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(13-10-2012, 11:15 PM)Guest Wrote: hi i m fully satisfied from this book and i m going through the the history of this book.

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INTRODUCTION TO TAGUCHI METHOD :
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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 :
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By performing a series of experiments each of which gives him someunderstanding. This requires making measurements after every expt.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 maydiscourage or will not allow a selection of parameters which oughtto be changed in the next expt. 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 mainproblem (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 set of experiments is complete and ought to give desired results. However, it does not easily lend itself to understanding of science behind the phenomenon. The analysis is not very easy (though it is 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 optimisations are 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, people, equipment etc).


(3) Taguchi Method :
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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 optimisation 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), as objective functions for optimisation, help in data analysis and prediction of optimum results.


Taguchi Method treats optimization problems in two categories,

[A] STATIC PROBLEMS
[B] DYNAMIC PROBLEMS :


[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 eventhough noise is present in the process. The process is then said to have become ROBUST.



There are 3 Signal-to-Noise ratios of common interest;
(I) SMALLER-THE-BETTER :
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n = -10 Log10 [ mean of sum of squares of measured data ]

This is usually chosen 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 Log10 [ mean of sum of sqaures of {measured - ideal} ]

(II) LARGER-THE-BETTER :
-------------------

n = -10 Log10 [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 :
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square of mean
n = 10 Log10 -----------------
variance

This 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) Uniformity in deposition /growth /plating /etching thickness.

The Taguchi method involves reducing the variation in a process through robust design of experiments. The overall objective of the method is to produce high quality product at low cost to the manufacturer. The Taguchi method was developed by Dr. Genichi Taguchi of Japan who maintained that variation. Taguchi developed a method for designing experiments to investigate how different parameters affect the mean and variance of a process performance characteristic that defines how well the process is functioning. The experimental design proposed by Taguchi involves using orthogonal arrays to organize the parameters affecting the process and the levels at which they should be varies. Instead of having to test all possible combinations like the factorial design, the Taguchi method tests pairs of combinations. This allows for the collection of the necessary data to determine which factors most affect product quality with a minimum amount of experimentation, thus saving time and resources. The Taguchi method is best used when there is an intermediate number of variables (3 to 50), few interactions between variables, and when only a few variables contribute significantly.
The Taguchi arrays can be derived or looked up. Small arrays can be drawn out manually; large arrays can be derived from deterministic algorithms. Generally, arrays can be found online. The arrays are selected by the number of parameters (variables) and the number of levels (states). This is further explained later in this article. Analysis of variance on the collected data from the Taguchi design of experiments can be used to select new parameter values to optimize the performance characteristic. The data from the arrays can be analyzed by plotting the data and performing a visual analysis, ANOVA, bin yield and Fisher's exact test, or Chi-squared test to test significance.