INTRODUCTION TO TAGUCHI METHOD

Every experimenter has to plan and conduct experiments to obtain
enough and relevant data so that he can infer the science behind the observed
phenomenon. He can do so by,

(1) trial-and-error approach :

------------------------------

performing a series of experiments each of which gives some understanding. This requires making measurements after every experiment so that analysis of observed data will allow him to decide what to do next - "Which parameters should be varied and by how much". Many a times such series does not progress much as negative results may discourage or will not allow a selection of parameters which ought to be changed in the next experiment. Therefore, such experimentation usually ends well before the number of experiments reach a double digit! The data is insufficient to draw any significant conclusions and the main problem (of understanding the science) still remains unsolved.

(2) Design of experiments :

-----------------------------

A well planned set of experiments, in which all parameters of interest
are varied over a specified range, is a much better approach to obtain
systematic data. Mathematically speaking, such a complete set of experiments
ought to give desired results. Usually the number of experiments and resources
(materials and time) required are prohibitively large. Often the experimenter
decides to perform a subset of the complete set of experiments to save
on time and money! However, it does not easily lend itself to understanding
of science behind the phenomenon. The analysis is not very easy (though
it may be easy for the mathematician/statistician) and thus effects of
various parameters on the observed data are not readily apparent. In many
cases, particularly those in which some optimization is required, the method
does not point to the BEST settings of parameters. A classic example illustrating
the drawback of design of experiments is found in the planning of a world
cup event, say football. While all matches are well arranged with respect
to the different teams and different venues on different dates and yet
the planning does not care about the result of any match (win or lose)!!!!
Obviously, such a strategy is not desirable for conducting scientific experiments
(except for co-ordinating various institutions, committees, people, equipment,
materials etc.).

(3) TAGUCHI Method :

--------------------------

Dr. Taguchi of Nippon Telephones and Telegraph Company, Japan has developed a method based on " ORTHOGONAL ARRAY " experiments which gives much reduced " variance " for the experiment with " optimum settings " of control parameters. Thus the marriage of Design of Experiments with optimization of control parameters to obtain BEST results is achieved in the Taguchi Method. "Orthogonal Arrays" (OA) provide a set of well balanced (minimum) experiments and Dr. Taguchi's Signal-to-Noise ratios (S/N), which are log functions of desired output, serve as objective functions for optimization, help in data analysis and prediction of optimum results.

**Taguchi Method treats optimization problems in two
categories,**

[A]STATIC PROBLEMS :

Generally, a process to be optimized has several control factors which directly decide the target or desired value of the output. The optimization then involves determining the best control factor levels so that the output is at the the target value. Such a problem is called as a "STATIC PROBLEM".This is best explained using a P-Diagram which is shown below ("P" stands for Process or Product). Noise is shown to be present in the process but should have no effect on the output! This is the primary aim of the Taguchi experiments - to minimize variations in output even though noise is present in the process. The process is then said to have become ROBUST.

[B]:

If the product to be optimized has a signal input that directly decides the output, the optimization involves determining the best control factor levels so that the "input signal / output" ratio is closest to the desired relationship. Such a problem is called as a "DYNAMIC PROBLEM".

This is best explained by a P-Diagram which is shown below. Again, the primary aim of the Taguchi experiments - to minimize variations in output even though noise is present in the process- is achieved by getting improved linearity in the input/output relationship.

[A] STATIC PROBLEM(BATCH PROCESS OPTIMIZATION):----------------------------------------------------------------------------

There are 3 Signal-to-Noise ratios of common interest for optimization of Static Problems;

(I) SMALLER-THE-BETTER :--------------------------------------n = -10 Log

_{10}[ mean of sum of squares of measured data ]This is usually the chosen S/N ratio for all undesirable characteristics like " defects " etc. for which the ideal value is zero. Also, when an ideal value is finite and its maximum or minimum value is defined (like maximum purity is 100% or maximum Tc is 92K or minimum time for making a telephone connection is 1 sec) then the difference between measured data and ideal value is expected to be as small as possible. The generic form of S/N ratio then becomes,

n = -10 Log

_{10}[ mean of sum of squares of {measured - ideal} ]

(II) LARGER-THE-BETTER :-------------------------------------n = -10 Log

_{10}[mean of sum squares of reciprocal of measured data]This case has been converted to SMALLER-THE-BETTER by taking the reciprocals of measured data and then taking the S/N ratio as in the smaller-the-better case.

(III) NOMINAL-THE-BEST :-----------------------------------square of mean

n = 10 Log_{10}-----------------

varianceThis case arises when a specified value is MOST desired, meaning that neither a smaller nor a larger value is desirable.

Examples are;

(i) most parts in mechanical fittings have dimensions which are nominal-the-best type.

(ii) Ratios of chemicals or mixtures are nominally the best type.

e.g. Aqua regia 1:3 of HNO3:HCL

Ratio of Sulphur, KNO3 and Carbon in gun powder(iii) Thickness should be uniform in deposition /growth /plating /etching..

[B](TECHNOLOGY DEVELOPMENT):------------------------------------------------------------------------------In dynamic problems, we come across many applications where the output is supposed to follow input signal in a predetermined manner. Generally, a linear relationship between "input" "output" is desirable.

For example : Accelerator peddle in cars,

volume control in audio amplifiers,

document copier (with magnification or reduction)

various types of moldings

etc.

There are 2 characteristics of common interest in "follow-the-leader" or "Transformations" type of applications,(i) Slope of the I/O characteristics

and

(ii) Linearity of the I/O characteristics

(minimum deviation from the best-fit straight line)

The Signal-to-Noise ratio for these 2 characteristics have been defined as;

(I) SENSITIVITY {SLOPE}:----------------------------------

It is often treated as Larger-The-Better when the output is a desirable characteristics (as in the case of Sensors, where the slope indicates the sensitivity).

n = 10 Log_{10} [square of slope or beta of the I/O characteristics]

On the other hand, when the output is an undesired characteristics, it can be treated as Smaller-the-Better.

n = -10 Log_{10} [square of slope or beta of
the I/O characteristics]

-----------------------------------------------

Most dynamic characteristics are required to have direct proportionality between the input and output. These applications are therefore called as "TRANSFORMATIONS". The straight line relationship between I/O must be truly linear i.e. with as little deviations from the straight line as possible.

Square of slope or beta

n = 10 Log_{10} ----------------------------

variance

Variance in this case is the mean of the sum of squares of deviations of measured data points from the best-fit straight line (linear regression).

(4)

----------------------------------------------------

Taguchi method is a scientifically disciplined mechanism for evaluating
and implementing improvements in products, processes, materials, equipment,
and facilities. These improvements are aimed at improving the desired characteristics
and *simultaneously *reducing the number of defects by studying the
key variables controlling the process and optimizing the procedures or
design to yield the best results.

The method is applicable over a wide range of engineering fields that include processes that manufacture raw materials, sub systems, products for professional and consumer markets. In fact, the method can be applied to any process be it engineering fabrication, computer-aided-design, banking and service sectors etc. Taguchi method is useful for 'tuning' a given process for 'best' results.

Taguchi proposed a standard 8-step procedure for applying his method for optimizing any process,

**8-STEPS IN TAGUCHI
METHODOLOGY:**

Step-1: IDENTIFY THE MAIN FUNCTION, SIDE EFFECTS, AND FAILURE MODE

Step-2: IDENTIFY THE *N**OISE*
FACTORS, TESTING CONDITIONS, AND QUALITY CHARACTERISTICS

Step-3: IDENTIFY THE OBJECTIVE FUNCTION TO BE OPTIMIZED

Step-4: IDENTIFY THE CONTROL FACTORS AND THEIR LEVELS

Step-5: SELECT THE ORTHOGONAL ARRAY MATRIX EXPERIMENT

Step-6: CONDUCT THE MATRIX EXPERIMENT

Step-7: ANALYZE THE DATA, PREDICT THE OPTIMUM LEVELS AND PERFORMANCE

Step-8: PERFORM THE VERIFICATION EXPERIMENT AND PLAN THE FUTURE ACTION

**SUMMARY :**

Every experimenter develops a nominal process/product that has the desired functionality as demanded by users. Beginning with these nominal processes, he wishes to optimize the processes/products by varying the control factors at his disposal, such that the results are reliable and repeatable (i.e. show less variations).In Taguchi Method, the word "optimization" implies "determination of BEST levels of control factors". In turn, the BEST levels of control factors are those that maximize the Signal-to-Noise ratios. The Signal-to-Noise ratios are log functions of desired output characteristics. The experiments, that are conducted to determine the BEST levels, are based on "Orthogonal Arrays", are balanced with respect to all control factors and yet are minimum in number. This in turn implies that the resources (materials and time) required for the experiments are also minimum.

Taguchi method divides all problems into 2 categories - STATIC or DYNAMIC. While the Dynamic problems have a SIGNAL factor, the Static problems do not have any signal factor. In Static problems, the optimization is achieved by using 3 Signal-to-Noise ratios - smaller-the-better, LARGER-THE-BETTER and nominal-the-best. In Dynamic problems, the optimization is achieved by using 2 Signal-to-Noise ratios - Slope and Linearity.

Taguchi Method is a process/product optimization method that is based on 8-steps of planning, conducting and evaluating results of matrix experiments to determine the best levels of control factors. The primary goal is to keep the variance in the output very low even in the presence of noise inputs. Thus, the processes/products are made ROBUST against all variations.

- - end of Intro - -

Read an Intro meant for Indian Industry

Go back to Taguchi Page

Go back to Apte's web-page

modified 26-Aug-2000 / 3-Oct-2000 / 14-Dec-2000