NANDAGOPAL RAMACHANDRAN
Management Systems Engineering
Virginia Polytechnic Institute and State University
Blacksburg, VA - 24061, USA
 
 

Abstract

This paper discusses the Taguchi Method of designing products and processes to achieve cost reduction and increase profits. In the modern era of competition companies need to supply high quality products at low costs to stay alive. Taguchi quality engineering is based on the objective of minimizing variability in critical design parameters that will affect product performance characteristics. Variability in critical design parameters will increase the costs, which is expressed in the form of a loss function. This is a quadratic relationship between cost and the variation of critical parameter design values from the target value. Organizations will have to focus on minimizing variability in the product through process and product design to reduce costs. However, certain variability is difficult to control, which are referred to as noise. Products need to be designed so that they are robust to noise, which could cause variation of product performance from the target value. Taguchi methodology provides an efficiently designed experimental approach that helps to effectively understand the relationship of noise with the target performance. After experimentation, the results are summarized into a metric called the Signal-to-Noise ratio, which jointly considers how effectively the target value of the parameter has been achieved and the amount of variability that has been experienced. From this ratio a designer can identify parameter values that will have the greatest effect on the products performance. Using this the designer can identify the following, a) parameters that have no significant effect on product performance, so that the tolerance limits of these parameters can be relaxed and costs can be reduced. b) parameter values that minimize the effect of noise, thereby achieving a more robust design. c) parameter values that reduce costs without affecting the product performance. A new design for the product is arrived at with the new parameter values that will reduce costs considerably by reducing variability and increase quality.
 
 

Background and Problem Statement

 Many products manufactured are subjected to conditions that cannot be controlled during the production and usage of the product, like wear, ambient temperature, dust, humidity, etc. These problems are affecting the quality of product and increasing the costs. Companies are trying to improve quality of their products and services by trying to eliminate the problems and variations in the products and services. Eliminating the problem invariably increases the costs due to scrap, rework, costly experiments, etc. The companies can produce quality products at very low prices without eliminating the problems and variations but by making the design of the product and services insensitive to these variations and problems. The essence of Taguchi method is to desensitize the design of a product to the effect of variations. This allows for reducing costs without sacrificing product function or reliability.

 The first step in Taguchi method is to identify the factors that affect the product performance or reliability. Then statistically designed experiments are performed to determine the effect of varying values of the factors to the product performance. Finally the factor values selected for the design are those which are least sensitive to variation. Due to the lower sensitivity to variation the tolerances can be widened and costs can be reduced. The whole process of using Taguchi methodology for cost reduction can be modeled as in the following flow chart [6].
 

 

Noise Factors

 There are two classes of factors, control factors and noise factors. The parameters of a product that can be controlled during the manufacture as well as experimentation are the control factors.  The parameters that can be controlled in experimentation but not controlled in high volume manufacture are the noise factors. It is the noise factors that cause maximum variation in the product performance.

 Inspite of efforts to engineer products and processes that meet specifications, they deviate from the target values beyond the tolerance limits during manufacturing as well as customer use. These deviations are caused by noise factors. Examples of noise factors are ambient temperature variations, voltage variations in the case of electrical equipment, dust, humidity, etc.

 Noise factors cause substantial loss in various stages of a products life cycle. Costs incurred during manufacture are scrap, rework, expensive raw materials to counter effect of noise, increased production costs, increased labor costs, etc. The costs incurred during usage are high operational costs, warranty and service costs, spare parts inventory costs, costs due to loss in market share, etc.

Managing Noise factors- Taguchi Approach

 In conventional methods noise factors were identified and eliminated. Since identifying and elimination of noise is expensive, the conventional method of managing noise leads to high quality albeit at high costs. Products achieve high quality but they become non-competitive in pricing leading to loss in market share and generating low profits. For example if the noise factors were variations in plant and machinery, then new technology machinery would be the solution. Here the product quality will improve but the capital expenditure also increases. Conventional approach to improving product quality invariably leads to increasing of costs.

 In Taguchi approach of managing noise factors and increasing quality the noise factors are not eliminated but the product or process is made insensitive to the noise factors. Taguchi method advocates conducting of experiments with different values of control factors. Each value can be considered as a level for that factor. In experimentation each factor will have more than one level. In these experiments noise is injected into the product or process and the effect of noise on the product performance is measured. Then through data analysis procedures like analysis of variance (ANOVA) the best setting of the control factors are found such that the product performance becomes insensitive to noise. Thus a robust design that can withstand the noise factors is obtained.

 The design process involves three steps, system design, parameter design, and tolerance design. Parameter design involves the identification of the target values of the control factors that can be controlled during production process so that the product process becomes insensitive to noise. In tolerance design the tolerance for the control factor values are found so as to reduce costs due to rework, scrap, etc.

Signal-to-Noise Ratio (S/N)

 S/N ratio is a concurrent statistic, which looks at both signal and noise and rolls them into a single number. It is a performance measure to choose control levels that best cope with noise. For any experiment if the S/N ratio is maximum then it is the optimum setting for the control factors to eliminate the effect of noise. So the combination with maximum S/N ratio is selected.

 Taguchi has proposed different S/N ratios for different quality criteria. The S/N ratio for different quality criteria can be stated as follows [1].

1. Biggest is Best (e.g. strength, yield)
    The formula for calculating the S/N ratio is –10 log((?1/x2)/n)
    where x is the value of the observation and n is the total number of observations

2. Smallest is Best (e.g. contamination)
   The formula for S/N ratio is –10 log((?x2)/ n)

3. Nominal is Best (e.g. dimension)
   The formula for S/N ratio is –10 log(x~2/ SD2)
   Where x~ is the average of the observations and SD is the standard deviation.

Quality Loss Function
 
According to Taguchi quality is related inversely to the financial loss caused to the society after a product that doesn’t meet the specifications is shipped. This means that as the loss increases the quality decreases and the viceversa. This loss can be categorized into two groups [7].

1. Loss due to functional variation.
2. Loss due to harmful effects.

 Any time a product deviates from its target performance there is loss. But the ideal quality in which all the products produced will deliver target performance can never be achieved. The concept of zero defect vanishes and is replaced by defects in parts per million. The objective is to move more and more closer to zero defects without any additional costs. Taguchi methodology helps in moving closer towards the zero defects target without additional costs. Taguchi developed a loss function for the cost of quality, which is used to estimate the savings in costs by making products insensitive to noise.
 
 If the product deviates from its target performance there is loss and Taguchi methodology uses a loss function to calculate the financial loss caused by this deviation from target value. Loss function is the cost associated with a given quality characteristic value expressed as a function of its deviation from the target value.
 
The loss function used in Taguchi methods can be stated as follows [8],

L(x) = k (x - m)2

where  L(x) is the monetary loss in dollars,
m is the target value,
x is the actual value which is deviated from the target value,
k is the constant whose value depends on the magnitude of tolerance limits and monetary loss if the product deviates out of the target value.

The loss function can be proved as follows,
By equality relation

 L(x)     = L(x)
            = L(m + x - m)

The Taylor series expansion for the expression L(m + x - m) is

 L(x)     = L(m) + L’(m) / 1! * (x-m)! + L’’(m) / 2! * (x-m)2 +……………..

If the product performs at the target value then the loss is 0. ?L(m) and L’(m) are equal to zero. So there exists terms from the second derivative only. The terms greater than the second derivative is negligibly small and so they can be neglected.
 
 L(x)     =  L’’(m) / 2! *  (x-m)2

 L’’(m) / 2!  can be replaced by a constant k

The equation becomes L(x) = k(x-m)2

The value of constant can be obtained in the following way, if the cost due to the product exceeding the tolerance limit is ‘C’ and the tolerance is ‘t’ then the value of ‘k’ is given by the equation,

k = C / t2

The important consequence of the loss function equation is that the further the product varies from its target performance the greater the loss, as the function is quadratic in nature. Further this loss is a continuous function and not a sudden step when there is a deviation from the ideal. Based on this loss function quality can be defined as keeping the product’s performance on target with low variation. The loss function can be graphically represented as follows,
 
 
 

 

In Taguchi methodology all efforts are directed at minimization of variations in the product performance and adjusting the response at a desired target value. The variation in the product performance is caused by noise factors. The Taguchi approach involves an experimentally based technique to define the levels of the design parameters that will result in reducing the uncertainty in the product performance and make the performance less sensitive to noise factors [9].

The first step in the experimentation is to identify the noise factors and control factors that affect the product performance. After identifying the factors the next step is to construct an orthogonal  array matrix with the factors along the column. For example if there are 7 factors and two levels, the orthogonal array will consist of 7 columns and 8 rows. Orthogonality ensures that the effects of the factors are independent of effects of other factors and this is often desirable. The orthogonal arrays are often used to estimate the average effect of each factor as all remaining factors are varied. The array should be as small as possible to prevent added expense of costly experiments, which will not provide any additional information.

The orthogonal array is translated using required levels of selected parameters to create the experimenter’s log sheet. Then the experiments are conducted according to the conditions tabulated. All responses are measured for each experiment. It is highly desirable to repeat each experiment more than once in order to account for experimental errors.

Data Analysis and Loss function Evaluation

 The data obtained from the experiment is analyzed using two methods, response analysis and analysis of variance.

1. Response analysis

 The responses obtained from the different experiments are analyzed using response tables and graphical representation of the mean effects of each parameter [6]. The analysis helps in identifying the factors that have great impact on the product’s target performance. Signal-to-Noise ratio is used for the response analysis. This provides a sensitivity measurement of the quality characteristics for different levels of control and noise factors. The optimum design is the one in which S/N ratio is maximized or the design in which the variability resulting from the noise factors is minimized.

2. Analysis of Variance(ANOVA)

 ANOVA is performed to estimate experimental errors and to predict the relative significance of the design factors. It helps in finding the percentage contribution of each factor and providing quantitative measures of various effects. The ANOVA is summarized in the table [5].
 
 
 

Where n is the number of experiments conducted.

Here all the factors that do not have any real effect on the variance are denoted under the common term error.

 When the quality characteristic of a product deviates from the target value, a loss is incurred. Such a loss can be quantified in terms of costs of rework, scrap, etc, to regain customer satisfaction. The mathematical form of loss function derived earlier is used to evaluate the loss in monetary units.

L(x) = k (x-m)2
 
 Reducing the variability of parameters from the target value can reduce this cost. The important method to reduce this cost is specifying tolerances by applying tradeoffs between the costs of rejection and cost of meeting tight tolerances.

Tolerance Design

 In tolerance design decisions are made to how much variability to allow for each parameter. The necessary information to design tolerance are loss function value and the target value of each parameter. Through experimentation the optimum values of parameters to reduce effects of noise are arrived at. These optimum values help in reducing costs and improve quality. The parameters do not remain at the optimum value through the product’s life cycle. As the product varies further away from the target value the loss increases quadratically.

 To reduce variability tighter tolerances can be used. But tighter tolerances mean increased costs due to scrap and rework and looser tolerances mean increased loss function due to variability. Using loss function, tolerance is designed in such a way that the additional costs due to tighter tolerance is justified by the increased savings on loss function.

 Integrating the tolerances to the target values of the parameters obtained from the experimentation the final design is arrived at. This design considerably reduces manufacturing costs without eliminating noise factors, increase quality, and increase profit through customer satisfaction.

New model for optimum response

 A model is constructed with the new optimum parameter values obtained from the new design. This model is used to approximate the relationship between the quality characteristics and its factor levels. In this model the total effect of the design factors is equal to the sum of effects of individual factors [6]. The optimum performance can be predicted by using the optimum conditions of the control parameters.

 The validity of the model is tested by a confirmation run under the predicted optimum conditions. If there is any mismatch between predicted and actual then the interaction effects of factors should be eliminated from the model.

Conclusion
 
The use of Taguchi methods facilitates the reduction of manufacturing costs and other product costs through experimentally based design of processes and products. It is the noise factors that cannot be controlled in the actual production and usage of a product, which caused the product to deviate from its optimal performance. This deviation caused the costs to increase. By using the Taguchi method the effect of noise factors is eliminated by setting parameter values at an optimum. The costs are reduced and the quality is improved.

References:

1. Bendell, A (1988) Introduction to Taguchi Methodology, Proceedings of the 1988 European Conference on Taguchi Methods, London, UK.

2. Taguchi, G (1988) Introduction to Quality Engineering – Designing quality into Products and Processes, Asian Productivity Organization, Tokyo, Japan.

3. Taguchi, G (1981) On-line Quality Control during Production, Japanese Standards Association, Tokyo, Japan.

4. Taguchi, G, & Wu, Y (1985) Introduction to Off-line  Quality Control, Central Japan Quality Control Association, Nagaya, Japan.

5. Wilson, G.B., Cannan, E., & Cartwright, G.J. (1988) Taguchi Methods and the Manufacture of Car Seat Cushions, Proceedings of the 1988 European Conference on Taguchi Methods, London, UK.

6. El-Gizawy, S.A., Jones, R.F., & Abu-Hamdan, M.G. (1992) Experimentally based Quality Design Methodology for Electromechanical Products, Journal of Engineering Design, Oxfordshire, UK, pp. 49-61.

7. Bakerjian, R (1992) Tool and Manufacturing Engineers Hand Book, Volume 6, Design for Manufacturability, Society of Manufacturing Engineers, Dearborn, Michigan.

8. Barker, B.T. (1990) Engineering Quality by Design, Mercel Dekker Inc. New York, USA

9. Lochner, H.R., & Matar, E.J.  Designing for Quality, Quality Resources, New York, USA

10. Logothetics, N., & Wynn, H.P. Quality through Design, Oxford Science Publications, Oxford, UK

11. http://kernow.curtin.edu.au/www/Taguchi/cae204.htm

12. http://www.menet.umn.edu/~case0048/quality/index.html

13. http://www.amsup.com/TAGUCHI/