Intelligent Information Management, 2010, 2, 26-39
doi:10.4236/iim.2010.21004 Published Online January 2010 (http://www.scirp.org/journal/iim)
Copyright © 2010 SciRes IIM
Simultaneous Optimization of Correlated Multiple Surface
Quality Characteristics of Mild Steel Turned Product
Saurav DATTA, Siba Sankar MAHAPATRA
Department of Mechanical Engineering, National Institute of Technology, Rourkela, India
Email: sdattaju@gmail.com, mahapatrass20 03@yahoo.com
Abstract
Present work highlights application of utility theory combined with Principal Component Analysis (PCA)
and Taguchi’s robust design for simultaneous optimization of correlated multiple surface quality characteris-
tics of mild steel machined product prepared by straight turning operation. The study aims at evaluating the
most favorable process environment followed by an optimal parametric combination for achieving high sur-
face quality. Traditional Taguchi based hybrid optimization approaches rely on the assumption that quality
indices are uncorrelated or independent. But it is felt that, in practice, there may be some correlation among
various quality indices (responses) under consideration. To overcome this limitation of Taguchi approach, the
present study proposes application of PCA to convert correlated responses into uncorrelated quality indices
called principal components. Finally based on utility theory, Taguchi method has been applied to solve this
optimization problem. The study demonstrates detailed methodology and concludes robustness and flexibil-
ity of the proposed optimization technique and validates its effectiveness through a case study in which cor-
related multiple response characteristics of turning operation have been optimized.
Keywords: utility theory, principal component analysis, Taguchi’s robust design, straight turning
1. Introduction
Literature depicts that a considerable amount of work has
been carried out by previous investigators for modeling,
simulation and parametric optimization of surface prop-
erties of the product in turning operation. Apart from
optimizing a single response (process output), multi-
objective optimization problems have also been solved
using Taguchi method followed by grey relation theory.
Lin et al. [1] adopted an abdicative network to con-
struct a prediction model for surface roughness and cut-
ting force. Feng and Wang [2] investigated for the pre-
diction of surface roughness in finish turning operation
by developing an empirical model through considering
working parameters: work piece hardness (material),
feed, cutting tool point angle, depth of cut, spindle speed,
and cutting time. Data mining techniques, nonlinear re-
gression analysis with logarithmic data transformation
were employed for developing the empirical model to
predict the surface roughness.
Suresh et al. [3] focused on machining mild steel by
TiN-coated tungsten carbide (CNMG) cutting tools for
developing a surface roughness prediction model by us-
ing Response Surface Methodology (RSM). Genetic
Algorithms (GA) used to optimize the objective function
and compared with RSM results. Kirby et al. [4] devel-
oped the prediction model for surface roughness in turn-
ing operation. Őzel and Karpat [5] studied for prediction
of surface roughness and tool flank wear by utilizing the
neural network model in comparison with regression
model. Kohli and Dixit [6] proposed a neural-network-
based methodology with the acceleration of the radial
vibration of the tool holder as feedback. For the surface
roughness prediction in turning process the back-propa-
gation algorithm was used for training the network
model. Pal and Chakraborty [7] studied on development
of a back propagation neural network model for predic-
tion of surface roughness in turning operation and used
mild steel work-pieces with high speed steel as the cut-
ting tool for performing a large number of experiments.
Ahmed [8] developed the methodology required for ob-
taining optimal process parameters for prediction of sur-
face roughness in Al turning. Abburi and Dixit [9] de-
veloped a knowledge-based system for the prediction of
surface roughness in turning process. Fuzzy set theory
and neural networks were utilized for this purpose.
Zhong et al. [10] predicted the surface roughness of
turned surfaces using networks with seven inputs namely
S. DATTA ET AL. 27
tool insert grade, work piece material, tool nose radius,
rake angle, depth of cut, spindle rate, and feed rate.
Doniavi et al. [11] used response surface methodology
(RSM) in order to develop empirical model for the pre-
diction of surface roughness by deciding the optimum
cutting condition in turning.
Kassab and Khoshnaw [12] examined the correlation
between surface roughness and cutting tool vibration for
turning operation. Al-Ahmari [13] developed empirical
models for tool life, surface roughness and cutting force
for turning operation. The methods used for developing
aforesaid models were Response Surface Methodology
(RSM) and neural networks (NN).
Thamizhmanii et al. [14] applied Taguchi method for
finding out the optimal value of surface roughness under
optimum cutting condition in turning SCM 440 alloy
steel. Wang and Lan [15] used Orthogonal Array of Ta-
guchi method coupled with grey relational analysis con-
sidering four parameters viz. speed, cutting depth, feed
rate, tool nose run off etc. for optimizing three responses:
surface roughness, tool wear and material removal rate in
precision turning on an ECOCA-3807 CNC Lathe. Sa-
hoo et al. [16] studied for optimization of machining
parameters combinations emphasizing on fractal charac-
teristics of surface profile generated in CNC turning op-
eration using Taguchi’s Orthogonal Array design. Reddy
et al. [17] adopted multiple regression model and artifi-
cial neural network to deal with surface roughness pre-
diction model for machining of aluminium alloys by
CNC turning. Lan et al. [18] considered four cutting pa-
rameters: speed, feed, depth of cut, and nose runoff var-
ied in three levels for predicting the surface roughness of
CNC turned product. Thamma [19] constructed the re-
gression model to find out the optimal combination of
process parameters in turning operation for Aluminium
6061 work pieces. The study highlighted that cutting
speed, feed rate, and nose radius had a major impact on
surface roughness. Fnides et al. [20] studied on machin-
ing of slide-lathing grade X38CrMoV5-1 steel treated at
50 HRC by a mixed ceramic tool (insert CC650) to re-
veal the influences of cutting parameters: feed rate, cut-
ting speed, depth of cut and flank wear on cutting forces
as well as on surface roughness. Biswas et al. [21] stud-
ied that on-line flank wear directly influenced the power
consumption, quality of the surface finish, tool life, pro-
ductivity etc. The authors developed a Neuro-Fuzzy
model for prediction of the tool wear. Shetty et al. [22]
discussed the use of Taguchi and response surface meth-
odologies for minimizing the surface roughness in turn-
ing of discontinuously reinforced aluminum composites
(DRACs) having aluminum alloy 6061 as the matrix and
containing 15 vol. % of silicon carbide particles of mean
diameter 25μm under pressured steam jet approach.
Literature highlights immense effort rendered by pre-
vious researchers to optimize various response parame-
ters in relation to turning operation. Application of hy-
brid Taguchi methods has been found widely attempted
by the investigators. However, the disadvantage of these
approaches is the unrealistic assumption of non-existence
of correlation among the responses. To overcome this
shortcoming, the present study suggests application of
Principal Component Analysis (PCA) to convert corre-
lated responses into uncorrelated quality indices called
principal components [23]. Based on quality loss of indi-
vidual quality indices, an overall utility degree has been
computed by exploring the concept of utility theory.
Thus, multiple objectives (responses) have been trans-
formed into an equivalent single objective function
(overall utility degree) which has been maximized finally
by using Taguchi method. To this end the study finally
verifies robustness and flexibility of the proposed opti-
mization methodology for solving correlated multi-cri-
teria optimization problem emphasizing off-line quality
control in straight turning operation.
2. Procedure Adapted for Optimization
The proposed optimization methodology combines Prin-
cipal Component Analysis (PCA) [23,24], utility concept
[25] and Taguchi method [26] based on selected Ta-
guchi’s Orthogonal Array (OA) Design of Experiment
(DOE). The detailed methodology is described below.
Assuming, the number of experimental runs in Ta-
guchi’s OA design is, and the number of quality cha-
racteristics is. The experimental results can be ex-
pressed by the following series:
m
n
123
,,,.........., ,....,
im
X
XXX X
Here,
1111 1
{(1),(2).........( ).....( )}
X
XXXk Xn
{ (1),(2)......... ()..... ()}
iiii i
X
XXXk Xn
{ (1),(2)......... ()..... ()}
mmmm m
X
XXXk Xn
Here, i
X
represents the experimental results
and is called the comparative sequence.
ith
Let, 0
X
be the reference sequence:
Let, 0000 0
{ (1),(2)......... ()..... ()}
X
XX XkXn
The value of the elements in the reference sequence
means the optimal value (ideal or desired value) of the
corresponding quality characteristic. 0
X
and i
X
both
includes elements, and 0
n()
k and i()
X
k repre-
sent the numeric value of element in the reference
sequence and the comparative sequence, respectively,
kth
1,2,.. ,kn......
.
Step 1: Normalization of the responses (quality
characteristics)
When the range of the series is too large or the optimal
value of a quality characteristic is too enormous, it will
Copyright © 2010 SciRes IIM
S. DATTA ET AL.
Copyright © 2010 SciRes IIM
28
here,
1,2,3......, .
1,2,3,........, .,
jn
kn
jk
cause the influence of some factors to be ignored. The
original experimental data must be normalized to elimi-
nate such effect. There are three different types of data
normalization according to whether we require the LB
(Lower-the-Better), the HB (Higher-the-Better) and NB
(Nominal-the-Best). The normalization is taken by the
following equations.
Here,
j
k
is the correlation coefficient between qual-
ity characteristic and quality characteristic k;
is the covariance of quality characteristic
and quality characteristic ;
j
(,Cov Q
j
)
jk
Q
k
j
k
Q
and
1) LB (Lower-the-Better)
Q
are the
standard deviation of quality characteristic
j
and quality
characteristic , respectively.
k
*min( )
() ()
i
i
i
X
k
Xk Xk
(1)
2) HB (Higher-the-Better) The correlation is checked by testing the following
hypothesis:
*()
() max( )
i
i
i
X
k
Xk
k
(2)
0
1
:0(
:0 (
jk
jk
)
)
H
Thereis no correlation
H
Thereis correlation
(6)
3) NB (Nominal-the-Best)
*0
0
min{( ),( )}
() max{( ),( )}
ib
i
ib
X
kX k
Xk
X
kX k
(3) Step 3: Calculation of the principal component score
1) Calculate the Eigenvalue k
and the correspond-
ing eigenvector ( 1,2,....
kk.., )
Here,
1,2,........, ;
1,2,.........,
im
kn
n
from the correlation
matrix formed by all quality characteristics.
*()
i
k
ith
is the normalized data of the element in
the sequence.
kth 2) Calculate the principal component scores of the
normalized reference sequence and comparative se-
quences using the equation shown below:
0()
b
X
kis the desired value of the quality char-
acteristic. After data normalization, the value of
kth
*()
i
k
*,
i
will be between 0 and 1. The series
X
i
can be viewed as the comparative se-
quence used in the present case.
1, .m2,3,........,
*
1
( )( ),0,1,2,.......,;1,2,........,.
n
iikj
j
YkX jimkn

(7)
Step 2: Checking for correlation between two qual-
ity characteristics
Let, (4)
*** *
01 2
{(),( ),( ),............,( )}
,1,2,.......,.
i
QX iXiXiXi
wherein
m
Here, is the principal component score of the
element in the series.
()
i
Yk
kth ith*()
i
j is the normal-
ized value of the element in the sequence,
and
jth ith
kj
is the element of eigenvector jth k
.
Step 4: Estimation of quality loss
0,i
Δ(k)
0, ()
ik
is the absolute value of difference between
0()
k and ()
i
X
k (difference between desired value
and experimental value for response. If re-
sponses are correlated then instead of using
ithkth
0()
k and
()
i
X
k0
Y, and should be used. ()k()
i
Yk
It is the normalized series of the quality charac-
teristic. The correlation coefficient between two quality
characteristics is calculated by the following equation:
ith
(,)
jk
jk
jk
QQ
CovQQ

(5)
**
0
0,
0
()(),
() () (),
i
i
i
X kX knosignificantcorrelationbetweenqualitycharacteristics
k
YkYkSignificantcorrelationbetween quality characteristics

(8)
Step 5: Adaptation of utility theory: Calculation of
overall utility index
12112 2
, ,.............,,,..................,
nn
UX XXfUXUXUXn
(9)
Here
ii
UX is the utility of the attribute.
th
i
According to the utility theory, if i
X
is the measure
of effectiveness of an attribute (or quality characteristics)
and there are attributes evaluating the outcome
space, then the joint utility function can be expressed as:
in
The overall utility function is the sum of individual
utilities if the attributes are independent, and is given as
follows:
S. DATTA ET AL. 29

12
1
, ,.................,
n
ni
i
UX XXUX

i

i
(10)
The attributes may be assigned weights depending
upon the relative importance or priorities of the charac-
teristics. The overall utility function after assigning wei-
ghts to the attributes can be expressed as:

12
1
, ,.................,.
n
nii
i
UX XXWUX
(11)
Here is the weight assigned to the attribute .
The sum of the weights for all the attributes must be
equal to 1.
i
W i
A preference scale for each quality characteristic is
constructed for determining its utility value. Two arbi-
trary numerical values (preference number) 0 and 9 are
assigned to the just acceptable and the best value of the
quality characteristic respectively. The preference num-
ber can be expressed on a logarithmic scale as fol-
lows:
i
P
'
log i
i
i
X
PA
X



(12)
Here i
X
is the value of any quality characteristic or
attribute ,
i'
i
X
is just acceptable value of quality
characteristic or attribute and i
A
is a constant. The
value
A
can be found by the condition that if *
i
X
X
(where *
X
is the optimal or best value), then 9
i
P
.
Therefore,
*
'
9
log
i
A
X
X
(13)
*'
i
X
X
The overall utility can be expressed as follows:
1
.
n
ii
i
UW
P (14)
Subject to the condition: (15)
1
1
n
i
i
W
Among various quality characteristics types, viz.
Lower-the-Better, Higher-the-Better, and Nominal-the-
Best suggested by Taguchi, the utility function would be
Higher-the-Better type. Therefore, if the quality function
is maximized, the quality characteristics considered for
its evaluation will automatically be optimized (maxi-
mized or minimized as the case may be).
In the proposed approach based on quality loss (of
principal components) utility values are calculated. Util-
ity values of individual principal components are accu-
mulated to calculate overall utility index. Overall utility
index servers as the single objective function for optimi-
zation.
Step 6: Optimization of overall utility index using
Taguchi method
Finally overall utility index is optimized (maximized)
using Taguchi method. For calculating S/N ratio; HB
criterion is selected.
3. Experiments and Data Collection
The present study has been done through the following
plan of experiment.
1) Checking and preparing the Centre Lathe (Manu-
factured by - Tussor machine tool India Pvt. Ltd. Coim-
batore, India) ready for performing the machining opera-
tion.
2) Cutting MS bars (AISI 1040) by power saw and
performing initial turning operation in Lathe to get de-
sired dimension of the work pieces.
3) Performing straight turning operation on MS speci-
men bars with various cutting environments involving
various combinations of process control parameters like:
spindle speed, feed and depth of cut. HSS MIRANDA
S-400 tool has been used.
4) Measuring surface roughness and surface profile
with the help of a portable stylus-type profilometer, Ta-
lysurf (Taylor Hobson, Surtronic 3+, UK) [Figure 1]
5) Data analysis
Figure 1. Photographic view of stylus during surface rough-
ness measurement
Copyright © 2010 SciRes IIM
S. DATTA ET AL.
Copyright © 2010 SciRes IIM
30
3.1. Process Variables and Their Limits
Table 1. Process variables and their limits
Process variables
Values in
coded form
Spindle Speed

N
(RPM)
Feed
f
(mm/rev)
Depth of cut
d
(mm)
-1 220 0.044 0.4
0 530 0.088 0.8
+1 860 0.132 1.2
The working ranges of the parameters for subsequent
design of experiment, based on Taguchi’s L9 Orthogonal
Array (OA) design have been selected. In the present
experimental study, spindle speed, feed rate and depth of
cut have been considered as process variables. The proc-
ess variables with their units (and notations) are listed in
Table 1.
3.2. Design of Experiment
Table 2. Taguchi’s L9 orthogonal array
Experiments have been carried out using Taguchi’s L9
Orthogonal Array (OA) experimental design which con-
sists of 9 combinations of spindle speed, longitudinal
feed rate and depth of cut. According to the design cata-
logue [Peace, G., S., (1993)] prepared by Taguchi, L9
Orthogonal Array design of experiment has been found
suitable in the present work. It considers three process
parameters (without interaction) to be varied in three
discrete levels. The experimental design has been shown
in Table 2 (all factors are in coded form).
Factorial combination
Sl. No.
A
B
C
1 -1 -1 -1
2 -1 0 0
3 -1 1 1
4 0 -1 0
5 0 0 1
6 0 1 -1
7 1 -1 1
8 1 0 -1
9 1 1 0
The coded number for variables used in Tables 1 and 2
are obtained from the following transformation equa-
tions:
Spindle speed: 0
NN
AN
(16)
Table 3. Various surface roughness parameters and their formulae
Parameter Description Formula
a
R
Arithmetic average of absolute values
1
1n
ai
i
R
y
n
,
qRMS
RR Root mean squared 2
1
1n
qi
i
R
y
n
v
R
Maximum valley depth min
vii
R
y
p
R
Maximum peak height max
pii
R
y
t
R
Maximum Height of the Profile
tpv
R
RR
s
k
R
Skew ness 3
3
1
1n
s
ki
qi
R
y
nR
ku
R
Kurtosis 4
4
1
1n
ku i
qi
R
y
nR
,
zDIN m
R
R
average distance between the highest peak and
lowest valley in each sampling length, ASME
Y14.36M - 1996 Surface Texture Symbols 1
1
s
zDIN ti
i
R
R
s
, where s is the number of sampling lengths,
and ti
R
is t
R
for the sampling length.
th
i
zJIS
R
Japanese Industrial Standard forz
R
, based on the
five highest peaks and lowest valleys over the
entire sampling length.
5
1
1
5
th zJISpivi
i
iRR R

, where pi
R
and vi
R
are the
th
i
highest peak, and lowest valley respectively.
S. DATTA ET AL. 31
Table 4. Experimental data related to surface roughness characteristics
a
R
q
R
ku
R
s
m
R
Sl. No. Run 1 Run 2 Run 3 Run 1 Run 2Run 3Run 1Run 2Run 3Run 1 Run 2 Run 3
1 3.12 3.29 3.05 3.96 4.09 3.73 3.603.53 4.98 0.115 0.114 0.104
2 4.05 4.76 5.35 5.11 6.05 6.56 3.713.97 2.72 0.130 0.164 0.190
3 3.84 4.04 3.83 4.71 4.93 4.69 2.762.98 3.09 0.124 0.122 0.131
4 6.56 5.61 5.10 7.90 6.67 6.23 3.013.13 2.76 0.201 0.183 0.160
5 3.75 4.24 3.11 4.62 5.22 3.89 3.164.30 4.09 0.138 0.138 0.138
6 3.23 4.15 4.24 3.97 4.93 5.25 2.902.68 2.67 0.145 0.151 0.156
7 1.30 1.46 1.43 1.54 1.85 1.77 2.765.36 3.51 0.0784 0.101 0.0898
8 4.05 3.89 3.29 4.85 4.54 3.95 2.512.05 2.36 0.129 0.145 0.136
9 3.67 4.10 3.88 4.66 4.87 4.75 3.922.69 3.58 0.110 0.176 0.116
Table 5. Surface roughness characteristics (average values)
Sl. No. a
R

m
q
R
m
ku
R
s
m
R

mm
1 3.153 3.927 4.037 0.111
2 4.720 5.907 3.467 0.161
3 3.903 4.777 2.943 0.126
4 5.757 6.933 2.967 0.181
5 3.700 4.577 3.850 0.138
6 3.873 4.717 2.750 0.151
7 1.397 1.720 3.877 0.090
8 3.743 4.447 2.307 0.137
9 3.883 4.760 3.397 0.134
Feed rate: 0
f
f
B
f
(17)
Depth of cut: 0
dd
Cd
(18)
Here A, B and C are the coded values of the variables
and respectively; and are the
values of spindle speed, feed rate and depth of cut at zero
level; and are the units or intervals of
variation in and respectively.
,Nf d
Nf
,N
00
,Nf 0
d
,d
df
3.3. Roughness Parameters under Consideration
Each of the roughness parameters is calculated using a
formula for describing the surface. There are many diffe-
rent roughness parameters in use, but Ra is the most
common. Other common parameters include ,
ku
R
s
m
R,
, and
z
Rq
R
s
k
R. Some parameters are used only in
certain industries or within certain countries. Since these
parameters reduce all of the information in a profile to a
single number, immense care must be taken in applying
and interpreting them. Small changes in how the raw
profile data is filtered, how the mean line is calculated,
and the physics of the measurement can greatly affect the
calculated parameter.
Each of the formulas listed in the Table 3 assumes that
the roughness profile has been filtered from the raw
profile data and the mean line has been calculated. The
roughness profile contains ordered, equally spaced
points along the trace, and is the vertical distance
from the mean line to the data point. Height is
assumed to be positive in the up direction, away from the
bulk material.
n
i
y
ith
In the present investigation, , and
a
Rq
Rku
R
s
m
R
have been selected for study.
3.4. Data Collection
AISI 1040 MS bars (of diameter 32mm and length 40mm)
required for conducting the experiment have been pre-
pared first. Nine numbers of samples of same material
and same dimensions have been made. Using different
levels of the process parameters nine specimens have
been turned in lathe accordingly. After machining, sur-
face roughness and surface profile of the turned surface
of the jobs have been measured precisely with the help of
a portable stylus-type profilometer, Talysurf (Taylor
Hobson, Surtronic 3+, UK).
The results of the experiments have been shown in Ta-
ble 4 in Appendix. Analysis has been made based on data
listed in Table 5 in Subsection 3.4. Optimization of vari-
Copyright © 2010 SciRes IIM
S. DATTA ET AL.
32
ous surface roughness characteristics (viz. centre line
average , root mean square roughness

a
R
q
R, kur-
tosis and mean line peak spacing

ku
R
s
m
R etc.)
have been made by Taguchi method coupled with PCA
analysis as well as utility concept. Confirmatory tests
have also been conducted finally to validate optimal re-
sults.
3.5. Optimization of Correlated Multiple Surface
Roughness Characteristics
Data (Table 5) related to various surface roughness char-
acteristics have been normalized first. For all surface
roughness parameters LB criterion (Equation 1) has been
selected. It is obvious because reduction in roughness
improves smoothness of the machined surface; i.e. it
proves surface finish. Normalized experimental data are
shown in Table 6.
The Pearson’s correlation coefficients between indi-
vidual responses have been computed using Equation 5.
Table 7 represents Pearson’s correlation coefficients. It
has been observed that all the responses are correlated
(coefficient of correlation having non-zero value). Table
8 presents eigenvalues, eigenvectors, accountability
proportion (AP) and cumulative accountability propor-
tion (CAP) computed for the four major quality indica-
tors
. It has been found that first three principal
components; 123
,,

can take care of 73.3%, 24.9%
and 1.8% variability in data respectively. The contribu-
tion of forth principal component: 4
have been found
negligible to interpret variability into data (0%). More-
over, cumulative accountability proportion (CAP) for
first three principal components has been found 100%.
Therefore, forth principal component should be ignored
and the first three principal components can be treated as
independent or uncorrelated quality indices instead of
four correlated surface quality indices. Correlated re-
sponses have been transformed into three independent
quality indices (major principal components) using
Equation 7. These have been furnished in Table 9. Qual-
ity loss estimates (difference between ideal and actual
gain) for aforesaid major principal components have
been calculated (Equation 8) and presented in Table 10.
Based on quality loss, utility values corresponding to the
four principal components have been computed using
Equations 12 and 13.
Table 6. Normalized response data
Sl. No. a
R
q
R
ku
R
s
m
R
Ideal sequence 1.0000 1.0000 1.0000 1.0000
1 0.4431 0.4380 0.5715 0.8108
2 0.2960 0.2912 0.6654 0.5590
3 0.3579 0.3601 0.7839 0.7143
4 0.2427 0.2481 0.7776 0.4972
5 0.3776 0.3758 0.5992 0.6522
6 0.3607 0.3646 0.8389 0.5960
7 1.0000 1.0000 0.5950 1.0000
8 0.3732 0.3868 1.0000 0.6569
9 0.3598 0.3613 0.6791 0.6716
Table 7. Correlation among quality characteristics
Sl. No. Correlation between responses Pearson correlation coefficient Comment
1 a
R
and q
R
1.000 Both are correlated
2 a
R
and ku
R
0.120 Both are correlated
3 a
R
and
s
m
R
0.940 Both are correlated
5 q
R
and ku
R
0.134 Both are correlated
6 q
R
and
s
m
R
0.938 Both are correlated
7 ku
R
and
s
m
R
0.019 Both are correlated
Copyright © 2010 SciRes IIM
S. DATTA ET AL. 33
Table 8. Eigenvalues, eigenvectors, accountability proportion (AP) and cumulative accountability proportion (CAP) com-
puted for the four major quality indicators
1
2
3
4
Eigenvalue 2.9313 0.0053 0.0733 0.0001
Eigenvector
0.581
0.581
0.082
0.565
0.017
0.002
0.992
0.124
0.402
0.405
0.094
0.816
0.708
0.706
0.010
0.003
AP 0.733 0.249 0.018 0.000
CAP 0.733 0.982 1.000 1.000
Table 9. Major principal components
Major Principal Components
Sl. No.
1
2
3
Ideal sequence -1.8090 0.8490 0.1030
1 -1.0169 0.4580 0.3598
2 -0.7116 0.5851 0.2818
3 -0.8850 0.6823 0.3668
4 -0.6298 0.7051 0.2808
5 -0.8554 0.5064 0.2845
6 -0.8269 0.7514 0.2725
7 -1.7758 0.4472 0.0649
8 -0.8947 0.9034 0.3234
9 -0.8541 0.5835 0.3209
Table 10. Quality loss estimates (for principal components)
Quality loss estimated corresponding to individual principal components
Sl. No.
1
2
3
1 0.7921 0.3910 0.2568
2 1.0974 0.2639 0.1788
3 0.9240 0.1667 0.2638
4 1.1792 0.1439 0.1778
5 0.9536 0.3426 0.1815
6 0.9821 0.0976 0.1695
7 0.0332 0.4018 0.0381
8 0.9143 0.0544 0.2204
9 0.9549 0.2655 0.2179
Table 11. Utility values related to individual principal components
Utility values of individual principal components
Sl. No.
1
2
3
1 1.0031 0.1224 0.1248
2 0.1811 1.8929 1.8099
3 0.6149 3.9584 0.0000
4 0.0001 4.6218 1.8360
5 0.5352 0.7169 1.7386
6 0.4612 6.3702 2.0566
7 8.9992 0.0004 9.0037
8 0.6414 8.9978 0.8371
9 0.5319 1.8658 0.8892
Copyright © 2010 SciRes IIM
S. DATTA ET AL.
Copyright © 2010 SciRes IIM
34
Table 12. Overall utility index
Sl. No. Overall utility index Corresponding S/N ratio
1 0.4167 -7.6035
2 1.2945 2.2420
3 1.5240 3.6597
4 2.1524 6.6585
5 0.9968 -0.0278
6 2.9624 9.4329
7 6.0005 15.5637
8 3.4918 10.8610
9 1.0955 0.7922
Table 13. Results of confirmatory experiment
Optimal setting
Prediction Experiment
Level of factors 111
A
BC
111
A
BC
S/N ratio of Overall utility index 11.1040 16.9610
Overall utility index 3.5909 7.0477
Figure 2. S/N ratio plot for overall utility index
In all the cases minimum observed value of the quality
loss (from Table 10) has been considered as its optimal
value or most expected value; whereas maximum ob-
served value for the quality loss has been treated as the
just acceptable value. Individual utility measures corre-
sponding to three major principal components have been
furnished in Table 11. The overall utility index has been
computed using Equation 14; tabulated in Table 12 with
their corresponding (Signal-to-Noise) S/N ratio. In this
computation it has been assumed that all quality indices
are equally important (same priority weightage, 33.33%).
Figure 2 reflects S/N ratio plot for overall utility index;
S/N ratio being computed using Equation (19).
2
1
11
()10log
t
ii
SN Higherthebetterty

 


(19)
Here is the number of measurements, and the
measured characteristic value i.e. it quality
indicator. Optimal parameter setting has been evaluated
from Figure 2. The optimal setting should confirm high-
est utility index (HB criterion).
ti
y
ith h
11
The predicted optimal setting becomes 1
A
B
C. Af-
ter evaluating the optimal parameter settings, the next
step is to predict and verify the optimal result using the
confirmatory test. Table 13 reflects the satisfactory result
of confirmatory experiment.
4. Conclusions
The foregoing study deals with optimization of multiple
surface roughness parameters in search of an optimal
parametric combination (favorable process environment)
capable of producing desired surface quality of the MS
S. DATTA ET AL. 35
turned product. The study proposes an integrated opti-
mization approach using Principal Component Analysis
(PCA), utility concept in combination with Taguchi’s
robust design methodology. The following conclusions
may be drawn from the results of the experiments and
analysis of the experimental data in connection with cor-
related multi-response optimization in turning.
1) Application of PCA has been recommended to
eliminate response correlation by converting correlated
responses into uncorrelated quality indices called princi-
pal components which have been as treated as response
variables for optimization.
2) Based on accountability proportion (AP) and
cumulative accountability proportion (CAP), PCA analy-
sis can reduce the number of response variables to be
taken under consideration for optimization. This is really
helpful in situations were large number of responses have
to be optimized simultaneously.
3) Utility based Taguchi method has been found
fruitful for evaluating the optimum parameter setting and
solving such a multi-objective optimization problem.
4) The said approach can be recommended for
continuous quality improvement and off-line quality
control of a process/product.
In the foregoing study, interaction effects of process
control parameters have been neglected. But in practical
case, this assumption may not be valid. Therefore, there
exists scope to incorporate these interactions in the analy-
ses of optimization. If interactive effects of factors are con-
sidered, it would be vary interesting to find how Taguchi
design of experiment changes from the previous case.
Another disadvantage of this approach is the unrealis-
tic assumption that the responses are treated as equally
important (equal priority weight). But, no specific guide-
line is available on assignment of priority weights to in-
dividual responses reflecting their relative importance.
These points can be addressed in future.
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S. DATTA ET AL. 37
APPENDIX
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-5
0
5
10
15
20
00.2 0.4 0.6 0.811.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.6 3.8 mm
Length = 4 mm Pt = 29.3 Scale = 50
(Sample 1: Run 1) Surface roughness and waviness profile curve at factor setting
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00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.6 3.8 mm
Length = 4 mm Pt = 37.7 Scale = 100
(Sample 2: Run 1) Surface roughness and waviness profile curve at factor setting
-40
-30
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-10
0
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20
30
40
50
00.2 0.4 0.6 0.811.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.63.8 mm
Length = 4 mm Pt = 32.2 Scale = 100
(Sample 3: Run 1) Surface roughness and waviness profile curve at factor setting
Copyright © 2010 SciRes IIM
S. DATTA ET AL.
38
-40
-30
-20
-10
0
10
20
30
40
50
00.2 0.4 0.6 0.811.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.63.8 mm
Length = 4 mm Pt = 56.1 Scale = 100
(Sample 4: Run 1) Surface roughness and waviness profile curve at factor setting
-50
-40
-30
-20
-10
0
10
20
30
40
00.2 0.4 0.6 0.811.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.63.8 mm
Length = 4 mm Pt = 32.1 Scale = 100
(Sample 5: Run 1) Surface roughness and waviness profile curve at factor setting
-40
-30
-20
-10
0
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20
30
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00.2 0.4 0.6 0.811.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.6 3.8 mm
Length = 4 mm Pt = 41 Scale = 100
(Sample 6: Run 1) Surface roughness and waviness profile curve at factor setting
Copyright © 2010 SciRes IIM
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Copyright © 2010 SciRes IIM
39
-10
-8
-6
-4
-2
0
2
4
6
8
00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 22.2 2.4 2.6 2.833.2 3.4 3.63.8 mm
Length = 4 mm Pt = 9.58 Scale = 20
(Sample 7: Run 1) Surface roughness and waviness profile curve at factor setting
-15
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0
5
10
15
20
25
30
00.2 0.4 0.6 0.811.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.63.8 mm
Length = 4 mm Pt = 30 Scale = 50
(Sample 8: Run 1) Surface roughness and waviness profile curve at factor setting
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-40
-30
-20
-10
0
10
20
30
40
00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.822.2 2.4 2.6 2.833.2 3.4 3.63.8 mm
Length = 4 mm Pt = 50.4 Scale = 100
(Sample 9: Run 1) Surface roughness and waviness profile curve at factor setting