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.     

Quality improvement for RC06 chip resistor

This paper studies a quality improvement case of extremely thin and light chip resistor RC06. We use an L₁₈(2¹ × 3⁷) orthogonal array allocating eight control factors in an experimental plan. The quality response data are inevitably considered to be ordered categorical. Six categories are classified for the quality of chips. Both Taguchi's accumulation analysis method (1966) and Nair's scoring scheme (1986) are employed in analysing the data. Furthermore, we develop a weighted probability scoring scheme (WPSS) and a signal-to-noise (SN) ratio to reach an optimal solution. Finally, a comparison among the three approaches is made.     

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.     

Taguchi methods in practice: An analysis of Goh's paradox

The background of ‘Goh's paradox’ in connection with the application of the common version of Genichi Taguchi's parameter design routine is examined. A detailed case study is used to show how the paradox can be resolved, as well as to assess the probability of success of marginal analysis in Taguchi's prescribed procedure for quality and reliability improvement.     

A comparison of deterministic and statistical sampling techniques for quality analysis of integrated circuits

There has been a great amount of publicity about Taguchi methods which employ deterministic sampling techniques for robust design. Also given wide exposition in the literature is tolerance design which achieves similar objectives but employs random sampling techniques. The question arises as to which approach—random or deterministic—is more suitable for robust design of integrated circuits. Robust design is a two-step process and quality analysis—the first step—involves the estimation of ‘quality factors’, which measure the effect of noise on the quality of system performance. This paper concentrates on the quality analysis of integrated circuits. A comparison is made between the deterministic sampling technique based on Taguchi's orthogonal arrays and the random sampling technique based on the Monte Carlo method, the objective being to determine which of the two gives more reliable (i.e. more consistent) estimates of quality factors. Results obtained indicated that the Monte Carlo method gave estimates of quality which were at least 40 per cent more consistent than orthogonal arrays. The accuracy of prediction of quality by Taguchi's orthogonal arrays is strongly affected by the choice of parameter quantization levels—a disadvantage—since there is a very large number (theoretically infinite) of choices of quantization levels for each parameter of an integrated circuit. The cost of the Monte Carlo method is independent of the dimensionality (number of designable parameters), being governed only by the confidence levels required for quality factors, whereas the size of orthogonal array required for a given problem is partly dependent on the number of circuit parameters. Two integrated circuits—a 7-parameter CMOS voltage reference and a 20-parameter bipolar operational amplifier—were employed in the investigation. Quality factors of interest included performance variability, acceptability (relative to customer specifications) and deviation from target.     

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.     

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.     

Robust Parameter Design of an EDM Process

The paper details a robust parameter design of an electrical discharge machining process. The influence of capacitance, pulse off‐time, pulse on‐time and pulse current on both the average and variability of surface roughness and material removal rate of a titanium alloy was investigated. The analysis revealed that to attain robustness against the impact of noise parameters, no capacitance should be applied. Furthermore, increasing pulse on‐time and its current increased the average of both the surface roughness and material removal rate. Two approaches were suggested to deal with the trade‐off between minimizing the former and maximizing the latter. The study confirmed empirically the inferiority of Taguchi's S/N ratios to a robust design method involving the use of log(s) together with a simple graphical tool for determining the appropriate data transformation called lambda plot. In fact, it was revealed that the employed S/N ratios were driven mainly by the average and involved unaided, unexplained and unjustified transformations. The log(s), on the other hand, provided an independent means of quantifying the variability and, when integrated with lambda plot, rendered not only a simplified analysis but also a better process understanding. The study is the first to report the use of this powerful approach in the context of electrical discharge machining parameter design. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Signal-to-noise ratio development for quality engineering

Dr. Taguchi developed the concept of signal-to-noise (SN) ratio in quality engineering to evaluate the performance of a system. The objective is to develop systems which are robust against noise factors. The SN ratio indicates the degree of the predictable performance of a product or process in the presence of noise factors. Parameter design of the Taguchi method optimizes the SN ratio in the domain of control factors, so that performance could be made insensitive to the noise factors in order to improve product quality. If the domain of the control factors is a continuous space, the problem is a non-linear programming problem. Usually, in practice, there are only a few available levels for the control factors. Thus, experimental design methods can be useful for such problems. The SN ratio for four cases of dynamic characteristic problems is developed in this paper. This paper also gives the method to compute SN ratios for both equispaced and non-equispaced intervals for levels of signal factors. Two examples are presented to illustrate the method.     

Fuzzy logic-based FMEA robust design: a quantitative approach for robustness against groupthink in group/team decision-making

Group/team decision-making is an integral part of almost all failure mode and effects analysis (FMEA) projects. A dysfunctional aspect of this decision-making fashion in fuzzy FMEA is that group/team members’ designs for membership functions and IF-THEN rules may be overshadowed by a member’s design. This problem is caused by groupthink, a pitfall known by the Organisational Behaviour science. This study aims to develop a fuzzy FMEA approach which is robust to the problem. We applied the Taguchi’s robust parameter design and investigated the effects of various control parameters namely Defuzzification, Aggregation, And and Implication operators for the fuzzy inference system (FIS). Our experiments illustrate that the control parameters, in the above-mentioned order, have the most effect on the signal-to-noise ratio (SNR). These factors’ optimal setting consists of the Centroid, Sum, Minimum and Minimum levels, respectively.     

A review of the ‘taguchi methods’ for off-line quality control

The Taguchi methods have recently become popular in the U.S.A following a realization of their importance in Japanese quality design. This review is an initial attempt to extract the important ideas while drawing on the ‘Western’ experience with response surface methodology and experimental design.     

Quality optimization (multi‐characteristics) through Taguchi's technique and utility concept

The work of Taguchi for determining the optimal settings of controllable factors through off‐line experiments focuses on products with a single quality characteristic or response. However, most products have several quality characteristics or responses of interest. Taguchi's technique in itself optimizes a single response or performance characteristic yielding a set of process parameters. This particular setting may not give desired results for other characteristics of the product. In such cases, a need arises to obtain a single setting (optimal setting) of the process parameters, which can be used to produce the products with optimum or near optimum quality characteristics as a whole. Multi‐characteristic response optimization may be the solution of the above problem. In the present paper a case study on V‐processed castings of Al–7%Si alloy, utilizing a simplified multi‐criterion methodology based on Taguchi's approach and utility concept, is discussed. Copyright © 2000 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.     

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.     

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.     

An intelligent approach to robust multi-response process design

In order to meet strict customer demands in a global highly-complex industrial sector, it is necessary to design manufacturing processes based on a clear understanding of the customer's requirements and usage of a product, by translating this knowledge into the process parameter design. This paper presents an integrative, general and intelligent approach to the multi-response process design, based on Taguchi's method, multivariate statistical methods and artificial intelligence techniques. The proposed model considers process design in a general case where analytical relations and interdependency in a process are unknown, thus making it applicable to various types of processes, and incorporates customer demands for several (possible correlated) characteristics of a product. The implementation of the suggested approach is presented on a study that discusses the design of a thermosonic copper wire bonding process in the semiconductor industry, for assembly of microelectronic devices used in automotive applications. The results confirm the effectiveness of the approach in the presence of different types of correlated product quality characteristics.     

An assessment of the kernel‐distance‐based multivariate control chart through an industrial application

Traditional multivariate quality control charts assume that quality characteristics follow a multivariate normal distribution. However, in many industrial applications the process distribution is not known, implying the need to construct a flexible control chart appropriate for real applications. A promising approach is to use support vector machines in statistical process control. This paper focuses on the application of the ‘kernel‐distance‐based multivariate control chart’, also known as the ‘k‐chart’, to a real industrial process, and its assessment by comparing it to Hotelling's T² control chart, based on the number of out‐of‐control observations and on the Average Run Length. The industrial application showed that the k‐chart is sensitive to small shifts in mean vector and outperforms the T² control chart in terms of Average Run Length. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimization of product and process design for quality and cost

Robust product and process design is an important technique for achieving high quality at low cost. It involves making the product's function much less sensitive to various sources of noise such as manufacturing variation, environmental variation and deterioration. This is a problem in optimization involving minimization of the mean square loss resulting from the deviation of the product's function from its target. Here we show that the optimization can be carried out in two steps: first maximize a quantity called signal-to-noise ratio (S/N) and then bring the performance on target by special adjustment parameters. The two-step procedure works for a wide variety of product functions and makes the optimization process more efficient and practical compared to the direct minimization of the quadratic loss function.     

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.