What is DOE:

The successful and efficient running of any system or any

process largely depends on the fact that how it has been

designed. Before a system or any process is developed it

need to go through many experiments and a fruitful

experiment helps the system or process to be designed

successfully. So Design of Experiment (DOE) has a very

important role in development of any system or a process.

Contd.DOE is a systematic approach for investigation

of a system or process. A series of structured

tests are designed in which planned changes

are made to the input variables of a process or

system. The effects of these changes on a pre-

defined output are then assessed. DOE is

important as a formal way of maximizing

information gained while minimizing resources

required. It has more to offer than ‘one change

at a time’ experimental methods, because it

allows a judgment on the significance to the

output of input variables acting alone, as well

input variables acting in combination with one

another.

Contd.Designed experiments are carried out in four

phases: planning, screening (also called process

characterization), optimization, and verification.

Planning :

Careful planning helps to avoid problems that

can occur during the execution of the

experimental plan. For example, personnel,

equipment availability, funding, and the

mechanical aspects of the system may affect

the ability to complete the experiment. The

following are some of the steps that may be

necessary. i) Problem Definition, ii) Object

Definition, iii) Development of an experimental

plan that will provide meaningful information,

iv) Making sure the process and measured

systems are in control.

Contd.Screening:

In many process development and

manufacturing applications, potentially

influential variables are numerous. Screening

reduce the number of variables by identifying

the key variables that affect product quality.

This reduction allows process improvement

efforts to be focused on the rally important

variables, or the “vital few.” Screening may also

suggest the “best” or optimal settings for these

factors, and indicate whether or not curvature

exists in the responses. Then, it can use

optimization methods to determine the best

settings and define the nature of the curvature.

Two – level full and fractional factorial designs

are used extensively in industry.

Contd.Optimization:

Next step after identified the “vital few” by

screening, the “best” or optimal values for

these experimental factors needed to be

determine. Optimal factor values depend on the

process objective. For example, maximize the

welding speed and minimize the laser power.

Verification:

Verification involves performing a follow – up

experiment at the predicted “best” processing

conditions to confirm the optimization results.

Taguchi Design:

Dr. Genichi Taguchi is regarded as the foremost

proponent of robust parameter design, which is

an engineering method for product or process

design that focuses on minimizing variation

and/ or sensitivity to noise. When used

properly, Taguchi designs provide a powerful

and efficient method for designing products

that operate consistently and optimally over a

variety of conditions. In robust parameter

design, the primary goal is to find factor

settings that minimize response variation, while

adjusting (or keeping) the process on target.

The fundamental Terms Used in Taguchi Design:

Orthogonal arrays: The taguchi method

utilizes orthogonal arrays from design of

experiments theory to study a large number of

variables with a small number of experiments.

Using orthogonal arrays significantly reduces

the number of experimental configurations to

be studied. Furthermore, the conclusions drawn

from small scale experiments are valid over the

entire experimental region spanned by the

control factors and their settings.

Orthogonal arrays are not unique to Taguchi.

They were discovered considerably earlier.

However, Taguchi has simplified their use by

providing tabulated sets of standard orthogonal

arrays and corresponding linear graphs to fit

specific projects.

Examples of standard orthogonal arrays:

L-4, L-8, L-12, L-16, L-32 and L-64 all at 2 levels

L-9, L-18 and L-27 at 3 & 2

levels

L-16 and L-32 modified at

4 levels

L-25 at 5 levels

Contd.

Table: 1Typical L16 orthogonal array with coded value:Std Run Factor

1Factor2

Factor3

Factor4

Factor5

Response1

1 1 1 1 1 1 1  6 2 2 2 1 4 3  8 3 2 4 3 2 1  2 4 1 2 2 2 2  5 5 2 1 2 3 4  4 6 1 4 4 4 4  10 7 3 2 4 3 1  15 8 4 3 2 4 1  16 9 4 4 1 3 2  14 10 4 2 3 1 4  13 11 4 1 4 2 3  7 12 2 3 4 1 2  12 13 3 4 2 1 3  11 14 3 3 1 2 4  3 15 1 3 3 3 3  9 16 3 1 3 4 2  

Table: 2Typical L18 orthogonal array with coded value:  Control Factors

Expt. No.

A B C D E F G H

1 1 1 1 1 1 1 1 12 1 1 2 2 2 2 2 23 1 1 3 3 3 3 3 34 1 2 1 1 2 2 3 35 1 2 2 2 3 3 1 16 1 2 3 3 1 1 2 27 1 3 1 2 1 3 2 38 1 3 2 3 2 1 3 19 1 3 3 1 3 2 1 210 2 1 1 3 3 2 2 111 2 1 2 1 1 3 3 212 2 1 3 2 2 1 1 313 2 2 1 2 3 1 3 214 2 2 2 3 1 2 1 315 2 2 3 1 2 3 2 116 2 3 1 3 2 3 1 217 2 3 2 1 3 1 2 318 2 3 3 2 1 2 3 1

S/N rations and MSD analysis: Taguchi

recommends the use of signal to noise (S/N) as

opposed to simple process optimizing process

parameters. The rationale is that while there is

a need to maximizing the mean (signal) in the

sense of its proximity to nominal value, it is also

desirable to minimize the process variations

(noise). The use of S/N accomplishes both

objectives simultaneously.

Contd.

In order to evaluate the influence of each

selected factor on the responses, the S/N for

each control factor should be calculated. The

signals have indicated that the effect on the

average responses, which would indicate the

sensitiveness of the experiment output to the

noise factors. The appropriate S/N ratio must be

chosen using previous knowledge, expertise,

absent signal factor (Static design), it is

possible to choose the S/N ratio depending on

the goal of the design. S/N ratio selection is

based on Mean Squared Deviation (MSD) for

analysis of repeated results. MSD expression

combines variation around the given target and

is consistent with Taguchi’s quality objective.

Contd.

The relationships among observed results, MSD and S/N rations are follows (1 to 4):For nominal is better--(1)

For smaller is better

For bigger is better

For all characteristicS/N = - 10Log (MSD) ------------------------------------------(4)

Contd.

Analysis of variance (Anova): Analysis of

variance (analysis of variance) is a general

method for studying sampled – data

relationships. The method enables the

difference between two or more sample means

to be analyzed, achieved by subdividing the

total sum of squares. One way Anova is the

simplest case. The purpose is to test for

significant differences between class means,

and this is done by analyzing the variances.

Contd.

Analysis of variance (Anova) is similar to

regression in that it is used to investigate and

model the relationship between a response

variable and one or more independent

variables. In effect, analysis of variance extends

the two sample t – test for testing the equality

of two population means to a more general null

hypothesis of comparing the equality of more

than two means, versus those that are not all

equal. Table 3 is a sample of the Anova table

used for analysis of the models developed in

this work. Sum of squares and mean square

errors are calculated using Eq. 5 to 8.

Contd.

Contd.

Table 3: Sample Anova table for a model:

Source SS df MS FV – Value Prob.>Fv

Model SSM p Each SS Divided by Its df

Each MS Divided by MSE

From Table or automatically from the software

P SSI  

S SS2  

F SS3  

PS SS12  

PF SS13  

SF SS23  

P2 SS11  

S2 SS22  

F2 SS33  

Residual SSE n – p – 1    

Cor. Total

SSt n – l - - -

Where,

p : Number of coefficients in the model.

df : Degree of freedom,

SS : Sum of squares,

MS : Mean squares,

n: Total number of runs

Cor. Total : Sum of squares total corrected for

the mean.

Contd.

Optimization:

The optimization will allow the industrial user to

achieve the optimum welding composition and

process parameter to achieve the desired weld

pool shape and mechanical properties. All

independent variables are measurable and can

be repeated with negligible error. The objective

function can be represented by :

Objective = f (x1, x2, …………… , xn)

----------------(9)

Where : n is number of independent variables.

Fig 1: Classification of modeling and optimization techniques:

Optimizing tools and techniques

Conventional techniques (Optimal Solution) Non - Conventional techniques [Near Optimal Solution(s)]

Design of Experiment (DOE) Mathematical Iterative search Meta Heuristic Search Problem specific Heuristic Search

Dynamic Programming (DP) – based algorithm

Non – linear Programming (NLP) – based algorithm

Linear Programming (LP) – based algorithm

Genetic algorithm

Simulated Annealing

Tabu Search

Taguchi Method - Based

Factorial Design based

Response surface Design Methodology (RSM) - based

Grey System Theory:

The multi-criteria decision-making problem

must be determined not with the exact criteria

values, but with fuzzy values or with values

taken from some intervals. Deng (1982)

developed the Grey system theory. According to

him, the Grey relational analysis has some

advantages: it involves simple calculations and

required a smaller number of samples; a typical

distribution of samples is not needed; the

quantified outcomes from the Grey relational

grade do not result in contradictory conclusions

from the qualitative analysis; the Grey

relational grade model is a transfer functional

model that is effective in dealing with

discreate4 data (Deng 1988).

The Meaning of ‘Grey’ in Grey System:

The cognition of our natural and/or artificial

universe has been a tedious and a progressive

process. The formulations of natural and

artificial laws are certainly not overnight

happenings. Nature to us is not white (full of

precise information), but on the other hand, it is

not black (completely lack of information)

either, and it is mostly grey (a mixture of black

and white). Our thinking, no matter how

analytical, is grey. While our action and

reaction, no matter how practical, is also grey.

In fact, since the beginning of our existence, we

are confined in a high dimensional grey

information relational space.

Grey Relational Model:

Existence of Grey Relation: Objective

observation of many existing systems shows

they consist of a number of subsystems, and

the relations between these subsystems are

extremely complex. In particular, the different

states of appearances and the randomness of

changes (chaotic system), cause great

confusion in the cognition of the true nature of

the systems. But the very essence of grey

system theory is to provide an analytic concept

of the grey relational degree of these

subsystems. Here the central methodology is to

seek out the relations (including the numerical

relations) between subsyste3ms and sub

causalities.

Contd.

We find, in the course of grey systems research,

that if the basic states of causal changes of two

subsystems are similar, their synchronized

degree of changes is high, and hence their grey

relational grade is high; otherwise their grey

relational grade is low. Therefore, we can

provide a quantitative measure in grey

relational analysis of systems during the course

of its dynamic. There are differences between

grey relational analysis and the regression

analysis of statistics. In that:

Contd.

1. They are different in their theoretical

foundations. Grey relational analysis is

based on the grey process of the grey

system theory, whereas regression analysis

is based on the random process of the

probability theory;

2. Grey relational analysis compares and

computes the dynamic causalities of the

subsystems of the given system, whereas

regression analysis focuses on the grouped

values of the random variables;

Contd.

3. Grey relational analysis requires very

minimal raw data (as few as 4 in cardinality),

whereas regression analysis require

sufficiently large set of sample data; and

4. Grey relational analysis mainly investigates

and dynamic process of the system, whereas

regression analysis mainly studies the static

behavior of the system.

Contd.

Grey Relational Numerical Method :

I. The Processing of Primitive Data

The physical meanings of the causal elements

in a system could be different. As a result there

are differences in the system’s data index

(catalog), and during the process of analytic

comparison, we find difficulty in reaching a

proper are correct conclusion. Therefore, we

use:

.

Contd.1. Mean value processing. We first compute the

mean values of all the primitive sequences

x1, X2,…-, Xp (data space of the dynamic).

Then we use these mean values to divide

values of the corresponding sequences to

obtain a collection of new sequences, which

is now called the mean valued sequences –

Xi, X2,….., Xp.

2. Initial value processing. We use the first

value of each sequence to divide each

succeeding value of the corresponding

sequence to form a collection of quotient

sequences, which are now called the

initialized sequences, Xi, X2,…., Xp.

Contd.In general when analyzing the dynamic process

of certain stable socio-economic systems, we

often employ this initial valued process.

Contd.

Contd.

Contd.

Contd.

Contd.

Contd.

Contd.

Contd.

References:

1. T. Muthuramalingama, B. Mohanb, “Application of Taguchi-grey multi responses optimization on process parameters in electro erosion”, Volume 58, December 2014, Pages 495–502

2. Mihir Patel, Vivek Deshpande, “Application of Taguchi Approach for Optimization Roughness for Boring operation of E 250 B0 for Standard IS: 2062 on CNC TC”, IJEDR | Volume 2, Issue 2 | ISSN: 2321-9939

3. Kaining Shi, Dinghua Zhang, Junxue Ren, Changfeng Yao and Yuan Yuan, “Multiobjective Optimization of Surface Integrity in Milling TB6 Alloy Based on Taguchi-Grey Relational Analysis”, Advances in Mechanical Engineering, Volume 2014, Article ID 280313, 7 pages.

Contd..

4. Raghuraman S, Thiruppathi K, Panneerselvam T and Santosh S, “OPTIMIZATION OF EDM PARAMETERS USING TAGUCHI METHOD AND GREY RELATIONAL ANALYSIS FOR MILD STEEL IS 2026”, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 2, Issue 7, July 2013

5. Ajeet Kumar rai, Shalini yadav Richa Dubey and Vivek Sachan, “Application of Taguchi Method in the Optimization of Boring Parameters”, International Journal of Advanced Research in Engineering and Technology, Volume 4, Issue 4, May – June 2013, pp. 191-199

6. B.Shivapragash, K.Chandrasekaran, C.Parthasarathy and M.Samuel, “Multiple Response Optimizations in Drilling Using Taguchi and Grey Relational Analysis”, International Journal of Modern Engineering Research (IJMER), Vol.3, Issue.2, March-April. 2013 pp-765-768.

Contd..

4. Raghuraman S, Thiruppathi K, Panneerselvam T and Santosh S, “OPTIMIZATION OF EDM PARAMETERS USING TAGUCHI METHOD AND GREY RELATIONAL ANALYSIS FOR MILD STEEL IS 2026”, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 2, Issue 7, July 2013

5. Ajeet Kumar rai, Shalini yadav Richa Dubey and Vivek Sachan, “Application of Taguchi Method in the Optimization of Boring Parameters”, International Journal of Advanced Research in Engineering and Technology, Volume 4, Issue 4, May – June 2013, pp. 191-199

6. B.Shivapragash, K.Chandrasekaran, C.Parthasarathy and M.Samuel, “Multiple Response Optimizations in Drilling Using Taguchi and Grey Relational Analysis”, International Journal of Modern Engineering Research (IJMER), Vol.3, Issue.2, March-April. 2013 pp-765-768.

Contd..

7. Reddy Sreenivasulu and Dr. Ch. Srinivas Rao, “Application of Grey Relational Analysis for Surface Roughness and Roughness Error in Driling of Al 6061 Alloy”, International Journal of Lean Thinking, Volume 3, Issue 2.

8. Hartaj Singh, “TAGUCHI OPTIMIZATION OF PROCESS PARAMETERS: A REVIEW AND CASE STUDY”, International Journal of Advanced Engineering Research and Studies, E-ISSN2249–8974.

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