著提高MEMS器件的信噪比。     

Robust design optimisation via surrogate network model and soft outer array design

Robust design searches for a performance optimum with least sensitivity to variable and parameter variations. Taguchi method applies an inner array for control factors and an outer array for noise factors to estimate the Signal-to-Noise ratio (S/N). However, the cross product arrays impose serious cost concerns for expensive samplings. Also, rigorous control of noise factors to pre-set levels is impractical in industrial applications. This study presents a soft computing-based robust optimisation that merges control and noise factors into a combined experimental design to establish a surrogate using artificial neural network. Genetic algorithm is applied to search in the sub-space of control factors in the surrogate with a soft outer array to estimate the S/N served as the evolution fitness. Performance variations due to the tolerances of control and uncontrollable factors can then be estimated without conducting actual experiments. The verifications of the predicted optima become additional learning samples to refine the surrogate, and the iteration continues until convergence. The robust optimisation of a micro-accelerometer with maximised gain is used as an illustrative example. The proposed algorithm provides a superior robust optimum using a much smaller sample and less controlling cost compared with Taguchi method and a conventional response surface method.     

Use of 2k-p designs in parameter design

This article shows that a single 2^k-p fractional factorial design matrix and the traditional data analysis techniques associated with this design can be used effectively to achieve the goal of parameter design while reducing the total number of experiments required. A real example is used to compare Taguchi's two-part design, and S/N analysis to a 2^k-p design and its associated analysis. Also, a flow diagram is presented to guide a practitioner through the parameter design process using a 2^k-p design. This flow diagram provides an annoted guide to the literature on 2^k-p decision and shows the design processes leading to proper choice of design and appropriate data analysis techniques.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

A Dominance-based Design Metric in Multiattribute Robust Design

This paper outlines the development of an effective and consistent ‘designing-in-quality’ strategy that can be used to deal with concepts of uncertainty, quality and robustness in engineering design. Specifically, this paper presents a decision analysis-based robust design metric that seamlessly integrates objective evaluations on the goodness of a design alternative with the designer’s intent and preferences. This is achieved through the development of a set of performance-reflecting dominance indices for the attributes and their utilization in a preference-influenced multiattribute utility formulation. Such a knowledge feedback-based decision model development will be particularly useful when dealing with complex iteration-based engineering design process where little information on the expected outcomes may be known a priori, or where product performance is computationally expensive to evaluate. Application of this robust design metric in a multi-stage experimentation and modeling design process is presented. The characteristics of the proposed design metric and the effectiveness of the overall design procedure in dealing with constrained engineering design problems are examined with the aid of demonstrative case studies and the results are discussed.     

Fast numerical methods for robust optimal design

A fast numerical approach for robust design optimization is presented. The core of the method is based on the state-of-the-art fast numerical methods for stochastic computations with parametric uncertainty. These methods employ generalized polynomial chaos (gPC) as a high-order representation for random quantities and a stochastic Galerkin (SG) or stochastic collocation (SC) approach to transform the original stochastic governing equations to a set of deterministic equations. The gPC-based SG and SC algorithms are able to produce highly accurate stochastic solutions with (much) reduced computational cost. It is demonstrated that they can serve as efficient forward problem solvers in robust design problems. Possible alternative definitions for robustness are also discussed. Traditional robust optimization seeks to minimize the variance (or standard deviation) of the response function while optimizing its mean. It can be shown that although variance can be used as a measure of uncertainty, it is a weak measure and may not fully reflect the output variability. Subsequently a strong measure in terms of the sensitivity derivatives of the response function is proposed as an alternative robust optimization definition. Numerical examples are provided to demonstrate the efficiency of the gPC-based algorithms, in both the traditional weak measure and the newly proposed strong measure.     

Multi‐response optimization in industrial experiments using Taguchi's quality loss function and principal component analysis

Many industrial experiments based on Taguchi's parameter design (PD) methodology deal with the optimization of a single performance quality characteristic. Studies have shown that the optimal factor settings for one performance characteristic are not necessarily compatible with those of other performance characteristics. Multi‐response problems have received very little attention among industrial engineers and Taguchi practitioners. Many Taguchi practitioners have employed engineering judgement for determining the final optimal condition when several responses are to be optimized. However, this approach always brings some level of uncertainty to the decision‐making process and is very subjective in nature. In order to rectify this problem, the author proposes an alternative approach using a powerful multivariate statistical method called principal component analysis (PCA). The paper also presents a case study in order to demonstrate the potential of this approach. Copyright © 2000 John Wiley & Sons, Ltd.     

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!