Tuesday 29 November 2016

INTRODUCTION TO TAGUCHI METHOD?




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INTRODUCTION TO TAGUCHI METHOD

Optimization of process parameters is done to have great control over quality, productivity and cost aspects of the process. Off-line quality control is considered to be an effective approach to improve product quality at a relatively low cost. Analysis of variance (ANOVA) is used to study the effect of process parameters on the machining process. The approach is based on Taguchi method, the signal-to-noise (S/N) ratio and the analysis of variance (ANOVA) are employed to study the performance characteristics.

Introduction
Taguchi methods are statistical methods developed by Genichi Taguchi to improve the quality of
manufactured goods and more recently also applied to engineering (Rosa et al. 2009), biotechnology (Rao et al. 2008, Rao et al. 2004), marketing and advertising (Selden 1997). Professional statisticians have welcomed the goals and improvements brought about by Taguchi methods, particularly by Taguchi's development of designs for studying variation. After World War II, the Japanese manufacturers were struggling to survive with very limited resources. If it were not for the advancements of Taguchi the country might not have stayed afloat let alone flourish as it has. Taguchi revolutionized the manufacturing process in Japan through cost savings. He understood, like many other engineers, that all manufacturing processes are affected by outside influences, noise. However, Taguchi realized methods of identifying those noise sources, which have the greatest effects on product variability. His ideas have been adopted by successful manufacturers around the globe because of their results in creating superior production processes at much lower costs.The enemy of mass production is variability. Success in reducing it will invariably simplify processes, reduce scrap, and lower costs” (Box and Bisgaard 1988). The main

objective in the Taguchi
method is to design robust systems that are reliable under uncontrollable conditions (Taguchi1978,
Byrne1987 and Phadke1989).The method aims to adjust the design parameters (known as the controfactors) to their optimal levels, such that the system response is robust – that is, insensitive to noise factors, which are hard or impossible to control (Phadke1989). In the 1980s Genichi Taguchi (1985; 1986; 1993) received international attention for his ideas on variation reduction, starting with the translation of his work published in Taguchi and Wu (1979).

Process Optimization
Process optimization is the discipline of adjusting a process to optimize some specified set of  parameters without violating some constraint. The most common goals are minimizing cost, maximizing throughout, and/or efficiency. This is one of the major quantitative tools in industrial decision-making. When optimizing a process, the goal is to maximize one or more of the process specifications, while keeping all others within their constraints. Process Optimization Tools Many relate process optimization directly to use of statistical techniques to identify the optimum solution. This is not true. Statistical techniques are definitely needed. However, a thorough understanding of the process is required prior to committing time to optimize it. Over the years, many methodologies have been developed for process optimization including Taguchi method, six sigma, lean manufacturing and others. All of these begin by an exercise to create the process map.
Taguchi’s method:
Taguchi's techniques have been used widely in engineering design (Ross 1996 & Phadke 1989). The Taguchi method contains system design, parameter design, and tolerance design procedures to achieve a robust process and result for the best product quality (Taguchi 1987 & 1993). The main trust of Taguchi's techniques is the use of parameter design (Ealey Lance A.1994), which is an engineering method for product or process design that focuses on determining the parameter (factor) settings producing the best levels of a quality characteristic (performance measure) with minimum variation. Taguchi designs provide a powerful and efficient method for designing processes that operate consistently and optimally over a variety of conditions. To determine the best design, it requires the use of a strategically designed experiment, which exposes the process to various levels of design parameters. Experimental design methods were developed in the early years of 20th century and have been extensively studied by statisticians since then, but they were not easy to use by practitioners (Phadke 1989). Taguchi's approach to design of experiments is easy to be adopted and applied for users with limited knowledge of statistics; hence it has gained a wide popularity in the engineering and scientific community. Taguchi specified three situations:
Larger the better (for example, agricultural yield); Smaller the better (for example, carbon dioxide emissions); and On-target, minimum-variation (for example, a mating part in an assembly).


P Diagram



Taguchi has used Signal-Noise (S/N) ratio as the quality characteristic of choice. S/N ratio is used as
measurable value instead of standard deviation due to the fact that, as the mean decreases, the
standard deviation also deceases and vice versa.
Contributions of Taguchi Methods:
Taguchi has made a very influential contribution to industrial statistics. Key elements of his quality
philosophy include the following:
Taguchi loss function (Ross 1996): used to measure financial loss to society resulting from poor
quality;
The philosophy of off-line quality control (Logothetis and Wynn 1989): designing products and
processes so that they are insensitive ("robust") to parameters outside the design engineer's control;
and Innovations in the statistical design of experiments: Atkinson, Donev, and Tobias, (2007), notably
the use of an outer array for factors that are uncontrollable in real life, but are systematically varied in
the experiment. Taguchi proposed a standard 8-step procedure for applying his method for
optimizing any process.
Taguchi's Rule for Manufacturing:
Taguchi realized that the best opportunity to eliminate variation is during the design of a product and
its manufacturing process. Consequently, he developed a strategy for quality engineering that can be
used in both contexts. The process has three stages:
I. System design
II. Parameter design
III. Tolerance design
System design
This is design at the conceptual level, involving creativity and innovation.
Parameter design
Once the concept is established, the nominal values of the various dimensions and design parameters
need to be set, the detail design phase of conventional engineering. This is sometimes called
robustification.
Tolerance design
With a successfully completed parameter design, and an understanding of the effect that the various
parameters have on performance, resources can be focused on reducing and controlling variation in the
critical few dimensions.

Eight-Steps in Taguchi Methodology:
Step-1: Identify the main function, side effects, and failure mode
Step-2: Identify the noise 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

Methodology Used: Taguchi Techniques
Dr. Taguchi's Signal-to-Noise ratios (S/N), which are log functions is 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 & desired output, serve as objective
functions for optimization, help in data analysis and prediction of optimum results.
Mathematical modeling:


ORTHOGONAL ARRAYS “(OAs) experiments
Using OAs significantly reduces the number of experimental configurations to be studied
Montgomery, (1991). The effect of many different parameters on the performance characteristic in a
process can be examined by using the orthogonal array experimental design proposed by Taguchi.
Once the parameters affecting a process that can be controlled have been determined, the levels at
which these parameters should be varied must be determined. Determining what levels of a variable
to test requires an in-depth understanding of the process, including the minimum, maximum, and
Shyam Kumar Karna & Rajeshwar Sahai
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current value of the parameter. If the difference between the minimum and maximum value of a
parameter is large, the values being tested can be further apart or more values can be tested. If the
range of a parameter is small, then less value can be tested or the values tested can be closer together.

The Taguchi method is a powerful tool for designing high quality systems. To increase the experimental efficiency, the L18 mixed orthogonal table in the Taguchi quality design. Ross (1988) is  used to determine the significant machining factors. In the experiments, we select six influential  machining parameters, such as cutting tools of different materials, depth of cut, cutting speed, feed  rate, working temperature and ultrasonic power, each of which has three different levels (high, medium and low levels).


Design of Experiment (Doe's) Requires Planning:
I. Design and Communicate the Objective:
II. Define the Process:
III. Select a Response and Measurement System:
IV. Ensure that the Measurement System is Adequate:
V. Select Factors to be studied:
VI. Select the Experimental Design:
VII. Set Factor Levels:
VIII. Final Design Considerations:
nalyzing and Examining Result:
(i) Determine the parameters signification (ANOVA)-Analysis of variance (Hafeez et.al 2002)
(ii) Conduct a main effect plot analysis to determine the optimal level of the control factors.
(iii) Execute a factor contribution rate analysis.
(iv) Confirm experiment and plan future application
Conclusion:
Taguchi started to develop new methods to optimize the process of engineering experimentation. He believed that the best way to improve quality was to design and build it into the product. He
developed the techniques which are now known as Taguchi Methods. His main contribution lies not in the mathematical formulation of the design of experiments, but rather in the accompanying philosophy. His concepts produced a unique and powerful quality improvement technique that
differs from traditional practices. He developed manufacturing systems that were “robust” or insensitive to daily and seasonal variations of environment, machine wear and other external factors.
The Taguchi approach to quality engineering places a great deal of emphasis on minimizing variation  as the main means of improving quality. The idea is to design products and processes whose performance is not affected by outside conditions and to build this in during the development and design stage through the use of experimental design. The method includes a set of tables that enable main variables and interactions to be investigated in a minimum number of trials. Taguchi Method uses the idea of Fundamental Functionality, which will facilitate people to identify the common goal because it will not change from case to case and can provide a robust standard for widely and frequently changing situations. It is also pointed out that the Taguchi Method is also very compatible with the human focused quality evaluation approach



(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] DYNAMIC PROBLEMS :
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 Log10 [ 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 Log10 [ mean of sum of squares 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 :
      -----------------------------------
                            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) Thickness should be uniform in deposition /growth /plating /etching..



[B] DYNAMIC PROBLEM  (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}:
     ----------------------------------


The slope of I/O characteristics should be at the specified value (usually 1). 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 Log10 [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 Log10 [square of slope or beta of the I/O characteristics]
 
(II) LINEARITY (LARGER-THE-BETTER) :
      -----------------------------------------------  
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 Log10 ----------------------------
                                     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) 8-STEPS  IN  TAGUCHI  METHODOLOGY :
     ---------------------------------------------------- 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  NOISE  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.  



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