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An Overview of Taguchi Method: Evolution, Concept and Interdisciplinary Applications

Samruddhi Rao, Pragati Samant, Athira Kadampatta, Reshma Shenoy

Abstract— This paper presents an overview of Taguchi Method, encompassing all major features which include evolution, concept, design steps, vital considerations, analysis and its interdisciplinary applications. In our approach we trace the evolution of this method with time to identify the vital concepts that contributed to its present formulation, thereby stating the significance of this method over other conventional techniques. A detailed study of design steps and analysis is presented. It also focuses on the applications of this method in diverse fields and states the benefits provided due to its employment. An attempt is also made to analyze the effectiveness of this method in combination with other methods thus highlighting its usage in both isolated and synergistic approaches. It thus reinforces the vitality of this method as an efficient tool of Robust Design.

Index Terms— ANOVA ,Fuzzy logic, Orthogonal Array, quality characteristic, quality loss function, robust design, Signal-to-Noise ratio

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1 INTRODUCTION

aguchi method was developed by Genichi Taguchi the father of quality engineering, who successfully integrated powerful applied statistical methods into engineering processes for achieving greater stability and capability. His was a proactive approach based on measurement, analysis, prediction and prevention and it focused primarily on, design- ing quality into products and processes rather than inspecting into them(Ross, 1988) . This method lays great emphasis on
responsiveness towards customer’s satisfaction.
Taguchi realized and appreciated the vitality of producing an outcome on target and concluded that, excessive variation in performance was the root cause of poor quality and was counterproductive to the society at large. He further stated that these variations in performance or deviation from target would manifests itself as inevitable loss to the society through early wear out , difficulty in integrating or interfacing with other parts, servicing, the need to include safety margins etc which if ignored would lead to customer dissatisfaction and loss of company reputation. In other words Taguchi accentu- ated the importance of reducing process variability around a specified target value and then bringing the process mean on target. This can be accomplished only by making processes insensitive to various sources of noise and the method is called Robust Parameter Design (Phadke, 1989).
Instead of reducing variation in individual components by

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Samruddhi Rao has completed her bachelor’s degree from Mumbai Univer- sity, India, E-mail: rao.samruddhi@gmail.com

Pragati Samant has completed her bachelor’s degree from Mumbai Univer- sity, India, E-mail: pragatisamant8@gmail.com

Athira Kadampatta has completed her bachelor’s degree from Mumbai

University, India, E-mail:athirakadampatta@gmail.com

Reshma Shenoy has completed her bachelor’s degree fromMumbai Univer- sity, India, E-mail:shenoyreshma04@gmail.com

specifying tighter tolerances, Taguchi addresses the issue by careful selection of design parameters called factors, resulting in a more robust design that is capable of withstanding varia- tions from unwanted sources. In order to achieve this he pro- posed an effective and an efficient method to determine the feasible combination of design parameters that reduces varia- bility in product responses. Hence Taguchi method of experi- mental design is a powerful approach to optimizing designs for performance, quality and cost (Ross, 1988; Peace, 1993).
Section II consists of evolution of the method followed by Section III which describes the basic concept behind Taguchi Method. Section IV explains various application domain of this method followed by Section V concluding our observa- tion.

2 EVOLUTION

The concept of quality has evolved with time, it today has be- come a philosophy encompassing all issues and engaging all individuals within an organization. It is no longer a simple result of an inspection process, but needs to be a company- wide management philosophy. Thus making quality im- provement programs an integral part of the strategic planning process of many successful companies (McKeown, 1992). In the past Inspection was the only method to ensure conformity to specific requirements, but the growth in production yields during the Industrial Revolution posed the demand for an upgraded quality control mechanism In 1911, the concept of quality took a huge leap forward with the contributions of Frederick W. Taylor who introduced several important con- cepts such as Functional specialization, Process analysis of time and motion and Quality control inspection etc[1].Taylor’s contribution thus served to be the precursors in the evolution of quality management and control. While the focus was pri- marily on productivity gains during Taylor’s time, in the
1920s, Dr. Walter Shewhart defined quality control as a proac- tive function rooted in process, rather than relying strictly on

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reactive measures resulting from inspection. He applied statis- tical theory to the management of quality, and developed the first modern control chart and demonstrated that eliminating variation in the process leads to a good standard of end prod- ucts. In order to eliminate variation the cause of variation was to be first identified for which the effects of various controlling factors needs to be studied. Traditionally, the effect of a par- ticular factor was studied by varying one factor at a time. This tradition was provided a fundamental break in the 1920’s when Sir RA Fisher, a British statistician suggested varying of all factors simultaneously in what is known as Design of Ex- periments[DOE]. In this method a deliberate change is made in one or more process factors (input variables), in order to observe the corresponding changes in the output or response factors. It is also assumed that all input variables interact with each other[1]. Thus DOE investigates all possible interactions between inputs at the same time. The data obtained is further analyzed to provide valid and objective conclusions. This method is also termed as Full- factorial experiments and in- volves a big round of tests. In order to slim down the amount of work Fractional factorial DOEs were used, in which only a sufficiently chosen fraction of the treatment combinations re- quired for the complete factorial experiment was selected to be run, although the savings obtained were marginal, such as a factor of two or four. A potential solution to this problem was provided with the invention of Orthogonal Arrays in the
1940’s in Britain, using which a very small subset of all possi- ble combinations were tested thereby reducing the computa- tional effort to a large extent.
Finally in the 1950’s Genichi Taguchi successfully applied Sir Fisher’ s Design of Experiments and Orthogonal Arrays to effective product development deriving the benefits of both the method. He also encouraged noisy inputs and incorpo- rated their effects during experimentation, thus making the product or process Robust [3].

3 CONCEPT OF ROBUST DESIGN

A product is said to be of best quality when it meets customer satisfaction. Taguchi method, thus, never estimates quality of a product on the basis of cost to the manufacturer alone, num- ber of defective pieces; whether it falls within the specified limits etc. It judges on the basis of deviation observed in the product’s response from the target. This response is termed as its quality characteristic. When a product fails before its ex- pected lifespan or its responses become poorer with time, it is said to have high quality loss.[6]
The cost due to rework, warranty cost, time energy and
money spent by customers for repairing, customer complaints
i.e. dissatisfaction, thus eventual loss of market share and rep- utation of the company together is termed as quality loss. To quantify this quality loss, we have quality loss function which depends on the standard deviation (σ) and variation of prod- uct from the target (µ-µ0 ) as given below:
Q =K’[ (µ-µ0 )2+σ2 ] (1)
Taguchi method implies that if the variation of the product from the mean is reduced, quality loss reduces. This reduction in variation is brought about by adjusting the mean nearer to the target with help of a scaling factor. Thus,
Quality loss after adjustment:
Qa ’ = η = 10 Log10 [µ2/ σ2] (2)
The ratio of (µ/σ)2 can be termed as signal to noise ratio since (µ) is the desired target value and (σ)2 is the variance i.e. noise. Signal to noise ratio depends on the quality characteris- tic to be optimized decided for a particular experiment.[2]
The most common types are
• Smaller the better [STD]:- This is chosen for all unde-
sirable characteristics like “defects “etc. for which the
ideal value is zero.
n = -10 Log10 [mean of sum of squares of {measured - ideal}
• larger the better [LTB] :- This is chosen for character- istics which are desirable whose value should be as large as possible
n = -10 Log10 [mean of sum squares of reciprocal of measured data]
• Nominal the better[NTB] :- This is chosen when a specified value is most desired

Square of mean

n = 10 Log10 ---------------------- variance


Fig. 1. Types of SNR
STB requires the performance value to go as small as possi- ble from a threshold value and LTB value requires vice versa. But NTB requires performance value to be as near as possible to the target which is desired. Thus SNR of NTB type is appre- ciated and for that, quality characteristic should be according- ly selected.[7] [12]
The parameters that influence the quality characteristics are

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also called as factors. They can be of 3 types-signal factors which directly influences the intended value of the product’s response (), noise factors which are difficult or expensive to control and cause variation () in the response, control factors which are selected to minimize the sensitivity of product’s response to all noise factors.[2]

Fig. 2. Block Diagram of Product/Process
Robust design projects in which the signal factor remains constant are called static projects, while others in which user can vary signal factors are called dynamic projects.
The design of a product or process is carried out in 3 steps.

3.1 Concept Design

It involves selection of product architecture or process tech- nology and examination of initial settings.

3.2 Parameter Design

It decides the optimum levels of control factors to maximize robustness and thereby enhances the performance. It involves the following steps:

3.2.1 Selection of parameters for experimentation

The system is analyzed to choose an appropriate quality char-
acteristic, such that it is continuous and monotonous function, easy to measure and is a direct indicator of energy transfer in the system. The objective function i.e. the SNR is selected based on the nature of the quality characteristic. The control
factors, their levels and noise factors are determined. Robust- ness of a product is ensured by selecting testing conditions that capture the effect of various noise factors. Also, Signal to Noise ratio (SNR) has to be defined such that it includes not only the average level of the response, but also the observed variation in its level due to noise factors.[2] The same experi- ment may be repeated several times to obtain different re- sponses corresponding to deliberately introduced variation in noise factors, to take into account deterioration and external noise.[2]

3.2.2 Selection of orthogonal array for conducting exper- iments

Orthogonal arrays are special matrices that enable the manu- facturer to choose the parameter values with minimum num-
ber of experiments. In the matrix experiment the columns of the orthogonal array represent factors to be studied and each row represents a unique combination of factor levels in indi- vidual experiments.[2]If a matrix is orthogonal, it implies that for any pair of columns all combination of factor levels occur equal number of times i.e. all factors are represented equally in all experiments. The total degree of freedom is required for the selection of a suitable orthogonal array. The degree of freedom is defined as the number of permissible variations in a process parameter to obtain a specific mean. To select an orthogonal array for experimentation, the number of rows in the array should at least be equal to the total degrees of free- dom of all factors and the overall mean combined. Once the orthogonal array has been selected, experiments are per- formed accordingly; and SNR for each experiment is calculat- ed and tabulated.

3.2.3 Analysis of experimental observations

Analysis of Mean (ANOM): Firstly, the overall mean value (m)
for all experiments is calculated. This is a balanced value, as
all levels of every factor are equally represented in the entire
set of experiments. For every influencing factor, the effect of
its various levels is calculated separately (mi ).The effect of a factor level is defined as the deviation of mi from the overall mean (m).The optimum level for each factor is chosen as the
one which gives highest positive effect on the mean.[2] Thus, analysis of mean is used to obtain the optimum combination of all influencing factors. The orthogonal structure of experi- mentation allows us to use the additive model for calculating the response for any individual combination of factors. The additive model states that combined effect of all the factor lev- els can be obtained by summing the deviations due to indi- vidual factor levels with the overall mean.
Analysis of Variance (ANOVA): ANOVA of a set of exper- iments is similar to Fourier analysis of a signal. Fourier analy- sis establishes the relative importance of the various harmon- ics that constitute a signal. It represents a signal as the addi- tion of various independent orthogonal harmonics. ANOVA represents the overall variance in the SNR as sum of variances due to each factor and variance due to error. ANOVA is used to compute the relative importance of each factor. To maintain the quality of the product, the most significant factors should be strictly controlled.

3.2.4 Verification experiment

Once the optimum combination of different factors has been
chosen, a verification experiment is performed to compare the estimated response with the observed response[10]. If they are in agreement, we adopt the optimum settings, otherwise the additive model fails and mutual dependency between the fac-
tors has to be studied.

3.2.5 Iteration method for further optimization

Experiments in Taguchi’s method are performed using dis-
crete levels of factors, which rules out the possibility of obtain-
ing a higher SNR at any level between the initially selected
levels. In order to make up for this, we perform further exper-

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imentation, selecting new levels around the optimum level determined previously. If the initial range of a factor level is extremely large, such iterations can improve the SNR signifi- cantly.

3.3 Tolerance design

It is used to reduce the tolerance of the product to most influ- ential factors by using improved materials and by adding ex- tra components for controlling tolerance factors.[10]

4 APPLICATIONS OF TAGUCHI METHOD

The robustness and simplicity of Taguchi method attributes to it finding application in a large number of diverse fields some of which are analyzed below:-

Fig . 3. Robust Design Applicability

4.1 Application in the field of Manufacturing

Taguchi’s robust design technique finds its application in a number of manufacturing processes, [17] one of which is Re- sistance Spot welding (RSW).RSW is an efficient method of joining metallic sheet parts, used in various manufacturing processes such as automobile industries, domestic appliances etc. It uses the heating effect of electric current due to opposi- tion provided by resistance to generate localized high temper- ature leading to temporary melting and fusion of the edges of metal sheets.
The quality of the joint and hence its durability depends on the welding diameter and the tensile strength of the sheet. Taguchi’s robust design technique can be applied to RSW method to improve the quality of the weld by selecting opti- mum control factors.
The observations of the Robust design process [15] can be tabulated as below
TABLE I.OBSERVATION TABLE

Quality Characteristic

Tensile Shear

Strength

Control Factors

Welding current Welding pressure Welding time

Factor levels

Low, Medium and High

Orthogonal array used

L9

Optimum levels for control factors

Medium current Medium pressure High weld time

SNR for initial level

9.0050dB

SNR for optimum level

13.1602dB

Improvement in SNR

4.1552 dB

Thus it can be concluded that the use of Taguchi’s optimi- zation leads to an improvement in the SNR by 4.36 dB i.e. around two fold increase in the tensile strength, due to the use of optimized factor values Also, ANOVA could be used to determine the factors that need to be strictly monitored.[16]

4.2 Application of Taguchi’s method in combination with Fuzzy logic for design of multi-characteristic product


Realistic product design necessitates many quality characteris- tics to be optimized. The optimum combination for a particu- lar characteristic need not be optimum for other characteris- tics. Relying on engineering judgment for making trade-off between several optimum factor levels can lead to avoidable degradation of some of the quality characteristics. Taguchi’s method is only efficient as far as optimization of a single per- formance characteristic is concerned. For this purpose, imme- diately after the step of matrix experimentation is complete, for each experiment, it is essential to club multiple resulting SNRs into a single multi-response performance index(MRPI). This clubbing can be efficiently done using a fuzzy logic unit. This MRPI can then be considered as the single performance characteristic to be optimized.[18]

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Fig. 4 Fuzzy Logic Unit for conversion of multiple quality
SNRs into a single MRPI
The fuzzy logic unit consist a knowledge base (KB) which is the collection of expert conversion rule base, required to achieve the optimum weightage to be given to various per- formance characteristics during combination. for every quality characteristic, fuzzy sets small (A), medium (B) and large(C) are defined separately using membership functions. For every run of the experiment, the SNRs corresponding to various quality characteristics are fed to the fuzzy logic unit, which returns a single MRPI.[19]First, a fuzzification unit maps measured input SNRs of crisp value into membership values in different classifying fuzzy sets-small, medium and large. If an SNR of the experiment, corresponding to a characteristic, is smaller as compared with the observed range of that charac- teristic, it gets a higher membership value in the fuzzy set
‘small’ and lower values in ‘medium’ and ‘large’ .Next, a fuzzy reasoning mechanism performs various fuzzy logic op- erations. It uses the rule base to infer the membership values into output fuzzy sets for the given fuzzy inputs. The output fuzzy sets represent classification of MRPI into very small, small, medium, large and very large values. Finally, a defuzzi- fication unit converts the inferred fuzzy membership values into a crisp MRPI for each experiment to be used for optimiza- tion.[19]
It must be noted that the experimentation matrix with or- thogonal columns can still be used for ANOM and ANOVA with MRPI as the only characteristic to be optimized. This di- rectly estimates a single optimum combination of influencing factor levels required for the peak MRPI. Thus, combination of Taguchi’s method with fuzzy logic extends and improves its applicability to design of products characterized by multiple responses.

4.3 Application in Telecommunication

Radio network consists of small geographical regions called as cell which has a base station to provide network to the use a fundamental aspect of radio network planning is the setting of the parameters that are associated with each base station, e.g., antenna tilts and angular settings. Due to limited frequency reuse spectrum, joint setting of all the parameters of the all the cells which has irregular terrain, features, regions and cover- age areas becomes a challenge. Finding the optimal parameter setting for each base station that maximizes a pre-defined per- formance metric is a difficult problem.
Conventional radio network-planning tools use optimiza- tion methods based on local search such as simulated anneal- ing (SA) and genetic algorithm. But major problems with these methods are their parameters require heuristic defini- tions for their initial values. These methods also depend on the neighboring structure of the current solution. To find an opti- mal value without these requirements, Taguchi methodology is used. Taguchi method uses the orthogonal array which greatly reduces the number of experiments thus saving time energy and cost.
This has been used in optimization of the following three typical cell-specific radio parameters of an LTE network: 1) the power control parameter; 2) the tilt of a transmit antenna 3) the azimuth orientation of a transmit antenna. Because Taguchi Method allows any type of parameter combinations, it can also easily be extended to jointly optimize different ra- dio network parameters, e.g., power control parameter combi- nation with azimuth orientation. Experiments have shown that when both algorithms were run with same optimization function and complexity Taguchi converges slightly higher optimization function.[11][14]

4.4 Dynamic systems

Systems in which, the response is required to follow the lev- els of the signal factor in a predefined manner are called Dy- namic systems. Control systems in which the output switches abruptly between 2 states i.e. on and off are called Bang-Bang controllers. A specific example could be a temperature control circuit, primarily consisting of a sensor, control circuit and a heating element. The temperature characteristic of the sensing medium plays a decisive role in determining the response of the heating element. In addition the transient nature of the target temperature adds to the complexity making it a Doubly Dynamic problem. Taguchi method can also be applied to such type of problems, first the levels of compounded noise factor are calculated, and next for each level of signal factor the testing conditions include all levels of compounded noise factor. Regression analysis is used and for an initial setting of control factors signal to noise ratio is calculated. The same procedure is repeated for all combinations of control factors in the orthogonal array and the best combination is finally select- ed resulting in significant improvement in signal to noise ra- tio.

4.5 Artificial neural networks

An Artificial Neural Network is an information processing paradigm composed of a large number of highly interconnect- ed processing elements called neurons. These neurons work in unison to perform the specified task. The neurons are weighted and the effect that each neuron has at decision mak- ing is dependent on the weight of that particular neu- tron. Taguchi methods may be applied to the training of Arti- ficial Neural Networks to perform a specific task, such as character recognition. In order to do so weights of the neural network are made the elements of the orthogonal array. Next Taguchi method and error analysis is applied to find the op- timum combination of weights for the network. Now, for character recognition each neuron is pre-assigned a specific character and it is trained to produce minimum error corre- sponding to that particular input. The character recognition process is initiated and the results are noted and it is conclud- ed that Optimum selection of weights by applying Taguchi method helps the results to confirm to the above mentioned condition. It is also much faster in comparison to other algo- rithms and in a general character recognition problem it is up to 10 times faster than a back- propagation algorithm. Taguchi method also allows users to analyze the system and calculate the interactions between different components thus providing

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an effective means to examine inner operation of the network through statistics.

5 CONCLUSION

This paper thus presents a detailed overview of Taguchi Method in terms of its evolution, concept, steps involved and its interdisciplinary applications. It could be concluded that this method with its perfect amalgamation of statistical and quality control techniques was one of the effective and effi- cient methods of its kind to highlight the benefits of designing quality into products upstream rather than inspecting out bad products downstream. It offers a quantitative solution to iden- tify design factors to optimize quality and reduce cost. Also the application of this method is not confined to a particular domain but also to other fields like product and service sec- tors. It thus is a powerful method as compared to the other intuitive and more cumbersome methods encompassing a large number of fields in terms of application

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