1. INTRODUCTION

Most experiments seek to maximize the response or yield of a certain

characteristics. Taguchi recommends the use of a three-stage process to achieve the

desirable product quality by design, three stages being system design, parameter design

and tolerance design. Parameter design can be regarded as a flexible alternative to the

classical fractional factorial design and is now a widely –used empirical approach in

various industries. It is used to design a product or process by selecting the optimum

condition of the parameter levels so that the product or process is least sensitive to the

effects of noise factors.

There are three types of factors are encountered when using the taguchi methods,

these being signal factors, control factors, and noise factors. Signal factors are the factors

that affect the average response. Control factors are factors that can also affect the

average response but, more importantly, can affect the extent of the variability about the

average response. It is set by the manufacturer and cannot be changed by the customer.

Noise factors that have an influence over a response but cannot be controlled in actual

applications. Manufacturer does not have direct control it can vary with the customer’s

environment and usage. Three types of noise factors are in usage outer noise, inner noise,

and product noise. Outer noise, which are caused by environmental conditions such as

humidity, temperature, pressure, operator skills etc. Inner noise: produces variation from

inside or within the product such as wear, fade of color, shrinkage etc. Product noise it is

part to part variation on the product itself such as tool wear, measuring equipments etc...

The strategy of using the taguchi method is to identify the control factors and

noise factors that may affect the response of the chosen quality characteristic, and then

utilize a suitable array (OA) to layout the experiment. In this way it is possible to

evaluate several factors simultaneously from a minimum number of tests. Although there

may be a number of approaches and techniques were used, complication and limitations

exist that improvements can be further need to solve the multi-response variables. In

this study an effective way for solving the multiresponse problem by modified MRSN

techniques were studied. This approach brings certainly good results when we compared

with the existing ones.

2. LITERATURE SURVEY

Tara man (1974) investigates multi machining output, multi independent variable

turning research by response surface methodology. The purpose of this research was to

develop a methodology which would allow determination of the cutting conditions

(cutting speed, feed rate and depth of cut) such that specified criterion for each of the

several machining dependent parameters such as (surface finish, tool force and tool life –

TL) could be achieved simultaneously. Derringer and Suich (1980) made use of modified

desirability functions, which measure the designer’s desirability over a range of response

values. They have utilized the modified desirability function approach for the

development of a tyre tread compound, which involves four responses (abrasion index,

modulus, elongation at break and hardness) and three independent variables.

Byrne and Taguchi (1987) illustrate a case of the optimization of two quality

characteristics: the force required to insert the tube into the connector and the pull off

force. The selected quality characteristics were independently optimized using Taguchi

approach and then the results were compared subjectively to select the best levels in

terms of the quality characteristics of interest.

Kacker (1985) and Leon etal, (1987) in this approach the process parameters are

divided into two groups: those which affect mean and variability, and those which affect

only mean. The PerMIA approach looks for a transformation of the response variables

such that the standard deviation of the transformed output becomes independent of the

mean. Then a two step optimization is performed by initially working with the first group

and afterwards working with the second group. Bryne and Taguchi, (1986); Phadke,

(1989), The S/N ratio developed by Dr. Taguchi is a performance measure to choose

control levels that best cope with noise. Hence noise factors are difficult to control in real

time applications. The S/N ratio takes both the mean and the variability into account. In

its simplest form, the S/N ratio is the ratio of the mean (signal) to the standard deviation

(noise). The S/N equation depends on the criterion for the quality characteristic to be

optimized. Phadke (1989) presents a case of products with multiple characteristics such

as surface defects and thickness in his example of polysilicon deposition. In order to

estimate the loss caused by quality characteristics, he assigned a weight from experience

to each quality characteristic.

Roy (1990) proposed a simple and pure engineering methodology for the

optimization of multiple responses. The methodology is called Overall Evaluation

Criteria (OEC) and the approach involves a high degree of subjectivity as the relative

weights of responses vary from one company to another. This certainty brings some risk

to the calculations of OEC and therefore is not widely accepted in industrial experiments.

Hatzis and Larntz (1992) constructed locally D-optimal designs for a nonlinear

multiresponse model describing the behavior of a biological system. Delcastillo and

Montgomery (1993) A more general approach that can be used is to formulate a multiple

response problem as a constrained optimization problem. This is done by selecting one of

the responses as the objective function and treating the other responses as constraints.

Elsayed and Chen (1993) present a model using loss function approach to determine the

optimal settings of the process parameters of the production process for products with

multiple characteristics. Derringer (1994) has used a balancing act optimizing product

properties for the abrasion resistance of a rubber shoe sole formulation by adding certain

fillers.

Young-Jou Lai and Shing I Chang, (1994) Multiresponse optimization techniques

are used to identity settings of process parameters that make the product's performance

close to target values in the presence of multiple quality characteristics. In this study, a

fuzzy multiresponse optimization procedure is proposed to search an appropriate

combination of process parameter settings based on multiple quality characteristics or

responses. Osyczka and Kundu (1995) used genetic algorithms with a combined fitness

function to achieve a multiple response optimum. Young-Jou Lai (1995) multiresponse

quality design techniques are used to identify settings of process parameters that make

the product's performance close to target values in the presence of multiple quality

characteristics. Del Castillo etal.,(1996)).The desirability methods are easy to

understand and implement, available in software , and provide flexibility in weighting

individual responses. Leeing tong (1996) normalized quality loss for all the items as to

be checked, which is time consuming and weights assigned to response varies from

company to company and from person to person.

Sunk.H.Park (1996) has used graphical superimposition for optimizing multi-

response problem is difficult to apply when the number of input variables exceeds three.

Tong et al. (1997) propose a procedure on the basis of the quality loss of each response so

as to achieve the optimization on multi-response problems in the taguchi method.The

procedure is a universal approach which can simultaneously deal with continuous and

discrete data. A plasma-enhanced chemical vapor deposition process experiment was

evaluated to prove that the proposed procedure yields a satisfactory result. Su and Tong

(1997) propose an effective procedure on the basis of principal component analysis

(PCA) to optimize the multi-response problems in the taguchi method. With the PCA, a

set of original responses can be transformed into a set of uncorrelated components. Tong

and Su (1997) also illustrated a rather interesting way of treating the multi-response

problems by using fuzzy attribute decision-making. This method defines the

optimization process as a decision making process in which decision goals and

constraints are represented by fuzzy sets.

Reddy et al. (1997) present an approach to optimize multi responses

simultaneously using goal programming in conjunction with Taguchi’s robust design

methodology. A case study for optimizing an injection moulding process is first carried

out using Taguchi’s robust design methodology. The optimization study revealed that the

optimum conditions obtained for one response are not completely compatible with those

of other responses. So trade offs were made in selection of levels for factors using

engineering judgment which increased the uncertainty in the decision-making process.

The further optimization study on the injection moulding process revealed that the

optimum conditions obtained using goal programming in conjunction with Taguchi’s

methodology have better goal attainment properties compared to robust design.

Reddy.P.B.S. & Nishina (1998), they practiced engineer’s judgement method that

will often bring some degree of uncertainty and therefore, validity of the results cannot be

guaranteed. Tsui (1999) investigated the response surface model (RSM) approach and

compared it to the Taguchi method for a dynamic robust design. Prasun Das (1999), The

desirability function technique has been a proven tool for multiresponse optimization

problems. Y. H. Chen (1999) in data analysis, signal-to-noise (S/N) ratios are used to

allow the control of the response as well as to reduce the variability about the response.

Prasun Das (1999) & Paterahis (2002) used full factorial experiment for their

studies, it increases experimental trials. This method does not enable the simultaneous

optimization of the means and variances of the multiple quality characteristics. Tarang et

al. (2000) report the use of fuzzy logic in the taguchi method to optimize the submerged

arc welding process with multiple performance characteristics. An orthogonal array

(OA), the signal-to-noise ratio, multi response performance index and analysis of

variance (ANOVA) are employed to study the performance characteristics in the

submerged arc welding process. The process parameters, namely arc current, arc voltage,

welding speed, electrode protrusion, and preheat temperature are optimized with

considerations of the performance characteristics, including deposition rate and dilution.

Experimental results confirm the effectiveness of the approach for optimizing multi-

machining characteristics. Antony (2000) presents a case study for optimizing multi-

responses in industrial experiments using Taguchi’s quality loss function in conjunction

with PCA.

D.Rajkumar & etal, (2000) in his study the S/N ratio is measured in unit decibels

(db). Higher S/N ratio is preferred because a high value of S/N implies that the signal is

much higher than the uncontrollable noise factors such temperature, humidity and

consistency in measurement of data.

Antony (2001) has developed a simple and practical step-by-step approach for

tackling multiple response or quality characteristic problems in Taguchi’s parameter

design experiments. The methodology uses the Taguchi’s quality loss function for

identifying the significant factor/interaction effects and also for determining the optimal

condition of the process. In order to demonstrate the potential of the proposed

methodology, a simple case study was carried out for optimizing three quality

characteristics, namely solder paste mass, solder paste height, and glue torque, for a

double-sided surface mounting technology electronic assembly operation. Six

controllable factors and one interaction effect were studied using an L8 OA experiment

advocated by Taguchi.

Paterakis.P.G.(2002) has used the desirability function for multi-response

optimization problem for multi variables. In this approach full factorial design is used to

complete the results, it increases the experimental trials. Myers and Montgomery (2002)

an explanation of the graphical approach can be found in this is method has clear

disadvantages, since it does not provide exact answers and, even for relatively small

dimensional problem, can be quite difficult to analyze. Dawel Lu and Jiju Antony (2002)

have used fuzzy-rule based inference system. It integrates with taugchi loss function, it

increase the complexity of the computational process and is not readily understood by

engineers with limited knowledge in mathematical skills.

Y. Vander Heyden & etal (2002), In this paper, the use of parallel co-ordinate

geometry (PCG) plots, principal component analysis (PCA) and N-way PCA as

visualization procedures for large multi-response experimental designs was compared

with the more traditional approach of calculating factor effects by multiple linear

regression. Lu and Antony (2002) present a robust and practical approach which takes

advantage of both the Taguchi method and a fuzzy-rule based inference system. A case

study illustrates the potential of this powerful integrated approach for tackling multiple

response optimization problems. The variance analysis used in the study identifies the

most critical and statistically significant parameters. Liao (2003) proposes an effective

procedure called PCR-TOPSIS that is based on process capability ratio theory and on the

theory of order preference by similarity to the ideal solution (TOPSIS) to optimize multi-

response problems. Using PCR-TOPSIS, multiple responses in each experiment are

transformed into a performance index and the optimal factors/levels combinations for the

multi-responses can thus be determined. M.N. Dhavlikar,(2003) This paper presents a

successful application of combined Taguchi and dual response methodology to determine

robust condition for minimization of out of roundness error of workpieces for centerless

grinding operation. From the confirmation runs, it was observed that this approach led to

successful identification of optimum process parameter values.

T.S. Li & etal, (2003) This study proposes a desirability function to solve multi-

response optimization problems. When the multi-response problem is transformed into a

single response problem, the single-response problem is divided into two problems: how

to specify the weights and how to transform each response into a more ‘‘desirable’’

response. In-Jun Jeong (2003), A common problem encountered in product or process

design is the selection of optimal parameters that involves simultaneous consideration of

multi-response characteristics, called a multi-response surface (MRS) problem. The

existing MRO approaches require that all the preference information of a decision maker

be articulated prior to solving the problem.

J.A.Ghani et al (2004) used an orthogonal array, S/N ratio and pareto ANOVA to

analyze the effect of these milling parameters. Hung-Chang Liao (2004) proposes an

effective procedure on the basis of the neural network (NN) and the data envelopment

analysis (DEA) to optimize the multi-response problems. Chih-Ming Hsu,(2004),This

study presents an integrated optimization approach based on neural networks, exponential

desirability functions and tabu search to optimize this complicated problem. The

proposed approach identi.es input control factor settings that maximize the overall

minimal satisfaction with all of the responses. P. Narender Singh & etal, (2004)

Optimization of process parameters is the key step in the Taguchi methods to achieve

high quality without cost inflation. Optimization of multiple response characteristics is

more complex compared to optimization of single performance characteristics. The

multi-response optimization of the process parameters viz., metal removal rate (MRR),

tool wear rate (TWR), taper (T), radial overcut (ROC), and surface roughness (SR) on

electric discharge machining (EDM) of Al–10%SiCP as cast metal matrix composites

using orthogonal array (OA) with Grey relational analysis is reported.

Kun-Lin Hsieh et al., (2005), This study proposes a procedure utilizing the

statistic regression analysis and desirability function to optimize the multi-response

problem with Taguchi’s dynamic system consideration. Firstly, the regression analysis is

employed to screen out the control factors significantly affecting the quality variation,

and the adjustment factors significantly affecting the sensitivity of a Taguchi’s dynamic

system. TahoYang(2005), the multiresponse simulation-optimization problem by a

multiple-attribute decision-making method - a technique for order preference by

similarity to ideal solution (TOPSIS). The method assumes that the control factors have

discrete values and that each control factor has exactly three control levels. Taguchi

quality-loss functions are adapted to model the factor mean and variance effects.

J.L. Lin, C.L. Lin (2005) In this paper, the use of the grey-fuzzy logic based on

orthogonal array for optimizing the electrical discharge machining process with multi-

response has been reported. An orthogonal array, grey relational generating, grey

relational coefficient, grey-fuzzy reasoning grade and analysis of variance are applied to

study the performance characteristics of the machining process. Istadi etal, (2005)The

paper deduced that both individual- and multi-responses optimizations are useful for the

recommendation of optimal process parameters and catalyst compositions for the CO2-

OCM process.

Hari Singh et al.,(2006) Optimizing multi-machining characteristics through

Taguchi’s approach and utility concept. The multi-machining characteristics have been

optimized simultaneously using Taguchi’s parameter design approach and the utility

concept. The paper used a single performance index, utility value, as a combined

response indicator of several responses. Ramakrishnan, et al (2006) in this study

optimization of WEDM operations using Taguchi’s robust design methodology with

multiple performance characteristics is proposed. In order to optimize the multiple

performance characteristics, Taguchi parametric design approach was not applied

directly. Since each performance characteristic may not have the same measurement unit

and of the same category in the S/N ratio analysis.

3. TAGUCHI’S SIGNAL TO NOISE (S/N) RATIO TECHNIQUE

When replicated experiments are performed, the analysis often includes the

transformation of the results into a signal-to-noise ratio (S/N).Then helps to identify the

optimum conditions of operation that would also induce the least variability produced by

the controllable as well as the uncontrollable factors. From the quality point of view,

there are three categories of quality characteristics in the measurement of S/N, these being

the Lower-the-better (LB), Nominal-the-best (NB), and the Higher-the-better (HB)

characteristics.Taguchi recommends analyzing the means and S/N ratio using conceptual

approach that involves graphing the effects and visually identifying the factors that

appears to be significant, without using ANOVA, thus making the analysis simple.In

general, the major steps in the application of Taguchi's parameter design are shown below

(Insert Fig. 1 The seven steps for conducting the experiment using Taguchi Method)

The results of the experiments are analyzed to achieve three objectives : (i) to

establish the best or the optimum condition for a product or a process; (ii) to estimate the

contribution of individual factors; and (iii) to estimate the response under the optimum

conditions.

4. POSSIBLE WAYS FOR SOLVING MULTI RESPONSE OPTIMIZATION

PROBLEM

When the multi-response problem is transformed into a single response problem,

the problem may be comes under any one of the category. One popular approach to

multiresponse optimization has been the use of a dimensionality reduction strategy. This

strategy converts a multiresponse problem into one with a single aggregate measure, and

solves it as a single objective optimization problem. The single aggregate measure has

often been defined as a desirability function or a loss function. The following methods

can be adopted for solving the multiresponse optimization.

• Quality loss function

• Desirability function technique

• Central composite design matrix

• JMP software

• Fuzzy logic and Neural network technique

• Non constrained optimization techniques like Genetic algorithm (GA), Simulated

annealing (SA)

• Loss function using principal component analysis (PCA)

• Utility model.

5. PROPOSED OPTIMIZATION TECHNIQUE FOR SOLVING MULTI-

RESPONSE VARIABLES

Applying the Taguchi method to optimize multi-response processes includes the

following considerations:

The attribute and loss functions in the multiple cases are always different for each

response. Therefore, the loss for each response cannot be compared and summed

directly.

The measurement units in the multiple cases are always different for each

response. Therefore, the loss caused by each unit for each response could be

different.

The importance in the multiple cases could be different for each response.

The adjustment factors should be chosen when the nominal-the-best quality

characteristics exist in multi-response cases.

This is especially true when one such factor is used to adjust the mean on target

and a significant change occurs in the values of other quality characteristics.

To solve the four problems mentioned above, an optimization procedure is

proposed in this section. An effective method capable of determining the multi

response signal to noise (MRSN) ratio is developed here through the integration of

quality loss for all responses with the application of Taguchi’s(1990) SN ratios.

1. The S/N ratio for loss function is given by S/N = 10log10 (Y2/ S2).Where, Y is

the average response and S2 is the variance of the response over various

experimental samples of design.

2. Reducing the variability first requires normalizing the scale of the quality loss of

each response. For each response, the quality loss at each trial is divided here by

the maximum quality loss in the j trials. Accordingly, the largest normalized value

is 1. The smaller the normalized value implies the smaller the quality loss.

3. Thus, the normalized quality loss ranges between 0 and 1. Therefore, the quality

loss for each response can be summed directly.

4. Second, an appropriate weight is assigned to each response for computing the

total normalized quality loss in each trial.

5. Transformed the experimental data into signal-to-noise ratios (η) is defined by

taguchi quadratic loss function method.

6. Normalized the S/N ratio of each objective based on the following formula.

ή = η i - η i min , i = 1, 2 …n.............................. (1) ηi max – ηi min

The responses of normalized S/N ratios are tabulated

7. Obtained the multiple response S/N ratios (MRSN) of each experiment by the

following definition and given by

n MRSN = ∑ Wi * ήi ……………………………………. (2) i=1

Where, Wi is the weight assigned to the ith objective and indicates the relative

importance of that objective. The optimal weight ratio of each experiment was obtained

by the following procedure.

Each response of the experiment was treated as a control factor and an appropriate

orthogonal array was selected as the weight matrix of the experiment. The proposed

procedure universally applicable to any type of multi-response problem and can

simultaneously deal with the continuous and discrete data types.

6. DISCUSSION

The desirability method was not primarily used due to mathematical complexity

of the approach; it cannot be easily or rapidly understood by the engineering community.

The PerMIA approach requires some specific prior knowledge about which factors

belong to the first group and which belong to the second. Also a convenient

transformation of the response variables may be difficult, if not impossible to define.

The Overall Evaluation Criteria (OEC) approach involves a high degree of

subjectivity as the relative weights of responses vary from one company to another. The

certainty brings some risk to the calculations of OEC and therefore is not widely accepted

in industrial experiments. Choosing which one of the responses be the objective function

may be difficult in some cases, in particular when the number of responses is large.

In quality loss function for all the items as to be checked, which is time

consuming and weights assigned to response varies from company to company and from

person to person. The approach is able to eliminate the uncertainty and subjectivity in the

decision-making process.

Fuzzy-rule based inference system illustrates the potential of this powerful

integrated approach for tackling multiple response optimization problems. It increases the

complexity of the computational process and is therefore not readily understood by

engineers with limited mathematical skills. The utility model can be extended to any

number of quality characteristics provided proper utility scales for the characteristics are

available from the realistic data. Therefore for solving the multiresponse variables

required a simple procedure in order to overcome the above difficulties.

7. CONCLUSION

Solving multi-response parameters simultaneously is a difficult task when one or

more responses involved in practical applications. There is a need for solving such

problems by a different approach. Based on the several studies it is found that the

complexity and difficulties are more especially when we deal with multiple responses

variables to be solved. Hence an attempt has been made for solving such multi-response

variables by modified simple MRSN techniques. A solution shows the best results when

it applies for practical applications.

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