M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
357–366
INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING
THE MACHINING PARAMETERS IN SiC POWDER MIXED –
EDDSG PROCESS TO MACHINE Ti6Al4V
INTEGRIRANA STATISTI^NA METODOLOGIJA ZA
OPTIMIZIRANJE PARAMETROV BRU[ENJA POVR[INE Ti6Al4V
ZLITINE Z EDDSG PROCESOM V ME[ANICI S SiC PRAHOM
Manoj Modi
1*
, Gopal Agarwal
2
1
Department of Mechanical Engineering, Acropolis Institute of Technology and Research, Indore, India
2
Department of Mechanical Engineering, Malaviya National Institute of Technology, Jaipur, Rajasthan, India
Prejem rokopisa – received: 2018-09-07; sprejem za objavo – accepted for publication: 2018-12-17
doi: 10.17222/mit.2018.194
The objective of this research work was targeted to investigate the hybrid-statistical methodology to deduce the economical-
machining-condition through multi-output optimization in silicon carbide powder mixed-Electro Discharge Diamond Surface
Grinding of Ti6Al4V. In this work, Grey-Fuzzy based principal component analysis along with Taguchi’s orthogonal array is
utilised for the multi-output optimization of hybrid-machining process parameters for minimal surface roughness, minimal
wheel-wear rate, and maximal material removal rate. Eighteen experiments have been conducted according to Taguchi’s L18
orthogonal array on in-house-designed and fabricated powder mixed-Electro Discharge Diamond Surface Grinding set-up. The
single Multi-Output Performance Index is calculated by the aggregation of all multi-responses by using Grey-Fuzzy-Taguchi
method based principal component analysis function. The optimum combination of process parameters and the effect of these
parameters on the Multi-Output Performance Index are determined by the use of ANOVA analysis and response table. For the
validation test, one additional confirmation experiment is conducted on this set-up according to the derived optimal condition
and the outcomes of the results showed satisfactory matching between the predicted and experimented result. The specific
contribution of this research work is to develop and describe the procedure of integrated statistical methodology for multi-output
optimization of machining parameters in powder mixed-Electro Discharge Diamond Surface Grinding of Ti6Al4V. This
integrated statistical approach hybridizes the concepts of Grey Relational Analysis, Fuzzy, principal component analysis and
Taguchi approach to find the optimum combination of machining parameters for economical machining. This optimum
combination of process parameters supports engineers to establish an economical and effective process.
Keywords: analysis of variance (ANOVA), powder mixed-electro discharge diamond surface grinding (PM-EDDSG), hybrid
process, grey relational analysis, fuzzy, principal component analysis (PCA), Taguchi’s method (TM), Ti-6Al-4V
Pri~ujo~ ~lanek opisuje raziskavo hibridne statisti~ne metodologije za dolo~itev ekonomi~nih pogojev mehanske obdelave z
ve~komponentno analizo optimizacije izhodnih podatkov bru{enja povr{ine Ti6Al4V zlitine s tako imenovanim postopkom
PM-EDDSG (diamantno bru{enje povr{ine z elektro erozijo v me{anici prahu). V tem delu je uporabljena osnovna
komponentna analiza, ki temelji na tako imenovani sivo-zabrisani logiki (angl.: Grey-Fuzzy) v kombinaciji s Taguchijevo
ortogonalno matriko, s katero naj bi napovedali izhodne pogoje za doseganje minimalne povr{inske hrapavosti, minimalne
obrabe brusilnega koluta in maksimalno hitrost odstranjevanja materiala pri hibridni mehanski obdelavi s PM-EDDSG
postopkom. Avtorji so izvedli osemnajst eksperimentov v skladu s Taguchijevo L18 ortogonalno matriko na doma dizajniranem
in izdelanem stroju za PM-EDDSG postopek. Posamezen ve~izhodni indeks u~inkovitosti (MOPI; angl.: Multi-Output
Performance Index) so izra~unali z zdru`itvijo vseh ve~kratnih odzivov in z uporabo G-F-T metode (angl.: Grey-Fuzzy-Taguchi
method), ki temelji na komponentni funkcijski analizi. Optimalno kombinacijo procesnih parametrov in vpliv teh parametrov na
MOPI so dolo~ili z uporabo ANOVA analize in tabele odzivov. Kot validacijski test so izvedli {e en dodatni eksperiment na
pri~ujo~i napravi pri dobljenih optimalnih pogojih. Rezultati preizkusa so pokazali zadovoljivo ujemanje med napovedanimi in z
eksperimentom dobljenimi rezultati. Specifi~ni prispevek tega raziskovalnega dela je razvoj in opis postopka integrirane
statisti~ne metodologije za ve~ izhodno optimizacijo parametrov mehanske obdelave povr{ine Ti6Al4V zlitine s PM-EDDSG
postopkom. Ta integrirani statisti~ni pristop zdru`uje koncepte sivo-zabrisane relacijske analize (angl.: Grey-Fuzzy Relational
Analysis), osnovne komponentne analize in Taguchijeve metode za dolo~itev optimalne kombinacije procesnih parametrov
ekonomi~ne mehanske obdelave. Ta optimalna kombinacija procesnih parametrov omogo~a procesnim in`enirjem uvajanje
novega ekonomi~nega in u~inkovitega procesa.
Klju~ne besede: analiza variance (ANOVA), diamantno bru{enje povr{ine z elektroerozijo v me{anici prahu (PM-EDDSG),
hibridni proces, siva relacijska analiza, zabrisanost, osnovna komponentna analiza (PCA), Taguchijeva metoda (TM), Ti-6Al-4V
1 INTRODUCTION
Powder Mixed-Electro Discharge Diamond Surface
Grinding is an emerging hybrid process for the ma-
chining of hard materials like Ti6Al4V. This material is
widely utilized in various applications, including bio-
medical, automotive, etc. Lin et al.
1
did experimentation
on the Electrical Discharge Machining of SKD11 steel
and reported that the material removal rate and electrode
wear ratio are improved together by using a Taguchi-
Fuzzy logic approach for solving the multi-output opti-
mization problem. Kung et al.
2
conducted experimen-
tation on Powder Mixed Electrical Discharge Machining
of 94WC-6Co and developed the models for material
Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366 357
UDK 519.233.4:669.715:621.9 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 53(3)357(2019)
*Corresponding author e-mail:
manojmnitjaipur1@gmail.com

removal rate and electrode wear ratio by Response
Surface Methodology. Further, they studied the influence
of input variables on the responses. Singh et al.
3
con-
ducted experimentation on the Electro Discharge Face
Grinding of WC-Co and studied the influence of process
variables over the responses. Lin et al.
4
carried out
experimentation on the Electrical Discharge Machining
of SKD11 steel and showed that a combined Grey
Relational Analysis-orthogonal array approach enhances
the machining performance in multi-output optimization.
This combined methodology improves the process
outputs, i.e., electrode wear ratio, material removal rate
and surface roughness in the Electrical Discharge
Machining process. Tarng et al.
5
carried out experiments
and reported the use of the Taguchi approach to find the
optimum combination of welding variables in the sub-
merged arc-welding of mild steel plates. Ko et al.
6
applied a Grey Relational Analysis and the Fuzzy-ortho-
gonal array method on Electrical Discharge Machining,
T z e n ge ta l .
7
applied the Fuzzy-Taguchi method on
Electrical Discharge Machining and Lin et al.
8
applied
Grey-Fuzzy method on Electrical Discharge Machining
for the multi-output optimization of process variables.
George et al.
9
applied the Taguchi method to find the
optimum combination of process variables on Electrical
Discharge Machining of C-C composites. Fung et al.
10
performed experimental work and presented the use of
the principal component analysis-Taguchi approach for
the optimization of multi-output in, fiber-reinforced
polybutylene terephthalate composites. Alagumurthi et
al.
11
have conducted experimental work on the grinding
of mild steel and compared the factorial design of expe-
riment with the Taguchi design of experiment approach,
used to find the optimal grinding conditions. They
reported that depth of cut, wheel speed and work speed
were important grinding parameters that affect the
grinding quality. Jean et al.
12
conducted experimental
work and reported the use of a principal component
analysis-Taguchi approach to develop a robust Electron
Beam Welding Treatment process with high efficiency
multiple-performance characteristics (MPCs). Dutta et
al.
13
conducted experimentation on Wire Electrical Dis-
charge Machining of D2 tool steel. They applied
Response Surface Methodology to develop the models
for each response and these models were used to predict
the behaviour of process variables on the responses.
They applied Grey Relational Analysis-Taguchi metho-
dology to find the optimal variables setting in multi-res-
ponse optimization. Lahane et al.
14
did experimental
work and proposed a Weighted Principal Component
method for multi-outputs optimization of the process
factors in the wire Electrical Discharge Machining of
HSS steel. V. K. Jain
15
reported that Hybrid Machining
Process performance is more effective as compared to
separate performance of component process with similar
input variables.
Based on the above literature review, there is the
necessity for efficient optimization methodology to take
care of the problems related to the co-occurring optimi-
zation of multi-correlated responses and their solutions.
Taguchi’s methodology has been broadly utilized for
process parameters optimization. This technique is
beneficial for single response optimization, however, in-
effective to optimize the multi-responses. In this research
work, Taguchi’s method is integrated with Grey-fuzzy
based principal component analysis to beat the drawback
in managing the difficulty of the simultaneous optimiza-
tion of multi-correlate responses.
This integrated statistical methodology is utilized to
derive an identical equivalent process-quality index by
combining the multi-responses to depict the overall qual-
ity of the process so that the difficulty of concurrent
optimization of multi-responses is substituted by the
problem of maximizing the process - Overall Quality
Index. That is why Taguchi’s Utility-Theory can be
efficiently utilized to maximize the process overall
quality.
In this research work, a unique integrated multi-out-
put optimization methodology is planned to deduce the
optimum combination of machining variables in the
Powder Mixed-Electro Discharge Diamond Surface
Grinding of Ti6Al4V. This integrated methodology hyb-
ridizes the concepts of Grey, Fuzzy, Principal Compo-
nent-Analysis and Taguchi to take care of the problem of
co-occurring optimization of three correlative Powder
Mixed-Electro Discharge Diamond Surface Grinding
process performance measures like material removal
rate, surface roughness, and wheel wear rate in ma-
chining of Ti6Al4V.
2 METHOD FOR MULTI-OUTPUT-OPTIMIZA-
TION
2.1 Grey Relational Analysis Method
In Grey Relational Analysis, the initial step is to nor-
malize the experimental data between zero-to-one by
using Equations (1) and (2). For material removal rate,
the higher is the better criterion is selected. Similarly, for
surface roughness and wheel wear rate, the lower is the
better criterion has been selected.
16
For higher is the better criterion (H-T-B),
xt
xt xt
xt xt
i
ii
ii
*
() ()
() ()
()
min
max min
=
−
−
00
00
() ()
() ()
(1)
For lower is the better criterion (L-T-B),
xt
xtxt
xt xt
i
ii
ii
*
() ()
() ()
()
max
max min
=
−
−
00
00
() ()
() ()
(2)
where,xt
i
() 0
()= original sequence,xt
i
(*)
()= value after
the Grey Relational normalization, min
()
xt
i
0
()= lowest
value ofxt
i
() 0
() , max
()
xt
i
0
()= maximum value ofxt
i
() 0
() ,
i = 1, 2, ..., p; t = 1, 2, ..., q, p = total experiment and q =
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
358 Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366

total observation data. The next step is to determine the
deviation sequence [Δ
oi
t () ] for every output ( = 0.5)
and then the Grey Relational Coefficient is determined
by using Equation (3).
()    xtxt
t
o i
oi
**
min max
max
(), ()
+
()+
=
ΔΔ
ΔΔ
(3)
()  xtxt
o i
**
(), () ≤1, Δ
oi o i
txtxt ()= (), ()
**
,
Δ=
max
**
maxmax
∀∈ ∀ ji t
o j
xtxt (), (),Δ=
min
**
minmin
∀∈ ∀ ji t
o j
xtxt (), ().
 is the distinguishing coefficient,
[]
 ∈ 01 , . Where,
xt
o
*
()= Reference sequence andxt
i
*
()= Comparability
sequence.
In the final step, the Grey Relational Grade is deter-
mined by using Equations (4) and (5) and its log S value
is calculated for the higher is the better (H-T-B) concept.
()   ()
(*) (*) (*) (*)
xx
q
xtxt
o i t
t
q
o i
,( ) , ( ) =
=
∑
1
1
(4)
 t
t
q
=
∑ =
1
1 (5)
where q is the number of process responses. The Grey
Relational Grade shows the interrelation betweenxt
o
(*)
()
andxt
i
(*)
() .
2.2 Taguchi’s Method
Taguchi’s Method is a technique usually used to
frame-up the orthogonal array of experiments, with less
variance between the experiment outcomes. This metho-
dology not only helps to develop the orthogonal array
but also minimize the numbers of experimental runs,
enough to optimize and analyze the process. There are
three kinds of signal-to-noise ratios: lower is the better
(L-T-B), higher is the better (H-T-B), and nominal is the
better (N-T-B), which is expressed in mathematical
forms by Equations (6), (7) and (8). An ANOVA analysis
is utilized for data-analysis to investigate the effect of
main machining variables on the output responses.
Lower is the better (L-T-B),
l
n
y
ii
i
n
=−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
∑ 10
1
2
1
log (6)
Higher is the better (H-T-B),
l
n y
i
i
i
n
=−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
∑ 10
11
2
1
log (7)
Nominal is the better (N-T-B),
l
ns
y
ii
i
n
=−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
∑ 10
1
2
1
log (8)
where y
i
is the measured output response at the i
th
trial,
n is the total number of experimental-runs, l
i
is the loss-
quality function at the i
th
trial and s denotes the standard
deviation.
2.3 Principal Component Analysis
Principal Component Analysis was introduced by
Pearson and Hotelling (1933). This methodology is uti-
lized to define the variance and covariance relation with
the help of linear composition of original parameters.
The PC
1
describes the maximal variance in the collected
data and the PC
2
describes the remaining variance that
was left by the PC
1
and so on. Suppose, the system-
variability is depicted by the p-components. The system
variability may be described by a smaller number, m
(m ≤ p), of the PCs, i.e., m PCs can account for the ma-
jority of variance within the original p parameters.
For the response variables, Z
1
, Z
2
… Z
p
, there is the
following PCs Y
i
(i =1, 2, 3, ..., p).
YaZaZ aZ
ip p 11 111 22
=++ + ...
YaZaZaZ
p p 22 1 12 222
=++ + ...
YaZaZaZ
m mm mp p
=++ +
11 22
...
whereaaa
mm mp 1
2
2
22
1 ++ += ...
Here, Y
1
is known as first principal component, Y
2
is
known as the second principal component and so on. The
m
th
component coefficient is the parts of the eigenvector
matching to the m
th
biggest eigenvalues. The principal
component analysis can be done on MINITAB software.
Principal Component Analysis is an effective metho-
dology to describe the slight number of components that
is responsible for the principal sources of variation in a
set of correlated-quality characteristics.
The procedure of Principal Component Analysis is as
follows:
a) Calculate the signal-to-noise ratio for every output-
response by Equations (6) to (8).
b) Normalize the signal-to-noise ratio of every output
responses into 0 to 1 by the use of Equations (1) and
(2).
c) Carry out principal component analysis on the nor-
malized data.
d) Determine the eigen-values, and eigen-vectors.
e) Calculate the numbers of PCs, m, and compute.
2.4 Fuzzy Method
In this methodology, the fuzzy reasoning grade
(FRG
0
) is calculated by the use of the max-min fuzzy
interface and the centroid defuzzification methods. The
system of Fuzzy Logic contains 5 components; Fuzzifier,
Membership Function, Rules, Inference System, and De-
fuzzifier.
The fuzzy-logic-interface system for this research
work is developed using MathWorks TM MATLAB
®
8.1.0.604 (Release 2013a), Fuzzy Logic Toolbox. Here,
the basic structure of the fuzzy logic unit for two fuzzy
inputs with one fuzzy output is displayed in Figure 1.
Fuzzy linguistic description is the formal presenta-
tion of systems made through fuzzy IF-THEN rules.
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366 359

Rule one: IF (Y
1
is E
1
) and (Y
2
is G
1
) then (Z is F
1
)
else
Rule two: IF (Y
1
is E
2
) and (Y
2
is G
2
) then (Z is F
2
)
else
Rule twenty five: IF (Y
1
is E
25
) and (Y
2
is G
25
) then (Z
is F
25
) else
μ
Ei
, μ
Gi
and μ
Fi
are the membership functions corres-
ponding to the E
i
,G
i
and F
i
fuzzy subsets. In this re-
search work, five fuzzy-subsets are allotted to two
inputs and nine fuzzy subsets are allotted to the output
as displayed in Figure 4. The total possible number of
fuzzy rules used here is twenty-five. These fuzzy rules
are obtained with the evidence that a bigger log S value
corresponds to the major benefit to the process output.
Suppose, Y
1
and Y
2
are the values of the inputs, the
membership function of the multi-output Z can be dis-
played by Equation (9).
() 

FEGF
EG
ZYYZ
YY
nn
0111
12
12
() () () (). . .
() ()
=∧∧∨
∨∧∧ ()  F
n
Z ()
(9)
Here, ∧is related to minimal and ∨is related to maxi-
mal operation. For the defuzzification, centre-of-gravity
methodology is used, which convert multi-output μ
C
0
(Z)
into crisp fuzzy reasoning grade (FRG
0
) using Equation
(10).
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
360 Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366
Figure 1: Basic structure of fuzzy logic unit
Figure 2: Methodology of Integrated Statistical Grey-Fuzzy-TM based PCA Approach

FRG
ZZ
Z
F
F
0
0
0
=
∑
∑
  ()
()
(10)
3 METHODOLOGY FOR AN INTEGRATED
GREY-FUZZY-TAGUCHI-BASED PCA
APPROACH
The detail procedure for an integrated Grey-Fuzzy-
Taguchi-based PCA method is shown in Figure 2.
4 EXPERIMENTAL PART
Eighteen experiments were conducted according to
Taguchi’s L
18
orthogonal array on in-house-designed and
fabricated silicon carbide Powder Mixed-Electro Dis-
charge Diamond Surface Grinding set-up. All the details
of the Powder Mixed-Electro Discharge Diamond
Surface Grinding set-up are available at Modi et al.
17
The
schematic-photographic diagram of Powder Mixed-
Electro Discharge Diamond Surface Grinding frame-up
is displayed in Figure 3.
The various input parameters like powder concentra-
tion (gm/L), current (A), pulse-on-time(μs), wheel-speed
(min
–1
) and duty cycle (DC) were selected for the
experimental investigation. Depending upon the initial
experimental results and Electrical Discharge Machining
capacity, the variables range was selected as displayed in
Table 1.
Table 1: Various input variables and their levels
Symbol Control Factor Level 1 Level 2 Level 3
P-C
SiC Powder Concentra-
tion (gm/L)
24–
I Current (A) 1 5 9
T
on
Pulse-on-time (μs) 100 150 200
S Wheel Speed (min
–1
) 350 550 750
DC Duty Cycle 0.61 0.69 0.77
The detailed description of the bronze-diamond
wheel is displayed in Table 2.
Table 2: Detail description of bronze-diamond grinding wheel
Abrasive
Dia-
meter
Thick-
ness
Bond
mate-
rial
Concen-
tration
Bore
Depth
of
abra-
sive
Grit
size
Diamond
100
mm
10
mm
Bronze 75 %
32
mm
5
mm
80/100
In this experimentation, the work-piece material was
Ti6Al4V. The work-piece is flat and rectangular in
shape. The composition of Ti-6Al-4V (grade-5) is
Carbon = 0.02 %, Al = 6.05 %, Ti = 90.1 %,V=3.7%
and Fe = 0.13 %. The silicon carbide powder is added
into the dielectric fluid of the EDDSG set-up. The
powder particle size is approximately #30 μm and the
concentration range is from 2 gm/litre to 4 gm/litre.
Equation (11) was used to calculate the material
removal rate and wheel wear rate for each machining
process.
MRR
WWR
DWW
t
( / min) mg =
×100
(11)
DWW is the difference in the work-piece/wheel
weight before and after the machining time equal to 30
min. The material removal rate and wheel wear rate were
measured by using the High Precision Electronic
Balance, WENSAR, HPB-310 Model. The surface
roughness of the machined work-piece was measured by
the Surtronic-25 surface roughness tester at the cut-off
value of 0.8 mm. The digital tachometer was used for the
grinding wheel speed measurement.
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366 361
Figure 4: a) Membership function of inputs, b) Membership function
of output, c) Fuzzy-Interface system at 2-level
Figure 3: Schematic diagram of in-house-designed and fabricated
Powder Mixed-Electro discharge diamond surface grinding set-up

5 PROCESSING OF EXPERIMENTAL DATA
Here, Table 3 displays the L
18
orthogonal array, out-
put responses, log S value, and normalised log S value.
Table 4 displays the deviation sequence and Grey
Relational Coefficient. Table 5 displays the eigenvalues,
eigenvector. Table 6 displays the fuzzy rules. Table 7
displays the principal components and multi-output per-
formance index and Table 8 displays the response and
ANOVA for multi-output performance index.
Figure 5 displays the fuzzy logic reasoning proce-
dure for the test result 8; Figure 6 displays the surface
plot of multi-output performance index with inputs; Fig-
ure 7 displays the % contribution of machining process-
parameters on multi-output performance index, and
Figure 8 displays the signal to noise-ratio plot of multi-
output performance index.
Calculation of the deviation sequence and Grey Rela-
tional Coefficient (GRC).
Table 4: Displays the deviation sequence and GRC
Exp.
No.
Deviation sequence GRC
MRR R a WWR MRR R
a WWR
1 0.560 0.792 1.000 0.472 0.387 0.333
2 0.466 0.864 0.613 0.518 0.367 0.449
3 0.541 1.000 0.107 0.480 0.333 0.824
4 0.412 0.409 0.967 0.548 0.550 0.341
5 0.262 0.250 0.507 0.657 0.667 0.497
6 0.512 0.383 0.000 0.494 0.566 1.000
7 0.000 0.122 0.306 0.999 0.805 0.620
8 0.421 0.175 0.590 0.543 0.741 0.459
9 0.335 0.048 0.321 0.599 0.913 0.609
10 0.475 0.839 0.702 0.513 0.373 0.416
11 1.001 0.981 0.581 0.333 0.338 0.463
12 0.850 0.839 0.080 0.370 0.373 0.862
13 0.246 0.132 0.818 0.670 0.792 0.379
14 0.541 0.312 0.241 0.480 0.616 0.675
15 0.610 0.587 0.323 0.451 0.460 0.608
16 0.466 0.140 0.848 0.518 0.781 0.371
17 0.640 0.071 0.936 0.438 0.876 0.348
18 0.230 0.000 0.668 0.685 1.000 0.428
Principal Component Analysis for eigenvalue and
eigenvector.
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
362 Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366
Figure 5: Fuzzy logic reasoning procedure for the test result 8
Table 3: L
18
orthogonal array, output responses, log S value, and normalised log S value
Exp. No
Control Factor Responses log S value Normalized log S value
P-C I T
on SD C
MRR
(mg/min)
R a
(μm)
WWR
(gm/min)
MRR R
a WWR MRR R
a WWR
1111111.50 1.54 0.0078 3.52 –3.75 42.16 0.44 0.21 0.000
2112221.60 1.33 0.0162 4.08 –2.48 35.81 0.53 0.14 0.387
3113331.52 1.01 0.0421 3.64 –0.09 27.51 0.46 0.00 0.893
4121121.66 3.34 0.0083 4.40 –10.47 41.62 0.59 0.59 0.033
5122231.84 4.61 0.0198 5.30 –13.27 34.07 0.74 0.75 0.493
6123311.55 3.52 0.0515 3.81 –10.93 25.76 0.49 0.62 1.000
7131212.20 5.98 0.0289 6.85 –15.53 30.78 1.00 0.88 0.694
8132321.65 5.37 0.0169 4.35 –14.60 35.44 0.58 0.83 0.410
9133131.75 6.94 0.0281 4.86 –16.83 31.03 0.67 0.95 0.679
1 0211331.59 1.40 0.0137 4.03 –2.92 37.27 0.52 0.16 0.298
1 1212111.11 1.05 0.0172 0.91 –0.42 35.29 0.00 0.02 0.419
1 2213221.23 1.40 0.0443 1.80 –2.92 27.07 0.15 0.16 0.920
1 3221231.86 5.86 0.0110 5.39 –15.36 39.17 0.75 0.87 0.182
1 4222311.52 4.07 0.0327 3.64 –12.19 29.71 0.46 0.69 0.759
1 5223121.45 2.33 0.0280 3.23 –7.35 31.06 0.39 0.41 0.677
1 6231321.60 5.76 0.0104 4.08 –15.21 39.66 0.53 0.86 0.152
1 7232131.42 6.63 0.0088 3.05 –16.43 41.11 0.36 0.93 0.064
1 8233211.88 7.65 0.0146 5.48 –17.67 36.71 0.77 1.00 0.332

Table 5: Displays the eigenvalues, and eigenvector
PC
1 PC
2 PC 3
Eigenvalue 1.6666 0.9246 0.4089
Eigenvector
[0.640, 0.681,
–0.354]
[–0.383, 0.117,
0.916]
[–0.666, 0.722,
0.186]
Proportion 0.556 0.308 0.136
Cumulative 0.556 0.864 1.000
Primarily, the principal components (PCs) are divi-
ded into two categories with eigenvalue > 1 and eigen-
value < 1. MPI-1 is calculated through PC
2
and PC
3
as
input with eigenvalue < 1. Final multi-output perform-
ance index is calculated through PC
1
and MPI-1 as the
input by using the similar membership functions and
rules.
Table 6: Twenty-five fuzzy rules in tabular form
MPI
Input 1
VS S M L VL
Input 2
VS
S
M
L
VL
TV SSS MM
VS S SM M ML
SS MMM LL
SM M ML L VL
MM LLV LH
The Fuzzy logic reasoning procedure for the test
result 8 is displayed in Figure 5. The surface plot of the
multi-output performance index is displayed in Figure 6.
Calculation of multi-output performance index
(MPI).
6 RESULTS AND DISCUSSION
The ANOVA test was performed on the multi-output
performance index. The influence of various machining
process parameters on the multi-output performance
index and the ANOVA analysis result is displayed in
Table 8. The optimum combination of various process
parameters obtained through the integrated statistical
optimization method for the multi-output optimization in
Powder Mixed-Electro Discharge Diamond Surface
Grinding of Ti6Al4V, is powder concentration with level
one; current with level three; pulse-on-time with level
three; the speed with level two and duty cycle with level
three. For the validation test, one additional confirmation
experiment was performed on this set-up according to
the derived optimal condition and the outcomes of the
result showed satisfactory matching between predicted
and experimented results. The confirmation test result is
listed in Table 9, which displays the closure correlation
between the experimental and predicted values.
A Scanning Electron Microscopy investigation has
been conducted on the produced machine surface
through silicon carbide powder mixed-Electro Discharge
Diamond Surface Grinding process under optimal condi-
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366 363
Table 8: Response and ANOVA for multi-output performance index (MPI)
Response table
Symbol
ANOVA table
Level 1 Level 2 Level 3 Max-Min DF SS MS F P C (%)
–8.118
p
–10.062 1.945 P-C 1 0.001200 0.001200 0.03 0.860 0.258
–13.967 –8.907 –4.397
p
9.570 I 2 0.382457 0.191229 5.26 0.035 82.47
–8.763 –9.685 –8.823
p
0.922 T
ON
2 0.000869 0.000435 0.01 0.988 0.187
–10.970 –6.430
p
–9.871 4.540 S 2 0.037324 0.018662 0.51 0.617 8.049
–10.802 –8.373 –8.096
p
2.707 DC 2 0.041857 0.020929 0.58 0.584 9.026
Error 8 0.291024 0.036378
Total 17 0.754733
Figure 6: Surface Plot of MPI with inputs
Table 7: Principal Components and multi-output performance index
(MPI)
Exp.
no.
Principal
components
Normalise PCs
MPI-1 MPI
PC
1
PC
2
PC
3
PC
1
PC
2
PC
3
1 0.448 0.531 0.027 0.335 0.000 0.059 0.500 0.379
2 0.423 0.653 0.003 0.302 0.190 0.000 0.500 0.348
3 0.242 0.978 0.073 0.072 0.698 0.175 0.417 0.188
4 0.605 0.587 0.095 0.535 0.087 0.230 0.103 0.285
5 0.699 0.785 0.136 0.656 0.397 0.332 0.300 0.458
6 0.348 1.171 0.265 0.207 1.001 0.652 0.500 0.287
7 0.968 1.045 0.031 1.000 0.803 0.069 0.464 0.500
8 0.690 0.715 0.258 0.644 0.288 0.637 0.429 0.547
9 0.790 0.894 0.373 0.772 0.567 0.922 0.809 0.875
10 0.435 0.621 0.005 0.319 0.141 0.004 0.060 0.124
11 0.279 0.591 0.108 0.119 0.094 0.262 0.112 0.042
12 0.186 0.975 0.182 0.000 0.694 0.447 0.609 0.500
13 0.834 0.696 0.196 0.829 0.258 0.481 0.298 0.591
14 0.488 0.874 0.250 0.386 0.536 0.616 0.617 0.503
15 0.387 0.783 0.144 0.257 0.395 0.352 0.322 0.191
16 0.732 0.630 0.288 0.698 0.154 0.710 0.414 0.594
17 0.754 0.589 0.405 0.726 0.091 1.003 0.500 0.675
18 0.968 0.771 0.345 1.000 0.376 0.853 0.662 0.500

tions. Figure 9 displays the SEM image of the: a) pro-
duced machined surface at optimum condition (I=9A,
T
on
= 200 μs, DC = 0.77, S = 550 min
–1
, P-C=2gmof
powder/L); b) White recast layer thickness at optimum
condition (I =9A ,T
on
= 200 μs, DC = 0.77, S = 550
RPM, P-C = 2 gm of powder/L). These images revealed
that satisfactory output-responses are acquired through
the suggested integrated statistical methodology.
6.1 Confirmation test
The estimated grade
 ()   =+ −
=
∑
mim
i
n
1
(12)
where  m
is the average grade,  i
is the optimum level
average grade and šn’ is the total significant design va-
riables that affect the multi-output response. To ensure
the enhancement in quality performance, a confirmation
test is performed. The outcome of this test is displayed
in Table 9.
7 CONCLUSIONS
In this research paper, an integrated statistical metho-
dology of Grey-Fuzzy-Taguchi’s Method based principal
component analysis has been utilized for multi-output
optimization of the machining parameters in silicon car-
bide powder mixed-Electro Discharge Diamond Surface
Grinding processes of Ti6Al4V. The single multi-output
performance index is calculated by the aggregation of all
multi-responses through Grey-Fuzzy-Taguchi’s Method-
based principal component analysis function. Hence,
ANOVA is applied on multi-output performance index to
calculate the signal-to-noise ratio with Higher is the
Better criterion.
The following conclusions could be drawn based on
the analysis of outcomes obtained through the suggested
approach and SEM image investigations:
M. MODI, G. AGARWAL: INTEGRATED STATISTICAL METHODOLOGY FOR OPTIMIZING THE MACHINING ...
364 Materiali in tehnologije / Materials and technology 53 (2019) 3, 357–366
Figure 9: a) SEM image of the produced machined surface in Powder
Mixed - EDDSG process with SiC powder under optimum conditions
(I =9A,T
on
= 200 μs, DC = 0.77, S = 550 min
–1
, P-C=2gmof
powder/L), b) SEM image of wrlt thickness with SiC powder under
optimum conditions (I=9A,T
on
= 200 μs, DC = 0.77, S = 550 min
–1
,
P-C = 2 gm of powder/L).
Figure 8: S/N-ratio plot of MPI
Figure 7: Percentage contribution of machining process parameters
on MPI
Table 9: Result of confirmation test
Factor Level
Initial Process
Parameters
Optimal Process parameter
Prediction Experiment
PC
1
I
1
T
on
1
S
1
D
1
PC
1
I
3
T
on
3
S
2
D
3
PC
1
I
3
T
on
3
S
2
D
3
MRR
(mg/min)
1.50 - 1.86
R a
(μm) 1.54 - 6.00
WWR
(gm/min)
0.0078 - 0.024
MPI 0.379 0.739 0.754
Improvement in MPI is 0.375

1. The optimal level of machining process parameters
derived from the integrated statistical methodology of
Grey-Fuzzy-Taguchi’s Method-based principal compo-
nent analysis approach are: 2 gm/L of powder concentra-
tion;9Aofcurrent; 200 μs of pulse-on-time; 550 revolu-
tion per min (min
–1
) of wheel speed and 0.77 of duty
cycle.
2. The experimental results of output responses under
optimal condition are material removal rate equal to 1.86
mg/min; R
a
equal to 6.00 μm; and wheel wear rate equal
to 0.024 gm/min.
3. It is observed through ANOVA results that the per-
centage contribution of various process parameters on
the process performance is powder concentration
(0.26 %); current (82.47 %); pulse-on-time (0.19 %);
wheel speed (8.05 %); and duty cycle (9.02 %). The
current is the most significant parameter that affects the
process performance.
4. The Multi-output Performance Index has been im-
proved by 0.375.
5. The SEM outcomes also equally satisfy the pre-
dicted outcomes from the suggested integrated statistical
methodology.
The suggested integrated statistical method may also
be utilized to optimize the problem of the co-occurring
optimization of multi-correlated responses in some other
production machining processes to improve the produc-
tion efficiency and also automate the production machin-
ing process based on the calculated optimum values.
Nomenclature
ANOVA Analysis of variance
PM-EDDSG Powder Mixed-Electro Discharge
Diamond Surface Grinding
HM Hybrid Machining
EDG Electro Discharge Grinding
EDM Electrical Discharge Machining
HMP Hybrid Machining Process
RSM Response Surface Methodology
DC Duty Cycle (%)
DWW Difference in work-piece/wheel weight
before and after the machining
WEDM Wire Electrical Discharge Machining
I Current (A)
MRR Material Removal Rate (mg/min)
WWR Wheel Wear Rate
R
a
Average Roughness of Surface (μm)
MIN
–1
Revolution per minute
S Wheel Speed (MIN
–1
)
T
on
Pulse on-time (μs)
t Time in min
 Density of work-piece material (gm/cm
3
)
P-C Powder Concentration
OA Orthogonal Array
CM Correlation Matrix
GRA Grey Relational Analysis
PCA Principal Component Analysis
a
mp
m
th
element in the p
th
eigen vector
TU-Theory Taguchi’s Utility Theory
OQI Overall Quality Index
H-T-B Higher is the better Criterion
L-T-B Lower is the better Criterion
N-T-B Nominal is the better Criterion
GRC Grey Relational Coefficient
GRG Grey Relational Grade
TM Taguchi’s Method
PC/PC
S
Principal Component / Principal Compo-
nents
MF/MF
S
Membership Function/Membership Func-
tions
MPI Multi-output Performance Index
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