Development of a Taguchi-based framework for optimizing two quality characteristics in Wire-EDM operations

Trad Alblawi. Joseph Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 6, Issue 1, (Part - 6) January 2016, pp.35-49
www.ijera.com 35|P a g e
Development of a Taguchi-based framework for optimizing two
quality characteristics in Wire-EDM operations
Trad Alblawi. Joseph, C. Chen· Ye Li
Abstract
A framework based on Taguchi parameter design was developed and successfully demonstrated to optimize two
quality characteristics- surface roughness and angular accuracy in Wire Electrical Discharge Machining (W-
EDM) process. An orthogonal array (OA)L9was used in the Taguchi experiment design for four controllable
factors, each with three levels. With one non-controllable factor investigated, 18 experiments were conducted in
the Taguchi-based experiment setting, compared to 34
(=81) parameter combination as required by a traditional
DOE setting. Conducted for the two response variables, Taguchi experiments from the case study gave the
optimal combination of pulse on time at 9µs (A1), feed rate at 35 in/min (B2), voltage at 8v (C2), and wire
tension at 165g (D3) for surface roughness optmization, and pulse on time at 13µs (A3), feed rate at 35 in/min
(B2), voltage at 8v (C2), and wire tension at 160g (D2) for angular accuracy optmization. This optimal parameter
setting combination was verified through a confirmation run that confirms the optimal quality responses of
126.1µin for surface roughness and 0.024º for angular accuracy. This research ultimately showed the dual
output variable improvement and the framework established itself as a means to solve similar problems in other
machining applications. The developed framework can serve as guidance for researchers to obtain multi-
variable optimal setting in a systematic way.
Keywords: WEDM· Taguchi method · Surface roughness · Angular accuracy
I. Introduction
As a non-traditional machining process, Wire
Electrical Discharge Machining (W-EDM) erodes
materials from a work piece by producing sparks
between the work piece and the tool electrode. The
process occurs in a dielectric liquid bath of deionized
water. W-EDM has been widely used in advanced
manufacturing processes for molds and die in fields
such as aerospace, automotive, and surgical
components. W-EDM machines are able to produce
complex 2D and 3D shapes. During W-EDM process,
spark erosion frequently occurs, which can create
more than one thousand sparks per second between
the wire (Anode) and the work piece (Cathode).
These sparks jump from the wire to the work piece
and erode metal at temperatures in the range of 8000
- 12000⁰ [1] as shown in Fig 1[3]. The nature of W-
EDM processes requires that both the work
piecematerial and the wire be conductive.
Fig.1 Principle of W-EDM [3]
Compared to traditional machining processes,
W-EDM machines are capable of holding to closer
tolerances and better surface finishes. Some W-EDM
machines are extremely accurateallowing them to
hold up to +/- 0.0001” and producing a surface finish
(Ra) of around 0.037 µm [4]. The advantages from
W-EDM processhave made it a reasonable alternative
to other subtractive machining processes. One major
advantage lies in the fact that there is little contact
force between the workpiece and the wire, and hence
it can machine weak or thin work pieces without
causing much deflection as in traditional machining
processes. Additionallya W-EDM machine has
several parameters including: pulse on time(a.k.a. the
duration of time) which isthe length of time that the
wire releases sparks,wire feed rate or the speed in
which the wire is fed through the work piece,wire
tension or the axial forces exerted on wire, and
voltage-the electrical charge passing from the wire to
the work piece. These parameters significantly
RESEARCH ARTICLE OPEN ACCESS

influence quality of parts made by W-EDM process
[5].
Since W-EDMis widely used in many
manufacturing applications, many researchers have
optimized machining parameters to improve quality
and reduce production costs.Taguchi method is a
very useful technique used to achieve higher quality
and reduce product cost [2].Taguchi method has been
used to study the performance of W-ED Mto improve
the output variable characteristics such as surface
roughness, dimension accuracy, material removal rate
(MRR).Table1 shows the summary of related
research using Taguchi method to improve and
optimize the performance of W-EDM.
Table 1 Summary of the researches
No Author/Year Parameters
Performance
Measures
Remark
Technique
Used
1
Harpreet et al./
(2012)[6]
pulse on/ pulse
off time
MRR
It was discovered that
with an increase in pulse
on time the MRR
decreased, and inversely
with an increase in pulse
off time MRR increased.
Taguchi
Methodology
2
Parveen Kumar et
al/(2013) [7]
Pulse on time,
pulse of time,
wire speed rate,
wire tension
MRR, Wire
Wear Rate.
Surface
Roughness
The result was found that
the pulse on time and the
wire speed rate are the
most significant
parameters.
Taguchi
Methodology
3
Atul
Kumar(2012)[8]
voltage, feed rate,
pulse on time,
pulse off time,
wire feed, servo
voltage, wire
tension, flushing
pressure
MRR, Surface
Roughness
It was found that pulse
on time and voltage have
the most significant
effect on MRR and
surface roughness.
Taguchi
Methodology
4
G.Lakshmikanth(2
014)[9]
pulse on time,
pulse off time,
wire feed
MRR, Surface
Roughness
In an investigation of the
effect of pulse on time,
pulse off time, and wire
feed, the factor of pulse
on time had the most
significant effect on
MRR and surface
roughness.
Taguchi
Methodology
5
Alpesh M. Patel et
al/(2013)[10]
wire feed, wire
tension, discharge
current, discharge
voltage
Electrode
Wear Rate
(EWR), MRR
The study demonstrated
that discharge current,
discharge voltage, and
wire tension greatly
influence EWR and
MMR.
Taguchi
Methodology
6
Sameh S. Habib
(2014)[11]
pulse on time,
pulse off time,
discharge current,
voltage
MRR, Surface
Roughness,
Gapsize
The study found that the
pulse on time has the
most significant
influence on MRR,
surface roughness, and
gap size
Taguchi
Methodology
7
Lokeswara
Rao(2013)[12]
pulse on time,
pulse off time,
peak current,
wire tension,
servo voltage,
servo feed
MRR, Surface
Roughness
The study found the
optimum cutting
parameters for WEDM,
the minimum surface
roughness, and the
maximum MRR.
Taguchi
Methodology

8
Jasvinder Pal et
al/(2014)[13]
pulse on time,
pulse off time,
peak current wire
feed, servo
voltage
Surface
Roughness
It was found that the
pulse on time, pulse off
time, and servo voltage
have a significant effect
on surface roughness.
Taguchi
Methodology
9
Jaganathan P et
al/(2012)[14]
applied voltage,
discharge current,
pulse width,
pulse interval
MRR, Surface
Roughness
It was found that factors
like applied voltage,
pulse width, and speed
have played a significant
role on MRR and surface
roughness.
Taguchi
Methodology
10
K.Hari et
al/(2014)[15]
pulse on time,
pulse off time,
servo voltage,
wire feed, peak
current, servo
feed
MRR, Surface
Roughness
It was found that pulse
on time, pulse off time,
and peak current are the
most significant
parameters that affect the
MRR and surface
roughness.
Taguchi
Methodology
As seen from the literature review in Table 1,
some studies show that while optimizing output
variables by changing input parameters, two output
variables can be improvedindividually, but not
simultaneously. This would significantly hinder the
application of Taguchi method in industry setting for
process improvement when two output variables need
to be optimized simultaneously. The objective of this
research is to design an overarching framework by
which dual output variable improvement can be
accomplished using one parameter level setting. For
the purpose of this research, Taguchi method is used
to determine the optimal parameters for surface
roughness and angular accuracy of workpieces
machined byW-EDMmahcines. The
subsequentsections will present the methodology and
a case study with experimental verification used to
show its efficacy
II. Methodology
In this research Taguchi method and Signal-to-
Noise (S/N) ratioare used for comparative analysis of
parameters’ effect on response variables. Two
response variables are tested for W-EDM process
optimization.As shown in Fig 2, the following steps
outline the procedure of experimentation in a
systematic way to find the optimum results.
Step 1:The first step in this procedure is to select the
machining operation that will be used in experiment.
Once the machining operation is selected, measurable
output variables should be identified as well.
Measurable output variables (OV in Fig. 2) are those
variables chosen to meet the needsfrom industry,
such as dimensional accuracy, angular accuracy,
surface roughness, material removal rate, and
electrode wire rate, etc.
Step 2: After choosing measurable output variables,
the next step involves running a baseline experiment
for analysis. The baseline experimentproduces initial
results of each output variable as a starting point for
optimization. From the baseline analysis, an initial
understanding of the machine capability with respect
to the output variables is established. The baseline
experiment result is then used as a gauge to compare
with the result from Taguchi method to verify the
improvement.
Step 3: Select proper controllable factors and noise
factor. Proper selection of controllablefactors is vital
to product quality. In order to understand those
factors affecting the process, a fishbone diagram is
used to identify the possible causes of a problem.
Step 4: Taguchi Parameter Design and Orthogonal
Array (OA) Matrix. Taguchi method has three
segments: system design, parameter design, and
tolerance design [17]. In this study,Taguchi
parameter design is used to determine the optimal
levels for the controllable system parameters.
InTaguchi parameter design there are two types of
factors that can affect product quality -controllable
factors and noise factors. A factor is considered
controllable if it iseasily manipulatedandhas a
significant impact on product quality.In W-EDM
process, pulse on time, wire tension, and voltage are
examples of controllable factors.A noise factor may
have a negative effect on product quality, but cannot
be controlled; temperature, vibration, or humidityare
typicalexamples of noise factors in the application of
Taguchi method [17]. Taguchi parameter design has
been proved to be a reliable way to evaluate and
implement improvements on product and process
[18]. Moreover Taguchi method usesOAin its
experiment design [5]. The advantage of using OA is
the ability to study a large number of variables with a
smaller number of experiments [8], and therefore the
experiment can be conducted in a much more
economical way compared to traditional Design of
Experiment practices.

Fig. 2 Methodology framework for two output variables using Taguchi method
Step 5: After the requiredOA matrix is determined,
machining experiment can be performed and data can
be collected from the machined workpieces through
measurement using appropriate measurement
instruments. Once the data is collected, S/N ratio is
calculated to analyze the measurement data. S/N ratio
is able to determine which controllable factors have
moreimpact on the quality characteristics of the

product. There are three possible situations
whereS/Nratio can be calculated depending on the
quality characteristic to be optimized.
Smaller the better
S
N
= −10log⁡(
1
n
yi
2n
i=1 ) (1)
Nominal the better
S
N
= 10 log(
(
1
n
𝑦 𝑖
n
i=1 )2
Sy
2 ) (2)
Larger the better
S
N
= −10 log(
1
n
1
yi
2
n
i=1 ) (3)
Where yi
2
is the result of the observed value, and n is
the number of times the experiment is repeated.In this
research S/N ratio is defined as Smaller the better for
optimizingboth quality characteristics.
Followed by the data collection and analysis, a T-test
for 99% confidence is used to findout if the noise
factor significantly affects the quality characteristics.
H₀: µLEVEL1 of NOISE FACTOR= µLEVEL2 of NOISE FACTOR
H₁: µLEVEL1 of NOISE FACTOR≠ µLEVEL2 of NOISE FACTOR
WhereµLEVEL1 ofNOISE FACTORis the mean collected from
level one of the noise factor and µLEVEL2 of NOISE
FACTORis the meancollected from level two of the
noise factor.
Step 6: After analyzing the data,the optimal
parameter settings will either be identical or not. If
the optimal parameter settings are identical, then one
confirmation run is performed. In this situation, the
confirmation run is an additional set of experiments
performed to validate that improvement for both first
quality characteristic (QC1)and second quality
characteristic (QC2)areachieved. However, if the
optimal parameter level settings are not identical,
then two confirmations runs are needed. Each
confirmation run uses itsownparameter level settingto
test both output variables of QC1 and QC2. Even
though there are two confirmation runs performed on
varying parameter levels, only one parameter level
setting is needed eventually for both output variables
improvement.
Step 7: If the outcome does not lead to anoptimized
parameter setting for the two quality characteristics,
then further tests are needed. Using the results from
each of the confirmation runs for QC1 and QC2, two
separate hypotheses are proposed to test whether or
not a single optimized parameter level setting is
possible.
The first hypothesis test is executed to see ifQC1
mean usingoptimized parameter levelsettings for
QC1will be significantly different fromQC1mean
from running the machining operation using the
optimized level settings for QC2.
Ho: µQC1 (from opt Q1) =µQC1 (from opt QC2)
H1: µQC1 (from opt Q1) ≠µQC1 (from opt QC2)
Where µQC1(from opt QC1)is the QC1mean from running
experiments using the optimized parameter level
settingsfor QC1, and µQC1(from opt QC2) is the QC1mean
from running experiments using the optimized
parameter level settingsfor QC2.
Similarly, the second hypothesis test is conducted to
see if QC2mean using optimized parameter level
settings for QC2will be significantly different from
theQC2mean from running the experiment using the
optimized level settings for QC1.
Ho: µQC2 (from opt QC2) =µQC2 (from opt QC1)
H1: µQC2 (from opt QC2) ≠µQC2 (from opt QC1)
Where µQC2(from opt QC2)is the QC2mean from running
settings for QC2, and µQ2(from opt Q1)is the QC2mean
from running experiments using the optimized
parameter level settings forQC1.
From the hypothesis test, there are two possible
outcomes. The first outcome is that the null
hypothesis is not rejected. This is possible in three
different ways. The first is that both null hypotheses
are not rejected and the second and third are that we
fail to reject one of the two null hypotheses. In case
of the first outcome where the null hypothesis is not
rejected, one confirmation run is enough to improve
both output variables. The second outcome is that
both null hypotheses are rejected. In that situation,
additional testing must be performed as follows.
From the previous stage of the framework if both null
hypotheses are rejected, an adjustment confirmation
run will be performed. The parameter level settings
that are not identical are first adjusted to a value
between the two non-identical parameter values. The
experiment is then performed and two final
hypotheses are tested. The first hypothesis test is
done to see if QC1mean from the optimized
parameter level settings for QC1will be significantly
differentfrom the QC1mean obtained from the
adjusted parameter level settings.
Ho: µQC1 (from adjusted setting) = µQC1 (from opt QC1)
H1: µQC1 (from adjusted setting)≠ µQC1 (from optQC1)
Where µQC1(from adjusted setting)is theQC1mean from the
adjusted parameter level settings, andµQ1(from opt Q1)is
the QC1mean from the optimized parameter level
settings forQC1.
The second hypothesis test is conducted to see if
QC2meanfrom the optimized parameter level settings
forQC2will be significantly different from the
QC2meanobtained from the adjusted parameter level
settings.
Ho: µQC2 (from adjusted setting)= µQC2 (from opt QC2)
H1: µQC2 (from adjusted setting) ≠µQC2 (from optQC2)
Where µQ2(from adjusted setting) is the QC2mean from the
adjusted parameter level settings and µQ2(from optQ2)is
the QC2mean from the optimizedparameter level
settings for QC2.
Ideally if both output variables are expected for
optimization, one prefers to see that neither of thetwo
null hypotheses is rejected. In this case the output
from the adjusted parameter level settings is not
significantly different from the output from the
optimized parameter settings for each quality
characteristic. However if one of the null hypotheses
is rejected, then simultaneous improvement for both
output variables was technically not possiblewith a

single parameter level setting. When this happens,
there are two options for the user. One is to select the
parameter level settings based on the more
importantquality characteristicfrom the two under
investigation. However in reality the practitioner of
this methodology may inquire into the difference of
the output from the adjusted parameter level settings
and the output from the baseline study for both QC1
and QC2. If there turns out to be a considerable
improvement for both QC1 and QC2 by using the
adjusted parameter settings, then the second option is
to continue to use the adjusted parameter settings for
both QC1 and QC2, for they both can still be
improved although not optimized.
III. Case Study
The experiment was carried out on aSodick VZ
300LW-EDM machine. The wire used in this
experiment is made of brass with adiameter of
0.25mm, and the work piece material is1080
steelsheet with a thickness of 0.175”. Dimensions of
the work pieceare shown in Fig 3.
Fig. 3Work piece dimension
3.1 Selection of output variables
In this research surface roughness and angular
accuracy were selected as response variables. A
Mitutoyo SJ-301profilometerwas used for measuring
surface roughness and a Mitutoyo RV507 CMM
machine was used for angular accuracy measurement.
3.2 Baseline analysis
The baseline run in this study was conducted
using the default parameter level setting for the W-
EDM operation. The parameter levels are: pulse on
time at 12µs, wire feed rate at 35units, voltage of9v,
and wire tension of 160 gram. These settings
produced the following results as shown in Table 2.
Table 2 Baseline results
Run 1 2 3 4 5 6 7 8 9 10 Average
Surface
Roughness
Ra µin
147.9 141.7 136.1.9 144.2 140.2 138.9 145.7 139.1 140.9 142.6 142.4
Angular
Accuracy θº
0.0958 0.0637 0.0872 0.0781 0.0692 0.0725 0.0713 0.0961 0.0734 0.1018 0.082
3.3 Controllable factor and noise factor selection
The cause and effect diagram (fishbone diagram)
outlined possible significant factors that could affect
the machine conditions and lead to products with
inferior quality. Fig. 4 displays the cause and effect
diagram. With the cause and effectanalysis, four
machining parameters (pulse on time, wire feed rate,
voltage, and wire tension)were selectedin this
research as controllable factors. The selection of
thesefour controllable factors arebased upon the
previous literatures summarized in Table-1and their
correlation to the output variablesof this research.
Vibration was selected as noise factor in this research
since it most accurately represents an uncontrollable
factor as seen in the machine shop environment.

Fig. 4 Cause and effect diagram for poor surface roughness and angular accuracy
3.4 Designing OA matrix experiment
The next step is to implement Taguchi parameter
design and OA matrixexperiment for the controllable
factors and noise factor. Taguchi experiment is used
in this research for a reduced cost incurred in the
experimentation compared to traditional experiment
design. Taguchi experiment involves four
controllable factors including pulse on time, feed
rate, voltage, and wire tension, each of which has
three accompanying levels. Table 3 shows the
Taguchi parameters design where vibration is
considered as the noise factor for its uncontrollable
effect on product quality.
Table 3Taguchi parameters design
P
A
R
A
M
E
T
E
R
S
--- Symbol Level- 1 Level- 2 Level-3
Pulse on time T On(µs) 9 11 13
Feed Rate FR(in/min) 30 35 40
Voltage V(volt) 7 8 9
Wire Tension WT(gram) 155 160 165
Noise
Factors
Vibration V on Off
Response
Variables
dimensional of
angles
surface roughness
Selection ofOAis based on thenumber of controllable factors(4 controllable factors in this research) and their
levels (3 levels for each controllable factor). In this research the OA will be a L9 table by whichnine experiments
will be done to study four controllable factors at three different levels for adequate experimental analysis. Table
4 shows the experiment design using an OA L9 table.
Humidity
Operator
Training
Machine Precision
Pulse on Time
Wire Tension
Poor
Surface
Roughness
and
Angular
Accuracy
MethodsMaterialMachine
Environment
Outside Vibration
Material Thickness
Program/NC
code
Manpowe
r
Operator Experience
Wire Feed Rate
Voltage
Material Hardness
Material Conductivity
Tool Quality
Material Type
Tool Type
Temperature

Table 4 Experiments designed usingOA L9
Exp. No.
Control Factors Noise Factor
T on FR V WT Vibration Vibration
1 1 1 1 1 ON OFF
2 1 2 2 2 ON OFF
3 1 3 3 3 ON OFF
4 2 1 2 3 ON OFF
5 2 2 3 1 ON OFF
6 2 3 1 2 ON OFF
7 3 1 3 2 ON OFF
8 3 2 1 3 ON OFF
9 3 3 2 1 ON OFF
IV. Results and Discussion
Subsequent to the Taguchi-based experiment
implementation, an analysis was done to reveal the
effect of the pulse on time, wire feed rate, voltage,
and wire tension on the quality characteristics of
surface roughness and angle accuracy. The
experiments were conducted using the L9OA matrix.
Tables 5 and 6 show the experimental results for
surface roughness and angular accuracy, respectively.
The average value (Y-bar) and S/N ratio were
calculated at different levels for the response
characteristics. S/N ratio of smaller the betterwas
computed using equation (1)for both surface
roughness and angle accuracy. The angle accuracy
value was calculated by measuring the angle first,
then subtracting it from 90 degree to show the
absolute angular deviation.
Table 5 Experiment results for surface roughness
Exp.
No.
Y-bar S/N RatioT on FR V WT V on V off
1 1 1 1 1 124.5 123.9 124.2 -41.88
2 1 2 2 2 122.6 120.2 121.4 -41.68
3 1 3 3 3 123.7 122.5 123.1 -41.81
4 2 1 2 3 128.6 124.3 126.45 -42.04
5 2 2 3 1 132.8 130.1 131.45 -42.38
6 2 3 1 2 137.2 135.9 136.55 -42.71
7 3 1 3 2 139.1 140.8 139.95 -42.92
8 3 2 1 3 134.2 137.9 136.05 -42.67
9 3 3 2 1 145.6 138.3 141.95 -43.05
Table 6 Experiment results for angle accuracy
Exp.
No.
Y-bar S/N RatioT on FR V WT V on V off
1 1 1 1 1 0.2366 0.2458 0.2412 12.35
2 1 2 2 2 0.1275 0.1259 0.1267 17.94
3 1 3 3 3 0.2721 0.2546 0.26335 11.58
4 2 1 2 3 0.1211 0.1312 0.12615 17.98
5 2 2 3 1 0.1446 0.1261 0.13535 17.35
6 2 3 1 2 0.1107 0.1013 0.106 19.49
7 3 1 3 2 0.0855 0.0174 0.05145 24.19
8 3 2 1 3 0.1382 0.0644 0.1013 19.35
9 3 3 2 1 0.0447 0.096 0.07035 22.51
4.1 Data analysis for surface roughness
Tables 7and 8show the responses of mean and
S/Nratio ofsurface roughness. From the collected
data, pulse on time is the most significant factor in
affecting surface roughness while voltage and wire
tension are shown to be less significant factors. It can
be observed that surface roughness increases with an
increase in pulse on time, and surface roughness
decreases with an increase in wire tension. Also
surface roughness is higher with the first level of
voltage and the third level of wire feed rate but
decreases when using the middle two levels. Fig.5

shows that the optimal parameter settings for surface
roughnessarefirst level of pulse on time (A1), second
level of wire feed rate (B2), second level of voltage
(C2), and third level of wire tension (D3).
Table 7Response tableof mean for surface roughness ra µin
Level A (T on) B (FR) C (V) D (WT)
1 122.9 130.2 132.3 132.5
2 131.5 129.6 129.9 132.6
3 139.3 133.9 131.5 128.5
Table 8Response table of signal to noise (S/N) ratio for surface roughness
1 -41.79 -42.28 -42.42 -42.43
2 -42.37 -42.25 -42.26 -42.44
3 -42.88 -42.52 -42.37 -42.17
Fig. 5 Effects of controllable parameters on surface roughness and S/N ratio
After the optimization was completed,the effect of
noise factor on W-EDM process was also studied by
using aT-test to determine if vibration is significant
to surface roughness.
H₀: µRa (vibration On) = µRa (vibration Off)
H₁: µRa (vibration On) ≠ µRa (vibration Off)
Where µRa (vibration On) is the mean of vibration-on
values and µRa (vibration Off) is the meanof vibration-off
values obtained from Table 5.
By using equation,
t =
µRa (vibration On)
− µRa (vibration Off )
SRa (vibration On )
2 + SRa (vibration Off )
2
n1+n2
The t-value for surface roughness is 0.430 which is
smaller than t critical value of 2.92(with alpha = 0.01,
degree of freedom =16).Therefore the null hypothesis
is not rejected, which means the vibration does not
affect surface roughness.
4.2 Data analysis for angular accuracy
Tables 9 and 10shows the responsesof mean and
S/N ratio of angular accuracy. From the collected
data, pulse on time and wire tension are the most
significant factors affecting angular accuracy, while
voltage and feed rate are shown to be less significant.
It can be observed that angular accuracy decreases
with an increase in pulse on time, and angular
accuracy is the best with the middle level of wire
tension. When observing the results of feed rate and

voltage, the middle two levels give thelowest
deviation from the nominal 90-degree. Fig.6 shows
that the optimal parameter settings arethird level of
pulse on time (A3), second level of wire feed rate
(B2), second level of voltage (C2), and second level of
wire tension (D2).
Table 9Response table of mean for angular accuracy θº
1 0.210 0.140 0.150 0.149
2 0.123 0.121 0.108 0.095
3 0.074 0.147 0.150 0.164
Table 10Response table ofS/N ratio for angular accuracy
1 13.96 18.17 17.06 17.40
2 18.27 18.21 19.48 20.54
3 22.02 17.86 17.71 16.30
Fig. 6 Effects of controllable parameters on angular
accuracy and S/N ratio
After optimization was completed for angular
accuracy, another hypothesis test for noise factor on
W-EDM process was conducted to determine if
vibration is significant to angular accuracy.
H₀: µθ (vibration On) = µθ (vibration Off)
H₁: µθ (vibration On) ≠ µθ (vibration Off)
Where µθ (vibration On) is the mean of vibration-on values
and µθ(vibration Off) is the meanof vibration-off values
obtained from Table 6.
By using equation,
t =
xRa (vibration On )− xRa (vibration Off )
SRa (vibration On )
2 + SRa (vibration Off )
2
n1+n2
The t-value for angular accuracy is 0.3758 which
is smaller than t critical value of 2.92(with alpha =
0.01, degree of freedom =16).So the null hypothesis
is not rejected, which means that the vibration does
not affect angular accuracy.
The above data analysisshows that the optimal
parameter levelsare not identicalfor surface
roughness and angular accuracy. Surface roughness

has levels of A1, B2, C2, and D3, while angular
accuracy haslevels of A3, B2, C2, and D2. Hencetwo
confirmation runs are needed foreach quality
characteristic on their own optimal parameter level
settings.
V. Confirmation runs
Confirmation run is an additional set of
experiments performed using the optimal parameter
values as determined from the Taguchi experiments.
For this researchconfirmationrunsare used to validate
that improvementsfor both surface roughness and
angular accuracy can beaccomplished. Tables 11 and
12show the outcomes of confirmation runs for both
surface roughness and angular accuracy quality
characteristics.
Table 11 Confirmation run for surface roughness and confidence interval
Run 1 2 3 4 5 6 7 8 9 10
Surface
Roughness
Ra µin
112.3 113.4 115.9 116.7 115.2 108.9 113.5 118.7 112.6 117.9
Mean = 114.51 Standard Deviation= 2.954 Upper CI = 117.545
T-value (99%) = ± 3.250 N= 10 Lower CI = 111.475
Table 12 Confirmation run for angular accuracy and confidence interval
Run 1 2 3 4 5 6 7 8 9 10
Angular
Accuracy
θº
0.0082 0.011 0.007 0.0084 0.0079 0.012 0.0091 0.0098 0.0095 0.0067
Mean = 0.00896 Standard Deviation= 0.0017 Upper CI = 0.01069
T-value (99%) = ± 3.250 N= 10 Lower CI = 0.00723
Based on the optimal setting (A1, B2, C2, and D3)
forsurface roughness, the predicted optimal value for
surface roughness is given as:
Predicted Ra = µA1+ µB2+ µC2+ µD3 – 3* Y-Avg =
117.30µin
Based on the optimal setting (A3, B2, C2, and D2)
forangular accuracy, the predicted optimal value for
angular accuracy is given as:
Predicted θ = µA3+ µB2+ µC2+ µD2 – 3* Y-Avg =
0.00935º
The letters with a number subscript in the above
two representations denote the optimal parameter
selections, and Y-Avg is the average of all response
data. Through comparing the predicted values and the
results from comfirmation runs, it can be shown
thatboth confirmation runs actually rendered more
improvement than what was expected, and the
predicted values fell between the upper and lower
bounds. The mean of surface roughness from
confirmation run is 114.51 µin, which is less than the
predicted 117.30 µin, and the mean of angular
accuracy from confirmation run is 0.00896 º, less
than the predicted 0.00935º.
Given the results from confirmation runs, a final
T-test for 99% confidence interval was conducted to
confirm the expected level of experimental
repeatability. For surface roughness, it can be
expected with 99% confidence that a part cut on aW-
EDM machine will have surface roughness values
between 111.475µinand 117.545µin. Likewise, an
angle feature cut using aW-EDMmachine will be
within the deviation range of 0.00723ºto 0.01069ºat
99% confidence.
VI. Merging two quality characteristics
into one optimal parameter setting
The case study shows non-identical parameter
settings for the two quality characteristics. The
optimal parameter for surface roughness is A1, B2,
C2, and D3andthat for angular accuracyis A3, B2, C2,
and D2. In order to optimize both quality
characteristics simultaneously, it is necessary to
reachone optimal parameter setting that can optimize
both surface roughness and angular accuracy at the
same time.
In this research a T-test was used to determine if
there is a significant difference in mean between the
surface roughnessproduced by the optimal parameter
levels for surface roughness itself and the surface
roughnessproduced by the optimal parameter levels
for angular accuracy.
Ho: µRa (from opt Ra) =µRa(from opt θ)
H1: µRa (from opt Ra) ≠µRa(from opt θ)
Where µRa (from opt Ra) is the mean of surface
roughnessfrom the experiments using the optimized
parameter level settingfor surface roughness, and µRa
from opt (θ) is the mean of surface roughnessfrom
settingfor angular accuracy.
Table 13 shows boththe surface roughnessdata from
the optimized parameter level for surface roughness

itself and the data from the optimized parameter level
for angular accuracy (θ).
By using equation, t =
xRa (from opt Ra )− xRa (from opt θ)
SRa (from opt Ra )
2 + SRa (from opt θ)
2
n1+n2
The t-value is -16.05 which falls outside of t-
critical value +/-2.898 (with alpha=0.01 degree of
freedom=18). Thus the null hypothesis is rejected.
The conclusion is that the non-identical parameter
setting doesaffect surface roughness.
Table 13 T-test comparing of two data (surface vs.
angular) for Ra
No.
(Ra) from opt
Surface
Roughness
(Ra) from
opt Angular
accuracy
1 112.3 133.6
2 113.4 141.1
3 115.9 145.6
4 116.7 134.7
5 115.2 138.6
6 108.9 139.7
7 113.5 135.2
8 118.7 137.9
9 112.6 135.6
10 117.9 138.2
Average 114.51 138.02
Standard
Deviation
2.95 3.57
SE Mean 1.46
T-value -16.05
Degree of
Freedom
17
T- alpha
value .01
± 2.898
Table 14 T-test comparing of two data (surface vs.
angular) for θ
No.
(θ) from opt
Angular
accuracy
(θ) from opt
Surface
Roughness
1 0.0082 0.0514
2 0.011 0.044
3 0.007 0.0925
4 0.0084 0.067
5 0.0079 0.0566
6 0.012 0.0426
7 0.0091 0.0866
8 0.0098 0.0372
9 0.0095 0.0361
10 0.0067 0.0964
Average 0.00896 .0610
Standard
Deviation
0.00168 0.0232
SE Mean 0.00737
T-value -7.067
Degree
of
Freedom
9
T- alpha
value .01
± 3.250
Similarly T-test was also used to determine if there is
a significant difference between the mean of angular
accuracyproduced bythe optimized parameter levels
for angular accuracy itself and the mean ofangular
accuracy produced by the optimized parameter level
for surface roughness.
Ho: µθ(from opt θ) =µθ (from opt Ra)
H1: µθ(from opt θ)≠µθ(from opt Ra)
Where µθ(from opt θ) is the mean of angular accuracy
from the experiments using the optimized parameter
level for angular accuracy, and µθ(from opt Ra) is the
mean of angular accuracy from the experiments using
the optimized parameter level for surface roughness.
Table 14 shows both the angular accuracy data from
the optimized parameter level for angular accuracy
and the data from the optimized parameter level for
surface roughness.
By using equation, t =
xθ(from opt θ)− xθ (from opt Ra )
Sθ(from opt θ)
2 + Sθ (from opt Ra )
2
n1+n2
The t-value is -7.067 which falls outside of t-critical
value ±3.250 (with alpha=0.01 degree of
freedom=18), and therefore the null hypothesis is
rejected. The conclusion is that the non-identical
parameter setting does affect angular accuracy.
Since both null hypotheses were rejected with the
above two T-tests, the optimal parameter settings for
surface roughness and angular accuracy need to be
adjusted into one optimal setting. With surface
roughness optimal levels of A1, B2, C2, and D3 and
angular accuracy optimal levels of A3, B2, C2, and D2,
the adjusted optimal levels are made at the middle
points of each individual parameter. Hence the
adjusted optimal levels in this case study are A2, B2,
C2, and D2.5.A final run was conducted using the
adjusted parameter level setting. Table 15 shows the
data collected from the finalrunwith the measurement
of the surface roughness and angular accuracyunder
the newly adjusted parameter settings of A2, B2, C2,
and D2.5. This data was then further compared in
another T-test to the data collected from the
confirmation runs made using each separate
optimized parameter level setting.

Table 15 Final runs with adjusted parameter for surface roughness and angular accuracy
A T-test was used to determine if there is a
significant difference between themean of surface
roughness(Ra)from the adjusted parameter levels and
themean of surface roughness(Ra)from the optimized
parameter levels for surface roughness.
Ho: µRa(from adjusted setting) = µRa(from opt Ra)
H1: µRa(from adjusted setting) ≠ µRa(from opt Ra)
Where µRa(from adjusted setting) is the mean ofsurface
roughness (Ra)from the adjusted parameter level
setting, and µRa(from opt Ra)is the mean of surface
roughness (Ra) from the optimized parameter level
setting forsurface roughness.Table 16 shows
thesurface roughness (Ra)from the adjusted
parameter level and thesurface roughness(Ra)from
the optimized parameter level for surface roughness.
By using equation,
t =
xRa (from adjusted setting ) − xRa (from opt Ra )
SRa (from adjusted setting )
2 + SRa (from opt Ra )
2
n1+n2
The t-value is -5.52 which falls outside of t-critical
value +/-3.250 (with alpha=0.01 degree of
freedom=18),therefore the null hypothesis is rejected.
This result means that the adjustment of parameter
levels does affect surface roughness.
Table 16T-test comparing of two data (surface vs.
adjusted) for Ra
No.
(Ra) from opt
Surface
Roughness
(Ra)from
Adjusted
Parameter
1 112.3 123.6
2 113.4 118.9
3 115.9 124.7
4 116.7 125.6
5 115.2 117.2
6 108.9 123.1
7 113.5 124
8 118.7 119.3
9 112.6 121.9
10 117.9 119.1
Average 114.51 121.74
Standard
Deviation
2.95 2.90
SE Mean 1.31
T-value -5.52
Degree of 9
Freedom
T- alpha
value .01
±3.250
Table 17 T-test comparing of two data (angular vs.
adjusted) for θ
No.
(θ) from opt
Angular accuracy
(θ)from
Adjusted
Parameter
1 0.0082 0.0423
2 0.011 0.0234
3 0.007 0.0306
4 0.0084 0.0365
5 0.0079 0.0317
6 0.012 0.0487
7 0.0091 0.0503
8 0.0098 0.0291
9 0.0095 0.0467
10 0.0067 0.0483
Average 0.00896 0.0388
Standard
Deviation
0.00168 0.0097
SE Mean 0.0031
T-value -9.56
Degree of
Freedom
10
T- alpha
value .01
±3.169
T-test was also used to determine if there is a
significant difference in mean value between the
angular accuracy(θ) collected from the adjusted
parameter level and theangular accuracy(θ)collected
from the optimized level for angular accuracy.
Ho: µθ(from adjusted setting) =µθ(from opt θ)
H1: µθ(from adjusted setting) ≠µθ(from opt θ)
Where µθ(from adjusted setting) is the mean of angular
accuracy(θ) from the adjusted parameter level setting,
and µθ(from opt θ) is the mean ofangular accuracy(θ)
from the optimized level settingfor angular accuracy.
Table 17 shows theangular accuracy(θ)from the
adjusted parameter level and the angular
accuracy(θ)from the optimized level for angular
accuracy.
Run 1 2 3 4 5 6 7 8 9 10
Averag
e
Surface
Roughnes
s Ra µin
123.6 118.9 124.7 125.6 117.2 123.1 124 119.3 121.9 119.1 121.7
Angular
Accuracy
θº
0.042
3
0.023
4
0.030
6
0.036
5
0.031
7
0.048
7
0.050
3
0.029
1
0.046
7
0.048
3
0.0388

By using equation,
t =
xθ(from adjusted setting ) − xµθ(from opt θ)
Sθ(from adjusted setting )
2 + Sµθ(from opt θ)
2
n1+n2
The t-value is -9.56 which is falls outside of t-critical
value +/-3.169 (with alpha=0.01 degree of
freedom=18),and the null hypothesis is rejected.
Consequently the adjustment of parameter levels
affects angular accuracy.
The finding of T-test shows that for both surface
roughness and angular accuracy the null hypotheses
are rejected. With both null hypotheses rejected, it is
concluded that a single optimized parameter level
setting could not be used for optimizing both output
variables at the same time. In this situation, one
optimized parameter level setting, either for surface
roughness or angular accuracy, should be chosen
depending on which quality characteristic is more
important to the user. Alternatively the user could
compare the outputs from the adjusted parameter
level setting with the outputs from baseline study. If
there is considerable improvement for both quality
characteristics from the responses of baseline study,
it is still worthy of using the adjusted parameter level
setting.
VII. Conclusion
This research presents a framework based on
Taguchi parameter design to optimize two quality
characteristics- surface roughness and angular
accuracy in Wire Electrical Discharge Machining
(W-EDM) process. Four factors were investigated as
controllable factors including pulse on time, wire
feed rate, voltage, and wire tension, while one factor-
vibration is considered as noise factor. The analysis
of experimental results concludes that pulse on time
is the most significant factor that impacts both
surface roughness and angle accuracy. Wire tension
is secondarysignificantto angle accuracy but was
shown to have lessinflunece on surface roughness.
Voltage was shown to have some effect on the
outputvariables while wire feed rate had little or no
effect.
From the initial baseline study, the output
variables of surface roughness and angular accuracy
were found to have average values of 142.4µin and
0.082º. By using Taguchi method with a L9 table
experiment design, the optimized parameter level
setting for each individual quality characteristic was
found. The confirmationrun conducted for surface
roughness had an average value of 114.51µin while
the confirmationrunconducted for angular accuracy
had an average value of 0.00896º.The difference in
optimal parameter level setting for these two output
variableslead to the adjustment of parameter levels
into one setting for further data analysis. Hence two
more runs of experiments were performed for each
output variable using the adjusted parameter setting.
Data analysis shows that the surface roughness value
was found to be 121.7µin, and the angular accuracy
value was found to be 0.0388º under the adjusted
parameter setting. Although the adjusted parameter
setting did not yield the same results compared to the
optimized parameter setting for each output variables,
overall improvement was still observed. As future
work, the authors plan to apply this methodology to
study the effect of other machining conditions such
as different wire type and work piece material on
other quality characteristics such as material removal
rate (MRR) and electrode wear ratio (EWR).
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Development of a Taguchi-based framework for optimizing two quality characteristics in Wire-EDM operations