# Taguchi method

The Taguchi method , named after its inventor Taguchi Gen'ichi (anglicized: Genichi Taguchi), is an experimental method that aims primarily at minimizing the spread around the target value . The Taguchi method tries to achieve this goal by making products , processes and systems as robust as possible . This means that they should be as insensitive as possible to interference ( noise ) to which they will be exposed in practice.

The Taguchi method is used in quality management and in Six Sigma .

## The loss function

Instead of viewing the required tolerances as limit values to be observed during production , the Taguchi method evaluates every deviation from the target value (even within the tolerance limits ) as an error that causes a concrete financial loss. This financial loss is modeled within the framework of the Taguchi method using the so-called loss function. From a mathematical point of view, the loss function represents a parabola . This means that the model assumes that a deviation from the nominal value that is twice as large causes four times as much financial loss. The financial loss is minimized if the value achieved corresponds exactly to the target value.

Taguchi's concept of loss is not limited to the financial loss that the manufacturer incurs if he produces a bad product. Rather, the loss function models the loss that society incurs when a consumer uses a product whose characteristics do not meet their target values. The idea of ​​minimizing the loss to society rather than the loss to one's own company is a break with traditional thinking.

${\ displaystyle L (y) = K (yT) ^ {2}}$

${\ displaystyle L}$= Loss of quality, = actually measured value, = nominal value, = estimated monetary value, which is related to the deviation from the nominal value ${\ displaystyle y}$${\ displaystyle T}$${\ displaystyle K}$

## Signal-to-disturbance ratio and robustness measure

As a measure of the dispersion around the set value of the proposal Taguchi is, the following is the so-called signal-to-interference ratio is used, the the signal-to-noise ratio (engl. Signal to Noise Ratio ) of the telecommunications (Taguchi once worked in this area) is modeled on. For this one also writes the S / N ratio for short.

${\ displaystyle {\ frac {S} {N}} = 10 \ log _ {10} \ left ({\ frac {{\ bar {Y}} ^ {2}} {s ^ {2}}} \ right )}$

with = effect of the signal = effect of the interference ( "noise") = average of target and = standard deviation ${\ displaystyle S}$${\ displaystyle N}$${\ displaystyle {\ bar {Y}}}$${\ displaystyle s}$

Since the S / N ratio contains the mean value of the target variable, it is therefore also dependent on its mean value position . This is useful for parameters where the standard deviation increases in step with the mean value due to physical relationships. However, if only the standard deviation is of interest , regardless of the mean value, then the robustness measure is sufficient for assessing the process or system instead of the S / N ratio. The robustness is then calculated using the following formula: ${\ displaystyle {\ bar {Y}}}$

${\ displaystyle {\ text {Robustness}} = 10 \ log _ {10} \ left ({\ frac {1} {s ^ {2}}} \ right)}$

These S / N formulas apply to characteristics that have a specified target value. Taguchi uses other S / N calculation formulas for features that should ideally have values ​​that are as large or as small as possible.

## The Taguchi development philosophy

Taguchi divides the development process into three steps:

• System design
• Parameter design
• Tolerance design

These three steps are also by him as offline quality control (Engl. Offline quality control called). Each of these steps has its own function:

In system design, the designers decide what kind of system is to be built, for example which technology is to be used, which components the system is to consist of, etc.

The parameter design is about optimizing all the parameters of the design (control variables, factors) so that the system is as insensitive as possible to interference. This means that ideal setpoints are determined for the various parameters. For this purpose, statistical experimental design methods used.

The tolerances for the system parameters are specified in the tolerance design . Statistical test planning methods are also used here. The aim is to determine the tolerances according to the actual effect of the parameters on the function of the system. If it can be shown that a factor does not have a major influence on the function, a wide tolerance is specified. This saves manufacturing costs.

## Taguchi designs

The orthogonal field L 8 (2 3 ). The trial factors are assigned to the seven columns. Plus and minus stand for the two examined levels of the factor (example: factor temperature; "+" then stands for the high temperature value, "-" for the low one). The lines correspond to the test runs and indicate which of its two levels each of the factors in the relevant test run must be placed on.

Experimental designs by Taguchi are essentially part plans factor (engl. Fractional factorial designs ), that is, there are played not all possible combinations of factor levels, but only a precisely selected subset. To create the so-called experimental designs are orthogonal arrays (engl. Orthogonal arrays ) are used which are tabulations in reference books.

Taguchi experimental designs for parameter optimization often involve an inner and an outer field; in the inner field are the control variables (design parameters freely configurable by the engineer), and in the outer field the disturbance variables (environmental factors, etc., which in practice are subject to unavoidable and uninfluenceable fluctuations and thus have an influence on the process result). The outer field ( outer array ) is usually much smaller than the inner one ( inner array ). For example, if the outer field comprises four test runs, each of the test runs of the inner field must be run four times, once for each combination of disturbance levels provided in the outer field.

The aim is to find the combinations of control variable levels in which the effects of the disturbance variables are minimized and at the same time the desired setpoint is maintained.

The tests are evaluated in three steps, which take into account the fact that adjustment to the target value is generally much easier to achieve than minimizing the spread:

1. Identify factors that have the greatest impact on the S / N ratio.
2. Put these factors on the levels that ensure maximum insensitivity to the disturbance variables (minimization of the scatter).
3. Adjustment of the mean value to the target value using the remaining factors that do not or only slightly influence the S / N ratio.

## reception

Taguchi's robustness-aiming quality philosophy, coupled with the use of statistical experimental design methods as a means of achieving this goal, has gained widespread recognition in the industry. The statistical methods he uses have, however, been judged to be unnecessarily complicated, inefficient, improper or in need of improvement. Starting points for criticism include the formulas for the S / N ratio, the inadequate statistical efficiency of the test plans composed of an inner and an outer field and the risk of mixing up the main and interactions resulting from the use of partial factor plans .

## literature

• Wilhelm Kleppmann: test planning . Optimize products and processes. 7th updated and expanded edition. Hanser, Munich et al. 2011, ISBN 978-3-446-42774-7 ( practical series quality knowledge ).

## Individual evidence

1. ^ A b D. C. Montgomery: Design and Analysis of Experiments . John Wiley & Sons, New York - Chichester - Brisbane - Toronto - Singapore, 1991, ISBN 0-471-52994-X , p. 416.
2. Thomas L. Albright, Robert W. Ingram, John W. Hill: Managerial Accounting. Information for decisions. South-Western, 2006, ISBN 0-324-22242-4 , pp. 255-262 (English).
3. Dr. J. Krottmaier, experimental planning, Verlag Industrielle Organization Zürich / Verlag TÜV Rheinland, 1991, ISBN 3-88585-812-6 and ISBN 3-85743-945-9 , p. 135, p. 186.
4. ^ A b D. C. Montgomery: Design and Analysis of Experiments . John Wiley & Sons, New York - Chichester - Brisbane - Toronto - Singapore, 1991, ISBN 0-471-52994-X , p. 418.
5. D. C. Montgomery: Design and Analysis of Experiments . John Wiley & Sons, New York - Chichester - Brisbane - Toronto - Singapore, 1991, ISBN 0-471-52994-X , p. 415.
6. ^ DC Montgomery: Design and Analysis of Experiments . John Wiley & Sons, New York - Chichester - Brisbane - Toronto - Singapore, 1991, ISBN 0-471-52994-X , p. 421.
7. ^ GEP Box, S. Bisgaard, CA Fung: An Explanation and Critique of Taguchi's Contributions to Quality Engineering . In: Quality and Reliability Engineering International , Vol. 4, pp. 123-131.
8. ^ DC Montgomery: Design and Analysis of Experiments . John Wiley & Sons, New York - Chichester - Brisbane - Toronto - Singapore, 1991, ISBN 0-471-52994-X , pp. 414-433.