Confirmation testing of the Taguchi methods by artificial neural-networks simulation

In Taguchi's methods of parameter design, a confirmation test is usually necessary to remove concerns about the choice of control parameters, experimental design, or assumptions about responses. This paper investigated the use of artificial neural-networks simulation to validate the set of control parameters identified as significant through Taguchi's methods, and to verify that the recommended settings for the control parameters are indeed optimal or near-optimal. Using the experimental layout and measured responses from a Taguchi parameter-design experiment, we applied cross-validate training to ascertain that the trained neural-network can reproduce acceptable results on unseen experimental layouts. We then used the trained neural-network to simulate and search for the global optimal settings for the control parameters, and the results compared with the recommended settings from the Taguchi parameter-design experiment.     

The use of a generalized signal-to-noise ratio to identify adjustment and dispersion factors in taguchi experiments

A signal-to-noise ratio proposed by Taguchi for ‘nominal the best’ can be made more flexible and used additionally for the cases ‘smaller the better’ and ‘larger the better’. The main feature which distinguishes this generalized ratio from Taguchi's signal-to-noise ratios is that its precise form is determined by the experimental data. Taken together with a transformation of the mean response it effectively identifies adjustment (signal) factors and dispersion factors. Examples are given to illustrate the routine operational procedure and also to demonstrate that Taguchi's signal-to-noise ratios can lead to inefficient, and sometimes incorrect, identification of design factors. Two important considerations are to preserve the evident appeal of the Taguchi method to engineers and also to provide a theoretical justification which is acceptable to statisticians. The principal objective of the joint transformation is to achieve approximate functional independence between the mean and variance in the new metric. This, in turn, leads to efficient identification of adjustment and dispersion factors. A comparison is made with a similar approach using Box and Cox transformations.     

Robust design for multiple dynamic quality characteristics using data envelopment analysis

The Taguchi method is extensively adopted in various industries to continuously improve product design in response to customer requirements. The dynamic system of the Taguchi method is frequently implemented to design products with flexible applications. However, Taguchi's dynamic system can be employed only for individual quality characteristic, and the relationship between the quality characteristic and the signal factor is assumed to be linear. Because of these restrictions, Taguchi's dynamic system is ineffective for multiple quality characteristics or when the quality characteristic has a nonlinear relationship with the signal factor. This study describes a novel procedure for optimizing a dynamic system based on data envelopment analysis. The proposed procedure overcomes the limitations of Taguchi's dynamic system. Two cases are analyzed to demonstrate the effectiveness of the proposed procedure. The results show that the proposed procedure can enhance multiple dynamic quality characteristics. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Continuous Taguchi—a model-based approach to Taguchi's ‘quality by design’ with arbitrary distributions

Statistical experimental design has been used in ‘off-line’ quality control to determine the optimal settings for a system even when the mathematical model is known. Taguchi demonstrated how signal-to-noise ratios could be used to improve the performance of a system through variance minimization. However, these statistical methods often do not use the full distribution information that may be available. Proposed in this paper is an extension and complement to Taguchi's use of experimental design and signal-to-noise ratios for known system models. The use of a probability transformation method with the mathematical system model will allow designers to perform parameter and tolerance design simultaneously using a method of ‘fast integration’. The result is a new method in the field of ‘quality by design’, which we call continuous Taguchi, that can handle both linear and non-linear systems, with components of any distribution type, with or without correlation of the variables. In addition, an interpretation of Taguchi's classification of factors is given in the context of our full distribution method. © 1998 John Wiley & Sons, Ltd.     

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.     

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.     

Robust design with dynamic characteristics using stochastic sequential quadratic programming

Robust design with dynamic characteristics is an important off-line quality engineering technique for improving product quality over a range of input conditions by reducing variations caused by uncontrolled factors. Since several studies have indicated that there are important limitations to Taguchi's S/N ratio analysis, the solution procedure for dynamic systems deserves further investigation. This paper proposes a stochastic optimization modeling procedure to overcome the difficulty in Taguchi's method to accommodate dynamic characteristics. The main idea underlying the proposed method is to minimize the total variations on quality characteristics while attaining the target performance over a range of input conditions. Due to the nonlinear nature of the stochastic optimization model, two stochastic versions of sequential quadratic programming respectively embedded with a Monte Carlo simulation and numerical approximations are devised to solve the problem. In the robust design of a temperature control circuit often discussed in dynamic problems, the proposed method performs efficiently and effectively. Compared with the Taguchi method, the design solved in this paper has smaller variations, indicating that the proposed method is a promising technique for dynamic-characteristic robust design.     

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.     

OPTIMIZING MULTI-RESPONSE PROBLEMS IN THE TAGUCHI METHOD BY FUZZY MULTIPLE ATTRIBUTE DECISION MAKING

One of the conventional approaches used in off-line quality control is the Taguchi method. However, most previous Taguchi method applications have only dealt with a single-response problem and the multi-response problem has received only limited attention. The theoretical analysis in this study reveals that Taguchi's quadratic loss function and the indifference curve in the TOPSIS (Technique for order preference by similarity to ideal solution) method have similar features. The Taguchi method deals with a one-dimensional problem and TOPSIS handles multi-dimensional problems. As a result, the relative closeness computed in TOPSIS can be used as a performance measurement index for optimizing multi-response problems in the Taguchi method. Next, an effective procedure is proposed by applying fuzzy set theory to multiple attribute decision making (MADM). The procedure can reduce the uncertainty for determining a weight of each response and it is a universal approach which can simultaneously deal with continuous and discrete data. Finally, the effectiveness of the proposed procedure is verified with an example of analysing a plasma enhanced chemical vapour deposition (PECVD) process experiment. © 1997 by John Wiley & Sons, Ltd.     

Optimization of Test Parameters for Magneto-Optic Imaging Using Taguchi's Parameter Design and Response-Model Approach

Magneto-optic/eddy current imaging (MOI) is becoming widely used for aging aircraft inspection for cracks and corrosion. However, many test parameters affect the accept/reject decision about a test sample and hence the overall performance of MOI system. The optimization of the parameters is extremely crucial in enhancing the performance of MOI system. This article uses the Taguchi method to change parameter values simultaneously to search for the optimum set of test parameters for maximizing system performance for a given sample geometry and critical crack. It is also important at the same time the system performance be unaffected by variations in parameters. Efficiency of Taguchi's partial factorial design is obvious. The optimum set of parameters is found by means of analyses of main effects. Analysis of variance identifies those parameters that need to be controlled carefully. A response-model approach is utilized as a complement to the Taguchi method.     

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.     

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.     

The Taguchi's Performance Statistic to Optimize Theophylline Beads Production in a High-Speed Granulator

An original process using a simple procedure is developed to produce theophylline active pellets. In order to improve this process, an optimization approach is applied. But rather than only trying to bring the process to the target optimal values, attempt is made to find operating conditions leading also to stable and non-sensitive pellets characteristics. In this purpose, the classic experimental design approach and response surface methodology are completed by using Taguchi's philosophy.     

Parametric optimization of surface roughness castings produced by Evaporative Pattern Casting process

In the present paper Taguchi's approach has been applied to the Evaporative Pattern Casting (EPC) process of Al–7%Si alloy to determine the most influential control factors which will provide better and consistent surface roughness to the castings regardless of the noise factors present. In order to evaluate the effect of process parameters such as grain fineness number, time of vibration, degree of vacuum and pouring temperature on surface roughness of EPC process castings, the Taguchi parameter design and optimization approach is used. Through the Taguchi's parameter design approach, optimal levels of process parameters have been determined. The results indicated that the grain fineness number, time of vibration, degree of vacuum were the significant parameters in deciding the surface roughness of Al–7%Si alloy castings. Pouring temperature was the insignificant parameter. The predicted optimal value of surface roughness of Al–7%Si alloy castings produced by EPC process was 2.31 μm. The results were confirmed by further experiments.     

Unification of robust design and goal programming for multiresponse optimization—a case study

Fixing the levels of input process parameters to meet a required specification of output is a common process quality control problem. Especially when the output has many quality characteristics, and each of these quality characteristics has to satisfy a given specification, difficulties may arise. One such problem was encountered in an injection moulding process. This process was optimized using Taguchi's Robust Design methodology. Details of the process, problems encountered and outcome of optimization are presented in this paper. The optimization study using Taguchi's methodology revealed that the optimum conditions obtained for one response are not completely compatible with those of other responses. So trade-offs were made in selection of levels for factors using engineering judgement. This increases the uncertainty in the decision making process. In this paper, an approach is presented to optimize multiresponses simultaneously using goal programming in conjunction with Taguchi's methodology. Details of modelling, analysis and inferences obtained with relevance to the case are presented. This study revealed that the optimum conditions obtained using goal programming in conjuction with Taguchi's methodology have better goal attainment properties compared to Robust design. To understand goal attainment behaviour of output characteristics for various process conditions, a detailed sensitivity analysis was also conducted. The outcome of this analysis is also discussed in this paper. © 1997 John Wiley & Sons, Ltd.     

An explanation and critique of taguchi's contributions to quality engineering

Recently there has been much interest and some controversy concerning the statistical methods employed by Professor Genichi Taguchi of Japan for improving the quality of products and processes. These methods include the use of fractional factorial designs and other orthogonal arrays, parameter design to minimize sensitivity to environmental factors, parameter design for minimizing transmitted variation, signal-to-noise ratios, loss functions, accumulation analysis, minute analysis and the analysis of life test data. This paper explains some of Taguchi's contributions to quality engineering and also provides a critical evaluation of his statistical methods. Our conclusion is that although on the one hand, Professor Taguchi's quality engineering ideas are of great importance and should become part of the working knowledge of every engineer, on the other hand, many of the techniques of statistical design and analysis he employs to put these ideas into practice are often inefficient and unnecessarily complicated and should be replaced or appropriately modified. In this short article only an overview is attempted, but references are appended where these matters are discussed in greater detail.     

SIMULATION METAMODELS OF SYSTEM AVAILABILITY AND OPTIMUM SPARE AND REPAIR UNITS

This paper presents a new approach to maximize the steady-state availability of a closed queuing multiechelon repairable system with cold standbys. The new method is based on the use of the Taguchi inner array design in simulation modeling of this problem. Regression models are developed based on the results generated from the balanced simulation design. Two special cases of the exponential and Erlang-2 service distributions are presented. These models were validated and shown to provide good approximations to simulation results. Within the specified domain of the problem's parameters, the total operating cost of this system is minimized to determine the optimum spare and repair units.     

A systematic approach to determine the optimal maintenance policy for an automated manufacturing system

We propose a systematic approach to determine the optimal maintenance policy for an automated manufacturing system which includes a flexible manufacturing cell (FMC) and several automated machine shops. The systematic approach combines simulation, fractional factorial design, noise or outer array of Taguchi design, regression metamodelling, and classical queueing analysis. A useful expression of the fractional utilization of the manufacturing system is derived and incorporated into formulating and solving the corresponding decision problem. The systematic approach provides an effective implementation procedure to handle practical maintenance problems found in a complex manufacturing environment. © 1997 John Wiley & Sons, Ltd.     

Reliability improvement via taguchi's robust design

Taguchi's robust design strategy, whose aim is to make processes and products insensitive to factors which are hard or impossible to control (termed noise factors), is an important paradigm for improving products and processes. We present an overview of the strategy and tactics for robust design and demonstrate its usefulness for reliability improvement. Two important components of robust design are a criterion for assessing the effect of the noise factors and experimentation according to specialized experimental plans. Recent criticism of Taguchi's criterion and his analysis of its estimates has led to an alternative approach of modelling the response directly. We give additional reasons for using this response-model approach in the context of reliability improvement. Using the model for the response, appropriate criteria for assessing the effect of the noise factors can then be evaluated. We consider an actual experiment and reanalyse its data to illustrate these ideas and method.