Quality engineering requires systematic experimentation with carefully developed prototypes whose performances are tested in actual field conditions. The objective of quality engineering is to discover optimum values of various design parameters to ensure the consistent performance of the product / process in actual use. In the past, the concept of quality has undergone different paradigm shift to accommodate various end-use characteristics. However, the focus of all those concepts has remained towards the customer satisfaction.

Measuring a fraction of products outside the specified limits, a measure of the quality loss due to scrap, miserably fails as a predictor of customer satisfaction. Reducing the specification limits, improving the on-line quality control to bring the specified units closer to the target and inspection of more samples in order to find the defective products before they reach the customers have been widely practiced in controlling the quality of various products. But such exercises are, often, not considered as good options since they address the symptoms and not the root cause of the problems.

Many experimental designs have been demonstrated in the field of experimental statistics for characterisation and optimisation of various design factors. Typically, the performance of any process or product is affected by a multitude of factors and over 70% of the malfunctions are traceable to the design factors. Since every performance can not be predicted by theory, experimentation or prototyping is resorted for empirical optimisation of the various process and products before launch.

Quality in Taguchi’s perspective

Genichi Taguchi, a Japanese engineer, studied various methods of Design of Experiments at Indian Statistical Institute in 1950s and later applied in a very creative manner to improve the product and process designs. In 1982, American Supplier Institute first introduced Taguchi methods in USA and his methods were popularised by Madhave Phadke and Raghu Kacher of the Bell Laboratories. Taguchi defines the quality as “the losses a product imparts to the society from the time it is supplied”. Taguchi’s contributions to quality engineering include loss function associated with a product or process, robust design and simplified statistical experiments using orthogonal arrays.

Taguchi methodology states that even the best available manufacturing technology by itself is not an assurance that the final product will, actually, function in the hands of its users as desired and so strongly advocated for the engineered products with robust performance [1, 2, 3]. Taguchi described entire concept in two basic ideas, namely, quality should be measured by the deviation from a special target value, rather than by conformance to preset tolerance limits and quality cannot be ensured through the inspection and rework, but must be built-in through the appropriate design of the process and product. The first concept underlines the basic difference between Taguchi methods and statistical process control (SPC) methodology. While SPC emphasises the attainment of an attribute within tolerance range, Taguchi methods emphasise the attainment of the specified target value and the elimination of variation.

Loss function

The essence of loss function advocated by Taguchi can be stated as follows: deviation of a product from the target performance generates loss to the society that varies with reference to the extent of variation. The loss is proved to be minimum when performance coincides with target and increases gradually as it deviates from the target. The Taguchi’s loss function establishes a financial measure of the user dissatisfaction with a product’s performance as it deviates from a target value that is often, overlooked by other experimental designs [ 3, 4].

Taguchi believes that the customer becomes increasingly dissatisfied as the performance departs farther away from the target. According to Taguchi, the cost of quality in relation with the deviation from the target is not linear because the customer’s frustration increases at a faster rate as more defects are found on a particular product and a quadratic curve to represent the customer’s dissatisfaction with a product’s performance (Figure 1). Based on the Taylor series approximation, the loss function increases as the quality characteristics deviates on either sides of the target value [4,5].

Figure 1. Taguchi’s Loss Function

If y is the performance characteristic measures on a continuous scale with the target performance level t, then loss caused [L(Y)] is given by a quadratic function :  Where delta  is cost of a defective product and m is LSL-T or 

T-USL. The average loss is proportional to the mean squared error of Y about its target value t. The loss function for n products is given by

Thus the average loss, caused by variability has two components.
1.The average performance (µ), being different from the target t, contributes the loss k (µ- t)2.
2.The loss ks2 results from the performance (yi) of the individual items being different from their own average µ.
The ideal condition is µ = t and s2 = 0. The quadratic loss function provides the necessary information (S/N) to achieve effective quality improvement.

Design and robust design

The basic scientific knowledge allows the designer to guide the design, with suitable design parameters that ensure good performance [1, 5, 6, 7, 8]. Design of a product or a process, essentially, involves various stages like concept design, parameter design and tolerance design, each addressing different set of aspects (Table 1).

Taguchi developed a strategy for quality engineering that can be used in the product design and its manufacturing process. In conventional DoE, variation between experimental replications is a nuisance that the experimenter like to eliminate, whereas in the Taguchi method, they are the central object of investigation. Taguchi’s method replicates each experiment with the aid of an outer array that deliberately include the sources of variation that a product would come across while in service. Such a design is called a minimum sensitivity design or a robust design and the Robust Design method is called Taguchi method [9].

Table 1. Scope and Significance of Design Concepts

Robust design can greatly reduce the off target performance caused by poorly controlled manufacturing conditions, temperature or humidity shifts, wider component tolerances used during fabrication and also field abuse that might occur due to adverse service conditions [1, 5, 9].

Table 2. Approaches for Taguchi method

To achieve the optimum design factor setting, Taguchi advocated a combination of two stage process in which the first step is related to the selection of robustness seeking factors and the second step with the selection of adjustment factors to achieve the desired target performance. The various stages in the experiment involve typically a four-step or elaborated eight-step process shown in the Table 2. Robust design results in a product or process that is insensitive to the effects of sources of variability even when the sources themselves have not been eliminated, by means of systematic approach (parameter design). It requires the evaluation of controllable products or process control factors in noisy environment from which the classical design of experiment methods seek isolation.

Orthogonal Arrays and Response Table

The design array used by Taguchi has the basis from other design of experiments like, fractional factorial, Plackett-Burman, Latin Square Design and mixed designs and consists of symmetrical subsets of all combination of treatments [1, 4, 5, 10]. The methodology minimizes performance or quality problems arising due to non-identical operating or environmental conditions using a simplified method known as orthogonal array experiment that helps to conduct a multifactor experiment towards establishing the best product or process design.

The orthogonal arrays that Taguchi advocated are saturated set of experiments allowing no scope for estimation of interactions between control factors also known as inner array factors but with additional interaction with an outer array consisting of noise factors. In a given possible combinations of various levels of the variable, the orthogonal array uses a special subset with a balanced nature, in which the missing combinations can also be predicted [4]. A manual procedure is available that quickly completes the calculation of effects from orthogonally designed experimental observations, using a special format known as “response table”, for recording and manipulating the observed data. This response table also includes random order column, using which the randomisation can be carried out.

The major characteristics of orthogonal arrays include following [10, 11]:
--Orthogonal arrays (OA) are special matrix experiments that allow the experimenter to study the main factor effects of several design parameters at once and efficiently.
--OA is a valid representation of the cause-effect relationship of the process under study.
--The crux of the OA method lies in choosing the level combinations of the input design variable for each experiment.
--The total number of rows in an OA determines the total number of experiments to be run in the investigation.
--In any pair of columns in an OA, all combinations of the treatments occur in equal number of times.
--Any treatment pair occurs once and only once between the two column, a property known as “balancing property”.
--Any two columns of OA are mutually orthogonal.
--The experiments guided by an OA may not use all columns but it must use every one of the array.
--Orthogonality implies that the entries in the array satisfy a special mathematical condition, where sum of all weighting factors involved in the equation that represents a function is zero. When additivity assumption holds, it is possible to estimate the main factor effects using a single set of experiments based on orthogonal design.
--Within the OA, further a sub-set can be analysed for a particular combination.
--Use of OAs to plan matrix experiments also ensures that if errors in each experiment are independent and have zero mean and equal variance and the estimated factor effects are mutually uncorrelated.

Two factors are said to interact when the influence of one on a response is found to depend on the setting of the other factor. But when there are other factors also involved in this, the factor estimates can be far from the true values, where the estimates can be improved by replicating the trials. The averages found, by replication have less variability and improve the precision. Replication of orthogonal experiments can also help us to see the factors that affect the average performance, factors that affect the variability of performance. In many cases, the dependence between process performance (y) and influencing parameters is generally restricted to the main effects, which are additive cause-effect model, with the form,
 y = µ + pi + qj + rk + sl + e
µ represents overall mean value of y in the region of experimentation in which one varies other factors. Further, p1, p2 and p3 are the deviations of y from µ caused by factor setting / levels with each factor with its own positive and negative effects only. One assumes the factor effects to be additive and separable from each other for a three level experiment, ie, p1 + p2 + p3 = 0 and similar relationship for q, r and s also. If the average variance for the error ei in a single experiment is (se)2, then average error (e7 + e8 + e9) / 3 will have the variance se2 / 3. If the additivity assumption is not valid, then error term will be independent of each other and not a random variable with zero mean and variance.
Verification of additivity is, often, checked by the verification experiment, with treatment set at known (usually the optimum) values and observing the outcome. A close agreement between the observed and predicted responses suggests that the reasonableness of the additivity assumption.

Experts often say that good experiments do not always make good products but good experiments will provide important information. Taguchi method states that whenever one does not completely know the effects of different factors, one should “empirically” identify the optimum settings of the design parameters by doing certain special experiments. Such experiments are carried out by judiciously exploiting the DP-noise interactions, after completing function design. While screening various design parameters, using a suitable cause-effect diagram is very much useful in elimination of several factors from consideration and also can facilitate experimentation of important factors at multiple levels that in turn has a good chance to show up their influences on the observations. Also, at initial stages, keeping wider levels would reveal the off-specification products, which would show the sensitivity of a parameter.

The following guidelines are useful while selecting ‘right’ quality characteristics and maximize the chances for additivity.
1.Quality characteristics (y) should be directly related to the basic mechanism of the process or products
2.Characteristics should be easy to measure.
3.As far as possible, the measured quality characteristics should be a continuous variable.

Noise factors

While in the cases of other experimental designs, uncontrollable factors are kept under observation while experimentation without including them in the purview of the experiments,

Taguchi method provides the means to include the effect of these factors in the experiments to make the performance of the process or process a robust one. Taguchi called these uncontrollable factors as noise factors a term derived from communication industry. Noise factors are either too hard or uneconomical to control, even though they cause unwanted variation in performance of the product or process [7, 8, 9, 10]. Taguchi reduced all the noise factors to three typical categories (Table 3), namely inner noise, outer noise and product noise. These noise factors, at distinct levels, are included in the noise OA as an outer array, while the levels of main factors are kept in the inner array. Under certain conditions, noise factors are studied at several levels, to improve the detection and exploitation of DP-noise interactions.

Signal-to-Noise ratios

Customers are satisfied when products perform on target and products that fail within ± d tolerances continue to cause a quality loss. Based on the experiences, the loss due to inadequate quality of a product or process has been found to be a quadratic loss function, ie, L (y) = k (y-target)2 and one may try to maximize the performance by minimizing the loss function. Instead of using the loss function directly, Taguchi, also, formulated a simple statistic namely S/N ratio, a logarithmic function, the ratio of mean performance to variation in mean performance due to uncontrollable factors, which is concurrent statistic and a special kind of data summary. S/N ratio is an ideal measurement to decide the best values or levels of control factors. The S/N ratio is the primary measurement used for products or process optimisation, represents the ratio of sensitivity to variability, and is used to optimise the robustness of a product or process [5].

In a set of statistical experiments, the average quality characteristics and standard deviation (caused by noise factors) are represented by µ and s with desired performance µo. Then one must make an adjustment in the design to get performance on target and the loss after adjustment is expressed as

in which µ2 represents the signal component and s2 represents the variance or noise of the signal component. Maximising

or S/N ratio becomes equivalent to minimising the loss after adjustment. For improving the additivity, the function is converted into logarithmic function and expressed in decibels as S/N = 10 log 10 . The maximisation of the S/N ratio by a suitable selection of the DPs makes the design 

robust. An appropriate S/N ratio needs to be selected for optimisation.

The S/ N ratio is a predictor of the quality loss that isolates the sensitivity of products to the noise factors. In robust design, one minimizes the sensitivity to noise by seeking combinations of the DP settings that maximize S/N ratio. The additivity of DP effects also becomes maximum, in the most appropriate S/N ratio. One can also select the most appropriate S/N ratio among several S/N ratios, for both scaling factors and adjusting factors. Table 4 shows the typical S/N ratios used in various situations.

A close agreement between the calculated maximum values of S/N ratio with actual ratio (by graphical method) suggests that the additivity assumption is a reasonable one, a prime requirement for the main effect model and its predictability for any treatment combinations within the influence space. If this verification fails, then the experiment repeated with higher factor order interactions using a larger OA or some other experimental design [12]. Graphic evaluation methods of main effects convey, rapidly, the relative magnitude of the different factor effects and quick identification of optimum setting for each factor under the experiment. They also display, visually, the relative effects of each of the individual design factors.

Taguchi methods may also use ANOVA, to determine the effect of a particular factor on the response or its variability with F tests on S/N ratios in the robust design studies. Before attempting regression exercise, cause-effect relationship between the variable in question by ANOVA or some other similar method is carried out.

Taguchi Methods – Relevances in Textiles

Optimisation of textile processes is often cumbersome since they are easily affected by a number of controllable and uncontrollable factors that may or may not be controllable. Taguchi method treats optimisation problems in two categories namely static problems that generally involve batch process optimisation that attain ‘one’ fixed performance level, eg, a static application for an injection moulding machine finds the best operating condition for a single mould design and dynamic problems, which is related to technology development, and similar situations as contingency planning for some unknown future requirements [4, 9, 13].

In some engineering problems, the signal factor is absent or it takes a fixed value and these problems are called static problems and corresponding S/N ratios are called S/N ratios. In dynamic applications, a signal factor moves the performance to some value and an adjustment factor modifies the design’s sensitivity to this factor; if the signal is plotted in horizontal axis and the response in the vertical axis, the adjustment factor will change the slope of the line. The adjustment factor adjusts the magnitude of change in a given setting. In problems in which the signal and response must follow a function called the “ideal function”, eg, linear relationship. Such problems are called dynamic problems and the corresponding S/N ratios are called dynamic S/N ratios [ 9].

Taguchi method has been used as a screening tool to determine the robust settings in the saw ginning of seed cotton using the design parameters including the paddle roll, saw and seed finger roller components and with field cleaner as the noise component to maximize FIBRE quality measurements [5]. Effect of various process parameters on drafted strands, in terms of relative fibre parallelisation, modified coefficient of relative fibre parallelisation, fibre straightness index and tenacities have also been analysed in the past under the response type ‘larger-is-better’ [12]. The following Table 5 lists certain prominent applications of Taguchi’s optimisation method in the field of textile manufacturing.

Taguchi methods Vs other methods

Statistical process control allows for faults and defects to be eliminated after manufacture (if detected) whereas Taguchi methods provide effective solution that prevents their occurrence. One at a time approach is inefficient when the number of variables is many and it can miss detection of critical interactions among the design variables [8]. There are various ways to optimise the effects of controllable variables using design of experiments techniques like factorial design, central composite, Box-Behnken, etc. The major drawback of all these techniques is their inability to include the effect of uncontrollable factors like environmental conditions, etc [12].

Taguchi method is simple technique compared to many sophisticated experimental techniques like response surface method is a combination of statistical experimental design fundamentals, regression modeling technique and optimisation methods [11, 12, 20]. Taguchi method has been considered to more effective than recently developed algorithms like genetic algorithm methods, which in many occasions require less human effect. Taguchi method is a scientifically disciplined mechanism for evaluating and implementing improvements in products, processes, materials and facilities.

The method is applicable over a wide range of engineering fields that include processes that manufacture raw materials, tuning the sub-systems in the engineering operations or in the service sector. Taguchi method separately calculates the individual or main effects of the independent variables on performance parameters while other designs give collective effect of variable in terms of equations or three dimensional curves or contour diagrams, which are often difficult to understand and interpret [12].

Main drawback of the Taguchi method is that it may not always determine the interactions effects like some of the other design of experiment techniques. It also assumes that the effects of each process variable on response is additive in nature, which is always not true in many practical situations. However, use of ANOVA and regression model in conjunction with the Taguchi method helps to quantify the contribution of each process variable, changing the response and therefore helps in ascertaining the additivity of the method.

Reference

1.Total Qualtiy Management,Volume 1, Indira Gandhi Open University, New Delhi 2001, 225 – 231. 2.http://www.wter.org/loyola/polymers/c7_s6.htm.
3.Bass I: Introduction to Taguchi Method Part I, through http://www.sixsigmafirst.com/intro2 taguchi1.htm.
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6. http://en.wikipedia.org/wiki/Taguchi_Methods.
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15. Kumar A, Ishtiaque S M, and Salhotra K R: Analysis of Spinning Process using the Taguchi Method: Part IV – Effect of Spinning Process Variables on Tensile Properties of Ring, Rotor and Air-jet Yarns, Journal of the Textile Institute, 97 (5) 2006 385 – 390.
16. Kumar A, Ishtiaque S M, and Salhotra K R: Analysis of Spinning Process using the Taguchi Method: Part III Effect of Spinning Process Variables on Migration Parameters of Ring, Rotor and Air-jet Yarn, Journal of the Textile Institute, 97 (5) 2006 377 – 384.
17. Webb C J, Waters G T, Thomas A J, and Liu G P: The Use of the Taguchi Design of Experiment Method in Optimising Splicing Conditions for a Nylon 66 Yarn, Journal of the Textile Institute, 98 (4) 2007, 327 – 336.
18. Farsani R E, Raissi S, Shokuhfar A and Sedghi A: Optimisation of Carbon FIBREs Made up of Commercial Polyacrylonitrile FIBRE using Screeing Design Method.
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20. Ray S: A Statistical Tool for Process Optimisation, Indian Textile Journal, 2006 (12) 24 – 30.

Note: For detailed version of this article please refer the print version of The Indian Textile Journal June 2008 issue.

Dr T Ramachandran
Department of Textile Technology,
PSG College of Technology,
Coimbatore, Tamil Nadu.

D Saravanan
Department of Textile Technology,
Bannari Amman Institute of Technology,
Sathyamangalam, Tamil Nadu.