Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
Este es un artículo de acceso abierto distribuido bajo los términos de una licencia de uso y distribución CC BY-NC 4.0. Para ver
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1
Complementary Material: Parametric Optimization of EN-31 Steel Using
Electric Discharge Machining
Material Complementario: Optimización paramétrica del acero EN-31 mediante
mecanizado por descarga eléctrica
Material Complementar: Otimização paramétrica do aço EN-31 utilizando
usinagem por eletroerosão
Muhammad Mansoor Uz Zaman Siddiqui
1
(*), Syed Amir Iqbal
2
, Ali Zulqarnain
3
, Adeel Tabassum
4
Recibido: 09/12/2025 Aceptado: 04/02/2026
Summary. - This investigative study was conducted for the parametric optimization of EN-31 material by using a non-
conventional machining known as Electric discharge machining (EDM). EN-31 is a steel alloy that is generally used in
aerospace industry, automotive parts manufacturing, die making etc. because it possesses high degree of rigidity with
extremely good compressive strength and resistance to abrasion. The primary objective of this study was to analyze the
impact of four input factors i.e. pulse on time (Ton), pulse off time (Toff), current (LV), voltage (HV) on the five output
responses i.e. machining time (Tm), MRR, EWR, Ra and base radius (R). In this study design of experiment (DOE)
approach with full factorial design was systematically conducted. Basic experimental runs were prepared and performed
and after that data was analyzed using ANOVA to identify significant input factors that has most impact on each output
response that are mentioned above. After identification of significant factors optimized input factors and output
responses were calculated using ANOVA. The results showed that for machining time (Tm), LV and Ton were
significant factors with optimized values of 50 A and 6.5 µs, respectively, resulting in a Tm of 654.29 seconds. For
material removal rate (MRR), Ton was the significant factor with an optimized value of 6.5 µs, achieving a maximum
MRR of 0.0157 g/min. For electrode wear rate (EWR), LV and Ton were significant with optimized values of 30 A
and 4 µs, respectively, resulting in a minimum EWR of 0.07 g/min. Ra optimization revealed that the combination of
HV, LV, Ton and Toff were significant, with optimized settings of 50 A, 0.7 V, 4.0 µs and 6.5 µs, respectively, yielding
a minimum Ra of 0.018 mm. For base radius (R), the significant factors were HV, LV, Ton and Toff, with optimized
values of 0.6152 V, 50 A, 6.5 µs and 6.5 µs, respectively, resulting in a base radius of 1.5 mm. This parametric
optimization is extremely significant because EN-31 is a material used in critical applications requiring high strength,
hardness and abrasion resistance such as automobile engine components, aerospace rocket parts and dies subjected to
extreme temperatures and pressures throughout their lifecycle. Optimizing EDM parameters facilitates the use of this
non-conventional machining process for manufacturing EN-31 parts thus enabling researchers, manufacturers,
designers and industry practitioners to achieve higher productivity, excellent surface finishes and lower manufacturing
costs as compared to traditional manufacturing techniques. This optimization allows for more efficient and effective
production of high-performance parts thus making it an invaluable advancement in various industrial sectors.
Keywords: EDM; Parameters; Machining; Processing; Roughness, EN-31; Optimization; DOE.
1
Engineer, Industrial and Manufacturing Engineering Department, University of Engineering and Technology Lahore (Pakistan),
mansoorresearch1986@gmail.com, ORCID iD: https://orcid.org/0009-0007-8992-7601
2
Professor, Department of Industrial Engineering, NED University of Engineering & Technology (Pakistan), samir@neduet.edu.pk,
ORCID iD: https://orcid.org/0000-0002-6812-6238
3
Assistant Professor, Department of Industrial Engineering, NED University of Engineering & Technology (Pakistan), alizul@neduet.edu.pk,
ORCID iD: https://orcid.org/0000-0001-5919-7811
4
Engineer, National University of Sciences and Technology (Pakistan), adeeltabassum1@gmail.com,
ORCID iD: https://orcid.org/0009-0006-9375-1090
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
2
Resumen. - Este estudio de investigación se realizó para la optimización paramétrica del material EN-31 utilizando
un mecanizado no convencional conocido como mecanizado por descarga eléctrica (EDM). El EN-31 es una aleación
de acero que se utiliza generalmente en la industria aeroespacial, la fabricación de piezas de automóviles, la
fabricación de matrices, etc., debido a que posee un alto grado de rigidez con una resistencia a la compresión y a la
abrasión extremadamente buenas. El objetivo principal de este estudio fue analizar el impacto de cuatro factores de
entrada, a saber, tiempo de pulso encendido (Ton), tiempo de pulso apagado (Toff), corriente (LV) y voltaje (HV) en
las cinco respuestas de salida, a saber, tiempo de mecanizado (Tm), MRR, EWR, Ra y radio base (R). En este estudio
se llevó a cabo sistemáticamente un enfoque de diseño de experimentos (DOE) con un diseño factorial completo. Se
prepararon y realizaron ensayos experimentales básicos y luego se analizaron los datos utilizando ANOVA para
identificar los factores de entrada significativos que tienen el mayor impacto en cada respuesta de salida mencionada
anteriormente. Después de la identificación de los factores significativos, los factores de entrada optimizados y las
respuestas de salida se calcularon utilizando ANOVA. Los resultados mostraron que para el tiempo de mecanizado
(Tm), LV y Ton fueron factores significativos con valores optimizados de 50 A y 6,5 µs, respectivamente, lo que resultó
en un Tm de 654,29 segundos. Para la tasa de remoción de material (MRR), Ton fue el factor significativo con un valor
optimizado de 6,5 µs, logrando un MRR máximo de 0,0157 g/min. Para la tasa de desgaste del electrodo (EWR), LV y
Ton fueron significativos con valores optimizados de 30 A y 4 µs, respectivamente, lo que resultó en un EWR mínimo
de 0,07 g/min. La optimización de Ra reveló que la combinación de HV, LV, Ton y Toff fueron significativas, con
configuraciones optimizadas de 50 A, 0,7 V, 4,0 µs y 6,5 µs, respectivamente, lo que produjo un Ra mínimo de 0,018
mm. Para el radio base (R), los factores significativos fueron HV, LV, Ton y Toff, con valores optimizados de 0,6152
V, 50 A, 6,5 µs y 6,5 µs, respectivamente, lo que resultó en un radio base de 1,5 mm.
Palabras clave: EDM; Parámetros; Mecanizado; Procesamiento; Rugosidad; EN-31; Optimización; DOE.
Resumo. - Este estudo investigativo foi conduzido para a otimização paramétrica do material EN-31 utilizando uma
usinagem não convencional conhecida como eletroerosão (EDM). O EN-31 é uma liga de aço geralmente utilizada
nas indústrias aeroespacial, de autopeças, de matrizes, etc., devido à sua alta rigidez, excelente resistência à
compressão e à abrasão. O objetivo principal deste estudo foi analisar o impacto de quatro fatores de entrada, ou seja,
tempo de pulso ligado (Ton), tempo de pulso desligado (Toff), corrente (LV) e tensão (HV), sobre as cinco respostas
de saída, ou seja, tempo de usinagem (Tm), taxa de remoção de material (MRR), taxa de desgaste da ferramenta
(EWR), rugosidade superficial (Ra) e raio da base (R). Neste estudo, foi aplicada uma abordagem de planejamento de
experimentos (DOE) com planejamento fatorial completo. Ensaios experimentais básicos foram preparados e
realizados, e os dados foram analisados por meio de ANOVA para identificar os fatores de entrada significativos que
mais impactam cada resposta de saída mencionada. Após a identificação dos fatores significativos, os fatores de
entrada otimizados e as respostas de saída foram calculados utilizando ANOVA. Os resultados mostraram que, para
o tempo de usinagem (Tm), a tensão de limiar (LV) e a taxa de variação da corrente (Ton) foram fatores significativos,
com valores otimizados de 50 A e 6,5 µs, respectivamente, resultando em um Tm de 654,29 segundos. Para a taxa de
remoção de material (MRR), a Ton foi o fator significativo, com um valor otimizado de 6,5 µs, atingindo uma MRR
máxima de 0,0157 g/min. Para a taxa de desgaste do eletrodo (EWR), a LV e a Ton foram significativas, com valores
otimizados de 30 A e 4 µs, respectivamente, resultando em uma EWR mínima de 0,07 g/min. A otimização da
rugosidade média (Ra) revelou que a combinação de alta tensão (HV), LV, Ton e Toff foi significativa, com
configurações otimizadas de 50 A, 0,7 V, 4,0 µs e 6,5 µs, respectivamente, resultando em uma Ra mínima de 0,018
mm. Para o raio da base (R), os fatores significativos foram HV, LV, Ton e Toff, com valores otimizados de 0,6152 V,
50 A, 6,5 µs e 6,5 µs, respectivamente, resultando em um raio da base de 1,5 mm.
Palavras-chave: EDM; Parâmetros; Usinagem; Processamento; Rugosidade; EN-31; Otimização; CORÇA.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
3
1. Experimental Inputs for EN-31 and all Replicates. -
Run
Order
HV
LV
Ton
Toff
Work
Piece
Material
Electrode
Material
Ea
Wa
Duty
Factor
%
1
0.3
30
4
5.5
EN31
Copper
17.353
218.795
42%
2
0.7
30
4
5.5
EN31
Copper
17.22
218.632
42%
3
0.3
50
4
5.5
EN31
Copper
17.512
218.462
42%
4
0.7
50
4
5.5
EN31
Copper
17.379
218.297
42%
5
0.3
30
6.5
5.5
EN31
Copper
14.833
218.122
54%
6
0.7
30
6.5
5.5
EN31
Copper
14.709
217.94
54%
7
0.3
50
6.5
5.5
EN31
Copper
18.872
217.754
54%
8
0.7
50
6.5
5.5
EN31
Copper
18.75
217.578
54%
9
0.3
30
4
6.5
EN31
Copper
11.438
217.384
38%
10
0.7
30
4
6.5
EN31
Copper
11.31
217.22
38%
11
0.3
50
4
6.5
EN31
Copper
13.924
217.065
38%
12
0.7
50
4
6.5
EN31
Copper
13.774
216.896
38%
13
0.3
30
6.5
6.5
EN31
Copper
17.868
216.732
50%
14
0.7
30
6.5
6.5
EN31
Copper
17.75
216.558
50%
15
0.3
50
6.5
6.5
EN31
Copper
16.041
216.377
50%
16
0.7
50
6.5
6.5
EN31
Copper
15.901
216.182
50%
17
0.3
30
4
5.5
EN31
Copper
14.624
216.047
42%
18
0.7
30
4
5.5
EN31
Copper
14.515
215.907
42%
19
0.3
50
4
5.5
EN31
Copper
11.844
215.739
42%
20
0.7
50
4
5.5
EN31
Copper
11.719
215.561
42%
21
0.3
30
6.5
5.5
EN31
Copper
17.35
215.387
54%
22
0.7
30
6.5
5.5
EN31
Copper
17.23
215.201
54%
23
0.3
50
6.5
5.5
EN31
Copper
17.395
215.03
54%
24
0.7
50
6.5
5.5
EN31
Copper
17.268
214.838
54%
25
0.3
30
4
6.5
EN31
Copper
14.872
214.648
38%
26
0.7
30
4
6.5
EN31
Copper
14.735
214.492
38%
27
0.3
50
4
6.5
EN31
Copper
10.39
214.322
38%
28
0.7
50
4
6.5
EN31
Copper
10.252
214.155
38%
29
0.3
30
6.5
6.5
EN31
Copper
10.011
213.997
50%
30
0.7
30
6.5
6.5
EN31
Copper
9.887
213.82
50%
31
0.3
50
6.5
6.5
EN31
Copper
17.405
213.668
50%
32
0.7
50
6.5
6.5
EN31
Copper
17.266
213.493
50%
33
0.3
30
4
5.5
EN31
Copper
17.542
218.109
42%
34
0.7
30
4
5.5
EN31
Copper
17.418
217.955
42%
35
0.3
50
4
5.5
EN31
Copper
14.917
217.797
42%
36
0.7
50
4
5.5
EN31
Copper
14.785
217.603
42%
37
0.3
30
6.5
5.5
EN31
Copper
15.222
217.43
54%
38
0.7
30
6.5
5.5
EN31
Copper
15.088
217.256
54%
39
0.3
50
6.5
5.5
EN31
Copper
17.929
217.065
54%
40
0.7
50
6.5
5.5
EN31
Copper
17.807
216.91
54%
41
0.3
30
4
6.5
EN31
Copper
10.625
216.73
38%
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
4
42
0.7
30
4
6.5
EN31
Copper
10.49
216.57
38%
43
0.3
50
4
6.5
EN31
Copper
14.119
216.39
38%
44
0.7
50
4
6.5
EN31
Copper
13.97
216.226
38%
45
0.3
30
6.5
6.5
EN31
Copper
13.812
216.06
50%
46
0.7
30
6.5
6.5
EN31
Copper
13.672
215.903
50%
47
0.3
50
6.5
6.5
EN31
Copper
14.06
215.707
50%
48
0.7
50
6.5
6.5
EN31
Copper
13.942
215.538
50%
Table II. Experimental Inputs for EN-31 and all Replicates.
2. Experimental Responses for EN-31 material and all Replicates. -
Run
Order
Machining
Time
MRR
MRR
EW
EW
Base
Radius
Surface
Roughness
(Ra)
(sec)
(g/min)
(mm3/min)
(g/min)
(mm3/min)
1
752
0.01301
1.67
0.01061
1.37
1.521
0.033
2
677
0.01507
1.93
0.01064
1.37
1.606
0.036
3
740
0.01338
1.71
0.01078
1.39
1.562
0.037
4
773
0.01358
1.74
0.01017
1.31
1.552
0.047
5
889
0.01228
1.57
0.00837
1.08
1.531
0.071
6
612
0.01824
2.33
0.01108
1.43
1.54
0.024
7
632
0.01671
2.14
0.01158
1.49
1.547
0.033
8
436
0.0267
3.42
0.01651
2.13
1.569
0.018
9
778
0.01265
1.62
0.00987
1.27
1.529
0.02
10
1003
0.00927
1.19
0.00754
0.97
1.527
0.021
11
1066
0.00951
1.22
0.00844
1.09
1.589
0.014
12
1104
0.00891
1.14
0.0075
0.97
1.531
0.022
13
617
0.01692
2.17
0.01147
1.48
1.539
0.047
14
427
0.02543
3.26
0.01728
2.23
1.573
0.022
15
638
0.01834
2.35
0.01317
1.7
1.615
0.019
16
452
0.01792
2.29
0.015
1.93
1.561
0.031
17
1251
0.00671
0.86
0.00523
0.67
1.723
0.013
18
1294
0.00779
1
0.00603
0.78
1.411
0.015
19
809
0.0132
1.69
0.00927
1.19
1.766
0.029
20
784
0.01332
1.71
0.01026
1.32
1.632
0.009
21
1051
0.01062
1.36
0.00685
0.88
1.667
0.012
22
535
0.01918
2.46
0.01234
1.59
1.57
0.028
23
458
0.02515
3.22
0.01664
2.14
1.6
0.021
24
635
0.01795
2.3
0.01162
1.5
1.592
0.045
25
1282
0.0073
0.93
0.00641
0.83
1.631
0.059
26
1357
0.00752
0.96
0.00557
0.72
1.493
0.035
27
1212
0.00827
1.06
0.00683
0.88
1.621
0.046
28
1107
0.00856
1.1
0.00748
0.96
1.612
0.018
29
931
0.01141
1.46
0.00799
1.03
1.588
0.024
30
1027
0.00888
1.14
0.00789
1.02
1.568
0.032
31
780
0.01346
1.72
0.01069
1.38
1.616
0.023
32
699
0.01485
1.9
0.01047
1.35
1.421
0.02
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
5
33
1073
0.00861
1.1
0.00693
0.89
1.833
0.011
34
1137
0.00834
1.07
0.0066
0.85
1.701
0.074
35
803
0.0145
1.86
0.00986
1.27
1.501
0.029
36
1260
0.00824
1.05
0.00595
0.77
1.458
0.04
37
1029
0.01015
1.3
0.00781
1.01
1.609
0.011
38
1033
0.01109
1.42
0.00697
0.9
1.587
0.03
39
837
0.01111
1.42
0.00875
1.13
1.63
0.006
40
810
0.01333
1.71
0.00956
1.23
1.587
0.03
41
1347
0.00713
0.91
0.00601
0.77
1.789
0.016
42
1214
0.0089
1.14
0.00618
0.8
1.697
0.017
43
902
0.01091
1.4
0.00945
1.22
1.412
0.027
44
1010
0.00986
1.26
0.00737
0.95
1.756
0.014
45
1014
0.00929
1.19
0.00828
1.07
1.464
0.029
46
688
0.01709
2.19
0.01099
1.42
1.86
0.014
47
552
0.01837
2.35
0.01283
1.65
1.777
0.02
48
787
0.01281
1.64
0.01067
1.37
1.23
0.021
Table III. Experimental Responses for EN-31 material and all Replicates.
3. EN-31 Workpiece Surface. - The images of EN-31 workpiece were taken at a magnification of 22 X.
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
1
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.3, LV = 30
2
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.7, LV = 30
3
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.3, LV = 50
4
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.7, LV = 50
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
6
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
5
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.3, LV = 30
6
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.7, LV = 30
7
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.3, LV = 50
8
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.7, LV = 50
9
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.3, LV = 30
10
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.7, LV = 30
11
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.3, LV = 50
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
7
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
12
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.7, LV = 50
13
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.3, LV = 30
14
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.7, LV = 30
15
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.3, LV = 50
16
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.7, LV = 50
Table IV. EN 31Workpiece Surface 22 X.
4. Copper Electrode Surface which Machined EN-31. - The electrode images that machined EN-31 were taken at a
magnification level of 17 X.
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
1
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.3, LV = 30
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
8
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
2
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.7, LV = 30
3
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.3, LV = 50
4
Ton = 4µs,Toff5.5 µs,Duty Factor = 42%, HV = 0.7, LV = 50
5
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.3, LV = 30
6
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.7, LV = 30
7
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.3, LV = 50
8
Ton = 6.5µs,Toff5.5 µs,Duty Factor = 54%, HV = 0.7, LV = 50
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
9
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
9
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.3, LV = 30
10
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.7, LV = 30
11
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.3, LV = 50
12
Ton = 4µs,Toff6.5 µs,Duty Factor = 38%, HV = 0.7, LV = 50
13
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.3, LV = 30
14
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.7, LV = 30
15
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.3, LV = 50
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
10
Experimental Runs
Replicate # 1
Replicate # 2
Replicate # 3
16
Ton = 6.5µs,Toff6.5 µs,Duty Factor = 50%, HV = 0.7, LV = 50
Table V. EN 31 – Copper Electrode – 17 X.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
11
5. Statistical Analysis of Experimental Results. -
5.1 Analysis of Results of EN-31. - The Minitab Analysis of the results of responses on EN-31 will be discussed in
this section.
5.2 Analysis of Results of Machining Time (Tm) for EN-31. - The ANOVA table for Tm is prepared in Minitab
considering all factors and then the significant factors are determined having p-value less than 0.05. The goal is kept in
mind i.e. Minimization of Machining Time.
Table VI. ANOVA Table of Tm for EN-31 considering all factors
Factorial Fit: Tm versus HV, LV, TON, TOFF
Estimated Effects and Coefficients for Tm (coded units)
TermEffectCoef SE Coef T P
Constant 881.3 30.82 28.59 0.000
HV -24.2 -12.1 30.82 -0.39 0.697
LV -155.5 -77.7 30.82 -2.52 0.017
TON -298.6 -149.3 30.82 -4.84 0.000
TOFF 70.2 35.1 30.82 1.14 0.264
HV*LV 59.9 30.0 30.82 0.97 0.338
HV*TON -83.0 -41.5 30.82 -1.35 0.188
HV*TOFF 3.9 2.0 30.82 0.06 0.950
LV*TON -22.6 -11.3 30.82 -0.37 0.717
LV*TOFF 40.8 20.4 30.82 0.66 0.512
TON*TOFF -98.9 -49.5 30.82 -1.60 0.118
HV*LV*TON 34.3 17.2 30.82 0.56 0.581
HV*LV*TOFF -38.1 -19.0 30.82 -0.62 0.541
HV*TON*TOFF 28.0 14.0 30.82 0.45 0.653
LV*TON*TOFF 4.6 2.3 30.82 0.07 0.941
HV*LV*TON*TOFF 8.5 4.3 30.82 0.14 0.891
S = 213.560 PRESS = 3283765
R-Sq = 54.35% R-Sq(pred) = 0.00% R-Sq(adj) = 32.95%
Analysis of Variance for Tm (coded units)
Source DF Seq SS AdjSSAdj MS F P
Main Effects 4 1426124 1426124 356531 7.82 0.000
2-Way Interactions 6 269475 269475 44912 0.98 0.452
3-Way Interactions 4 41210 41210 10302 0.23 0.922
4-Way Interactions 1 867 867 867 0.02 0.891
Residual Error 32 1459451 1459451 45608
Pure Error 32 1459451 1459451 45608
Total 47 3197127
Unusual Observations for Tm
ObsStdOrder Tm Fit SE Fit Residual St Resid
2 2 677.00 1036.00 123.30 -359.00 -2.06R
9 9 778.00 1135.67 123.30 -357.67 -2.05R
R denotes an observation with a large standardized residual.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
12
Table VII. Coefficient Table of Tm for EN-31 considering all factors.
3210-1-2-3-4-5
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A HV
B LV
C TO N
D TO F F
F actor N ame
Not Significant
Significant
Effect Type
C
B
Normal Plot of the Standardized Effects
(response is Tm, Alpha = 0.05)
Figure II. Normal Probability Plot of the standardized effects of Tm for EN-31 considering all factors.
5002500-250-500
99
90
50
10
1
Residual
Percent
12001050900750600
400
200
0
-200
-400
Fitted Value
Residual
3201600-160-320
10.0
7.5
5.0
2.5
0.0
Residual
Frequency
454035302520151051
400
200
0
-200
-400
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Tm
Figure III. Residual Plot of Tm for EN-31 considering all factors.
The ANOVA table as well as the Normal Probability Plot indicates that LV and Pulse On Time are significant factors
when considering Tm for EN-31. Now, the model is refitted by eliminating the non-significant values and
considering only LV and Pulse On Time as input factors.
Estimated Coefficients for Tm using data in uncoded units
Term Coef
Constant 1128.9
HV -3789.8
LV -116.122
TON 627.83
TOFF -54.34
HV*LV 200.279
HV*TON -296.67
HV*TOFF 907.25
LV*TON 3.6633
LV*TOFF 20.6042
TON*TOFF -81.800
HV*LV*TON -13.533
HV*LV*TOFF -36.892
HV*TON*TOFF -24.00
LV*TON*TOFF -1.3333
HV*LV*TON*TOFF 3.4000
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
13
Table VIII. ANOVA Table of Tm for EN-31 considering significant factors.
The p-values from the ANOVA table of refitted MODEL indicate that the models and these factors are significant.
3210-1-2-3-4-5-6
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
Not Significant
Significant
Effect Type
TON
LV
Normal Plot of the Standardized Effects
(response is Tm, Alpha = 0.05)
Figure IV. Normal Probability Plot of the standardized effects of Tm for EN-31 considering significant factors.
Factorial Fit: Tm versus LV, TON
Estimated Effects and Coefficients for Tm (coded units)
TermEffectCoef SE Coef T P
Constant 881.3 29.16 30.22 0.000
LV -155.5 -77.7 29.16 -2.67 0.011
TON -298.6 -149.3 29.16 -5.12 0.000
S = 202.053 PRESS = 2090257
R-Sq = 42.54% R-Sq(pred) = 34.62% R-Sq(adj) = 39.98%
Analysis of Variance for Tm (coded units)
Source DF Seq SS AdjSSAdj MS F P
Main Effects 2 1359987 1359987 679994 16.66 0.000
Residual Error 45 1837140 1837140 40825
Lack of Fit 1 6120 6120 6120 0.15 0.703
Pure Error 44 1831019 1831019 41614
Total 47 3197127
Unusual Observations for Tm
ObsStdOrder Tm Fit SE Fit Residual St Resid
2 2 677.00 1108.37 50.51 -431.37 -2.20R
R denotes an observation with a large standardized residual.
Estimated Coefficients for Tm using data in uncoded units
Term Coef
Constant 1819.36
LV -7.77500
TON -119.433
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
14
5002500-250-500
99
90
50
10
1
Residual
Percent
11001000900800700
400
200
0
-200
-400
Fitted Value
Residual
3002001000-100-200-300-400
12
9
6
3
0
Residual
Frequency
454035302520151051
400
200
0
-200
-400
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Tm
Figure V. Residual Plot of Tm for EN-31 considering all factors.
After developing the ANOVA tables for significant factors, the Main Effects Plot as well as the Interaction Plot is
prepared.
5030
1050
1000
950
900
850
800
750
700
6.54.0
LV
Mean
TON
Main Effects Plot for Tm
Data Means
Figure VI. Main Effects Plot of Tm for EN-31 considering significant factors.
The main effects plot shows steep slope of means indicating the significance of these factors
6.54.0
1100
1000
900
800
700
600
TON
Mean
30
50
LV
Interaction Plot for Tm
Data Means
Figure VII. Residual Plot of Tm for EN-31 considering Ton & LV.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
15
The interaction plot shows nonparallel lines of significance.
Next, the optimized values of significant factors are to be calculated. For optimization of Machining Time we have
set the Target Value to ‘0’ while the Upper Value to ‘427’ which is the minimum value of machining time and then
the value of Desirability functions is evaluated.
Figure VIII. Optimization Plot of Tm for EN-31 for significant factors.
d=0 emphasizes that y or response is more away from the target that is “Less emphasis on the Target”, because the
target was taken as “0” and response comes out to be far away from it (rather far from the Upper value that was
taken as 427). It could have been d=1 or close to 1, if the target was set close to 600 and upper value was taken as
greater than say 2000.
The Optimized value for LV is 50 while for TON is 6.5. For these values minimum Tm is 654.29 sec.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
16
5.3 Analysis of Results of Material Removal Rate (MRR) for EN-31. - The ANOVA table for MRR is prepared in
Minitab considering all factors and then the significant factors are determined having p-value less than 0.05. The goal
is kept in mind i.e. Maximization of Material Removal Rate.
Table IX. ANOVA Table of MRR for EN-31 considering all factors
Table X. Coefficient Table of MRR for EN-31 considering all factors
Factorial Fit: MRR versus HV, LV, TON, TOFF
Estimated Effects and Coefficients for MRR (coded units)
TermEffectCoef SE Coef T P
Constant 0.012954 0.000587 22.06 0.000
HV 0.000994 0.000497 0.000587 0.85 0.404
LV 0.002337 0.001168 0.000587 1.99 0.055
TON 0.005532 0.002766 0.000587 4.71 0.000
TOFF -0.001445 -0.000723 0.000587 -1.23 0.227
HV*LV -0.001566 -0.000783 0.000587 -1.33 0.192
HV*TON 0.001478 0.000739 0.000587 1.26 0.217
HV*TOFF -0.000456 -0.000228 0.000587 -0.39 0.700
LV*TON 0.000674 0.000337 0.000587 0.57 0.570
LV*TOFF -0.001504 -0.000752 0.000587 -1.28 0.209
TON*TOFF 0.000801 0.000400 0.000587 0.68 0.500
HV*LV*TON -0.000836 -0.000418 0.000587 -0.71 0.482
HV*LV*TOFF 0.000038 0.000019 0.000587 0.03 0.974
HV*TON*TOFF -0.000484 -0.000242 0.000587 -0.41 0.683
LV*TON*TOFF -0.000386 -0.000193 0.000587 -0.33 0.745
HV*LV*TON*TOFF -0.000699 -0.000349 0.000587 -0.60 0.556
S = 0.00406782 PRESS = 0.00119140
R-Sq = 52.57% R-Sq(pred) = 0.00% R-Sq(adj) = 30.34%
Analysis of Variance for MRR (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.00046961 0.00046961 0.00011740 7.10 0.000
2-Way Interactions 6 0.00009845 0.00009845 0.00001641 0.99 0.448
3-Way Interactions 4 0.00001300 0.00001300 0.00000325 0.20 0.938
4-Way Interactions 1 0.00000586 0.00000586 0.00000586 0.35 0.556
Residual Error 32 0.00052951 0.00052951 0.00001655
Pure Error 32 0.00052951 0.00052951 0.00001655
Total 47 0.00111643
Unusual Observations for MRR
ObsStdOrder MRR Fit SE Fit Residual StResid
8 8 0.026697 0.019328 0.002349 0.007369 2.22R
14 14 0.025433 0.017136 0.002349 0.008298 2.50R
23 23 0.025153 0.017658 0.002349 0.007495 2.26R
30 30 0.008880 0.017136 0.002349 -0.008255 -2.49R
R denotes an observation with a large standardized residual.
Estimated Coefficients for MRR using data in uncoded units
Term Coef
Constant -0.104561
HV 0.277012
LV 0.00412233
TON 0.0128062
TOFF 0.0205225
HV*LV -0.0084327
HV*TON -0.045838
HV*TOFF -0.051585
LV*TON -0.00054294
LV*TOFF -0.00073170
TON*TOFF -0.0027492
HV*LV*TON 0.00151000
HV*LV*TOFF 0.00148653
HV*TON*TOFF 0.0092474
LV*TON*TOFF 0.000108918
HV*LV*TON*TOFF -2.79541E-04
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
17
543210-1-2-3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A HV
B LV
C TO N
D TO F F
F actor N ame
Not Significant
Significant
Effect Type
C
Normal Plot of the Standardized Effects
(response is MRR, Alpha = 0.05)
Figure IX. Normal Probability Plot of the standardized effects of MRR for EN-31 considering all factors
0.0100.0050.000-0.005-0.010
99
90
50
10
1
Residual
Percent
0.02000.01750.01500.01250.0100
0.010
0.005
0.000
-0.005
-0.010
Fitted Value
Residual
0.0080.0040.000-0.004-0.008
16
12
8
4
0
Residual
Frequency
454035302520151051
0.010
0.005
0.000
-0.005
-0.010
Observation Order
Residual
Normal Probabilit y Plot Versus Fits
Histogram Versus Order
Residual Plots for MRR
Figure X. Residual Plot of MRR for EN-31 considering all factors
The ANOVA table as well as the Normal Probability Plot indicates that Pulse On Time is a significant factor when
considering MRR for EN-31. Now, the model is refitted by eliminating the non-significant values and considering
only Ton as an input factor.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
18
Table XI. ANOVA Table of MRR for EN-31 considering significant factors
The p-values from the ANOVA table of refitted MODEL indicate that the models and these factors are significant.
543210-1-2-3
99.9999
99.99
99
95
80
50
20
5
1
Standardized Effect
Percent
Not Significant
Significant
Effect Type
TON
Normal Plot of the Standardized Effects
(response is MRR, Alpha = 0.05)
Figure XI. Normal Probability Plot of the standardized effects of MRR for EN-31 considering significant factors
Factorial Fit: MRR versus TON
Estimated Effects and Coefficients for MRR (coded units)
TermEffectCoef SE Coef T P
Constant 0.012954 0.000583 22.24 0.000
TON 0.005532 0.002766 0.000583 4.75 0.000
S = 0.00403587 PRESS = 0.000815827
R-Sq = 32.89% R-Sq(pred) = 26.93% R-Sq(adj) = 31.43%
Analysis of Variance for MRR (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 1 0.00036717 0.00036717 0.00036717 22.54 0.000
Residual Error 46 0.00074926 0.00074926 0.00001629
Pure Error 46 0.00074926 0.00074926 0.00001629
Total 47 0.00111643
Unusual Observations for MRR
ObsStdOrder MRR Fit SE Fit Residual St Resid
8 8 0.026697 0.015720 0.000824 0.010977 2.78R
14 14 0.025433 0.015720 0.000824 0.009713 2.46R
23 23 0.025153 0.015720 0.000824 0.009433 2.39R
R denotes an observation with a large standardized residual.
Estimated Coefficients for MRR using data in uncoded units
Term Coef
Constant 0.00133817
TON 0.00221261
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
19
0.0100.0050.000-0.005-0.010
99
90
50
10
1
Residual
Percent
0.0160.0140.0120.010
0.010
0.005
0.000
-0.005
Fitted Value
Residual
0.0080.0040.000-0.004
12
9
6
3
0
Residual
Frequency
454035302520151051
0.010
0.005
0.000
-0.005
Observation Order
Residual
Normal Probability Plot Versus Fit s
Histogram Versus Order
Residual Plots for MRR
Figure XII. Residual Plot of MRR for EN-31 considering all factors.
After developing the ANOVA tables for significant factors, the Main Effects Plot as well as the Interaction Plot is
prepared for MRR.
6.54.0
0.016
0.015
0.014
0.013
0.012
0.011
0.010
TON
Mean
Main Effects Plot for MRR
Data Means
Figure XIII. Main Effects Plot of MRR for EN-31 considering significant factors.
The main effects plot shows steep slope of means indicating the significance of these factors.
6.54.0
0.018
0.017
0.016
0.015
0.014
0.013
0.012
0.011
0.010
0.009
TON
Mean
30
50
LV
Interaction Plot for MRR
Data Means
Figure XIV. Residual Plot of MRR for EN-31 considering Ton & LV.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
20
The interaction plot is drawn between Ton and LV since LV has a p-value of 0.055 that is near significant. The
interaction plot shows nonparallel lines of significance.
Next, the optimized values of significant factors are to be calculated. For optimization of Material Removal Rate,
we have set the Target Value to ‘1’ while the Lower Value to ‘.0267’ which is the Maximum value of Material
Removal Rate and then the value of Desirability functions is evaluated.
Figure XV. Optimization Plot of MRR for EN-31 for significant factors
The Weight of Specific Desirability Function (d) nearly equals to 0 i.e. emphasis on the Target (0). The Desirability
for a Response increases linearly.
d=0 emphasizes that y or response is more away from the target that is “Less emphasis on the Target”, because the
target was taken as “1” and response comes out to be far away from it (rather far from the Lower value that was
taken as 0.02670 g/min). It could have been d=1 or close to 1, if the target was set close to 0.015 and lower value
was taken as less than say 0.014.
The Optimized value for Ton is 6.5 µs for which maximum MRR is 0.0157 g/min.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
21
5.5 Analysis of Results of Electrode Wear Rate (EW) for EN-31. - The ANOVA table for EW is prepared in Minitab
considering all factors and then the significant factors are determined having p-value less than 0.05. The goal is kept
in mind i.e. Minimization of Electrode Wear Rate.
Table XII. ANOVA Table of EW for EN-31 considering all factors
Table XIII. Coefficient Table of EW for EN-31 considering all factors
Factorial Fit: EW versus HV, LV, TON, TOFF
Estimated Effects and Coefficients for EW (coded units)
TermEffectCoef SE Coef T P
Constant 0.009496 0.000361 26.32 0.000
HV 0.000313 0.000156 0.000361 0.43 0.668
LV 0.001913 0.000956 0.000361 2.65 0.012
TON 0.003077 0.001538 0.000361 4.26 0.000
TOFF -0.000209 -0.000104 0.000361 -0.29 0.774
HV*LV -0.000790 -0.000395 0.000361 -1.10 0.282
HV*TON 0.001016 0.000508 0.000361 1.41 0.169
HV*TOFF -0.000106 -0.000053 0.000361 -0.15 0.884
LV*TON 0.000601 0.000300 0.000361 0.83 0.411
LV*TOFF -0.000712 -0.000356 0.000361 -0.99 0.331
TON*TOFF 0.000931 0.000465 0.000361 1.29 0.206
HV*LV*TON -0.000508 -0.000254 0.000361 -0.70 0.487
HV*LV*TOFF 0.000098 0.000049 0.000361 0.14 0.893
HV*TON*TOFF 0.000088 0.000044 0.000361 0.12 0.903
LV*TON*TOFF -0.000314 -0.000157 0.000361 -0.44 0.666
HV*LV*TON*TOFF -0.000291 -0.000146 0.000361 -0.40 0.689
S = 0.00249984 PRESS = 0.000449941
R-Sq = 50.68% R-Sq(pred) = 0.00% R-Sq(adj) = 27.57%
Analysis of Variance for EW (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.00015918 0.00015918 0.00003980 6.37 0.001
2-Way Interactions 6 0.00004083 0.00004083 0.00000681 1.09 0.390
3-Way Interactions 4 0.00000448 0.00000448 0.00000112 0.18 0.947
4-Way Interactions 1 0.00000102 0.00000102 0.00000102 0.16 0.689
Residual Error 32 0.00019997 0.00019997 0.00000625
Pure Error 32 0.00019997 0.00019997 0.00000625
Total 47 0.00040549
Unusual Observations for EW
ObsStdOrder EW Fit SE Fit Residual StResid
14 14 0.017283 0.012053 0.001443 0.005230 2.56R
23 23 0.016638 0.012322 0.001443 0.004316 2.11R
30 30 0.007887 0.012053 0.001443 -0.004166 -2.04R
R denotes an observation with a large standardized residual.
Estimated Coefficients for EW using data in uncoded units
Term Coef
Constant -0.031162
HV 0.149405
LV 0.00141753
TON 0.0017536
TOFF 0.0078448
HV*LV -0.00362478
HV*TON -0.0239692
HV*TOFF -0.0287848
LV*TON -1.23684E-04
LV*TOFF -2.69289E-04
TON*TOFF -0.00075509
HV*LV*TON 0.00059704
HV*LV*TOFF 0.00066003
HV*TON*TOFF 0.0050104
LV*TON*TOFF 0.000033078
HV*LV*TON*TOFF -1.16425E-04
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
22
543210-1-2-3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A HV
B LV
C TO N
D T O F F
F actor N ame
Not Significant
Significant
Effect Type
C
B
Normal Plot of the Standardized Effects
(response is EW, Alpha = 0.05)
Figure XVI. Normal Probability Plot of the standardized effects of EW for EN-31 considering all factors
0.00500.00250.0000-0.0025-0.0050
99
90
50
10
1
Residual
Percent
0.01200.01050.00900.00750.0060
0.0050
0.0025
0.0000
-0.0025
-0.0050
Fitted Value
Residual
0.0040.0020.000-0.002-0.004
16
12
8
4
0
Residual
Frequency
454035302520151051
0.0050
0.0025
0.0000
-0.0025
-0.0050
Observation Order
Residual
Normal Probability Plot Versus Fit s
Histogram Versus Order
Residual Plots for EW
Figure XVII. Residual Plot of EW for EN-31 considering all factors
The ANOVA table as well as the Normal Probability Plot indicates that LV and Ton are significant factors when
considering EW for EN-31. Now, the model is refitted by eliminating the non-significant values and considering
only LV and Ton as input factors.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
23
Table XIV. ANOVA Table of EW for EN-31 considering significant factors
The p-values from the ANOVA table of the refitted MODEL indicate that the models as well as these factors are
significant.
543210-1-2-3
99.9
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
Not Significant
Significant
Effect Type
TON
LV
Normal Plot of the Standardized Effects
(response is EW, Alpha = 0.05)
Figure XVIII. Normal Probability Plot of the standardized effects of EW for EN-31 considering significant factors
Factorial Fit: EW versus LV, TON
Estimated Effects and Coefficients for EW (coded units)
TermEffectCoef SE Coef T P
Constant 0.009496 0.000339 28.02 0.000
LV 0.001913 0.000956 0.000339 2.82 0.007
TON 0.003077 0.001538 0.000339 4.54 0.000
S = 0.00234761 PRESS = 0.000282177
R-Sq = 38.84% R-Sq(pred) = 30.41% R-Sq(adj) = 36.12%
Analysis of Variance for EW (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 2 0.00015748 0.00015748 0.00007874 14.29 0.000
Residual Error 45 0.00024801 0.00024801 0.00000551
Lack of Fit 1 0.00000433 0.00000433 0.00000433 0.78 0.381
Pure Error 44 0.00024368 0.00024368 0.00000554
Total 47 0.00040549
Unusual Observations for EW
ObsStdOrder EW Fit SE Fit Residual St Resid
14 14 0.017283 0.010078 0.000587 0.007206 3.17R
23 23 0.016638 0.011990 0.000587 0.004647 2.04R
R denotes an observation with a large standardized residual.
Estimated Coefficients for EW using data in uncoded units
Term Coef
Constant -0.00079057
LV 9.56321E-05
TON 0.00123065
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
24
0.0060.0030.000-0.003-0.006
99
90
50
10
1
Residual
Percent
0.0120.0100.008
0.006
0.004
0.002
0.000
-0.002
Fitted Value
Residual
0.0060.0040.0020.000-0.002
10.0
7.5
5.0
2.5
0.0
Residual
Frequency
454035302520151051
0.006
0.004
0.002
0.000
-0.002
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for EW
Figure XIX. Residual Plot of EW for EN-31 considering all factors
After developing ANOVA tables for significant factors, Main Effects Plot and Interaction Plot is prepared for EW.
5030
0.0110
0.0105
0.0100
0.0095
0.0090
0.0085
0.0080
6.54.0
LV
Mean
TON
Main Effects Plot for EW
Data Means
Figure XX. Main Effects Plot of EW for EN-31 considering significant factors
The main effects plot shows steep slope of means indicating the significance of these factors.
6.54.0
0.013
0.012
0.011
0.010
0.009
0.008
0.007
TON
Mean
30
50
LV
Interaction Plot for EW
Data Means
Figure XXI. Residual Plot of EW for EN-31 considering Ton & LV
The interaction plot shows nonparallel lines of significance.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
25
Next, the optimized values of significant factors are to be calculated. For optimization of Electrode Wear Rate we
have set the Target Value to ‘0’ while the Upper Value to ‘0.00523 g/min’ which is the Minimum value of Electrode
Wear Rate and then the value of Desirability functions is evaluated.
Figure XXII. Optimization Plot of EW for EN-31 for significant factors
The Weight of Specific Desirability Function (d) nearly equals to 0 i.e. emphasis on the Target (0). The Desirability
for a Response increases linearly.
d=0 emphasizes that y or response is more away from the target that is “Less emphasis on the Target”, because the
target was taken as “1” and response comes out to be far away from it (rather far from the Upper value that was
taken as 0.00523 g/min). It could have been d=1 or close to 1, if the target was set close to 0.015 and lower value
was taken as less than say 0.014.
The Optimized value for LV is 30 & Ton is4 µs for whichminimumEW is 0.07 g/min.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
26
5.6 Analysis of Results of Surface Roughness (Ra) for EN-31. - The ANOVA table for Ra is prepared in Minitab
considering all factors and then the significant factors are determined having p-value less than 0.05. The goal is kept
in mind i.e. Minimization of Surface Roughness.
Table XV. ANOVA Table of Ra for EN-31 considering all factors.
Table XVI. Coefficient Table of Ra for EN-31 considering all factors
Factorial Fit: Ra versus HV, LV, TON, TOFF
Estimated Effects and Coefficients for Ra (coded units)
TermEffectCoef SE Coef T P
Constant 0.027354 0.002346 11.66 0.000
HV 0.000542 0.000271 0.002346 0.12 0.909
LV -0.003125 -0.001562 0.002346 -0.67 0.510
TON -0.002125 -0.001062 0.002346 -0.45 0.654
TOFF -0.003792 -0.001896 0.002346 -0.81 0.425
HV*LV 0.000375 0.000188 0.002346 0.08 0.937
HV*TON -0.000625 -0.000312 0.002346 -0.13 0.895
HV*TOFF -0.006958 -0.003479 0.002346 -1.48 0.148
LV*TON -0.001625 -0.000813 0.002346 -0.35 0.731
LV*TOFF -0.001958 -0.000979 0.002346 -0.42 0.679
TON*TOFF 0.001542 0.000771 0.002346 0.33 0.745
HV*LV*TON 0.006875 0.003437 0.002346 1.47 0.153
HV*LV*TOFF 0.002208 0.001104 0.002346 0.47 0.641
HV*TON*TOFF 0.003375 0.001688 0.002346 0.72 0.477
LV*TON*TOFF 0.001042 0.000521 0.002346 0.22 0.826
HV*LV*TON*TOFF -0.002458 -0.001229 0.002346 -0.52 0.604
S = 0.0162519 PRESS = 0.019017
R-Sq = 18.27% R-Sq(pred) = 0.00% R-Sq(adj) = 0.00%
Analysis of Variance for Ra (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.0003474 0.00034742 0.00008685 0.33 0.857
2-Way Interactions 6 0.0006936 0.00069362 0.00011560 0.44 0.848
3-Way Interactions 4 0.0007754 0.00077542 0.00019385 0.73 0.576
4-Way Interactions 1 0.0000725 0.00007252 0.00007252 0.27 0.604
Residual Error 32 0.0084520 0.00845200 0.00026412
Pure Error 32 0.0084520 0.00845200 0.00026412
Total 47 0.0103410
Unusual Observations for Ra
ObsStdOrder Ra Fit SE Fit Residual StResid
5 5 0.071000 0.031333 0.009383 0.039667 2.99R
18 18 0.015000 0.041667 0.009383 -0.026667 -2.01R
25 25 0.059000 0.031667 0.009383 0.027333 2.06R
34 34 0.074000 0.041667 0.009383 0.032333 2.44R
R denotes an observation with a large standardized residual.
Estimated Coefficients for Ra using data in uncoded units
Term Coef
Constant -1.28144
HV 2.43092
LV 0.0263475
TON 0.200975
TOFF 0.193233
HV*LV -0.0447250
HV*TON -0.373250
HV*TOFF -0.356333
LV*TON -0.00420250
LV*TOFF -0.00376667
TON*TOFF -0.0285167
HV*LV*TON 0.0072750
HV*LV*TOFF 0.0062667
HV*TON*TOFF 0.0528333
LV*TON*TOFF 0.00057500
HV*LV*TON*TOFF -0.00098333
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
27
3210-1-2-3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A HV
B LV
C TO N
D T O F F
F actor N ame
Not Significant
Significant
Effect Type
Normal Plot of the Standardized Effects
(response is Ra, Alpha = 0.05)
Figure XXIII. Normal Probability Plot of the standardized effects of Ra for EN-31 considering all factors
0.040.020.00-0.02-0.04
99
90
50
10
1
Residual
Percent
0.0400.0350.0300.0250.020
0.04
0.02
0.00
-0.02
Fitted Value
Residual
0.040.030.020.010.00-0.01-0.02
10.0
7.5
5.0
2.5
0.0
Residual
Frequency
454035302520151051
0.04
0.02
0.00
-0.02
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Ra
Figure XIV. Residual Plot of Ra for EN-31 considering all factors.
The ANOVA table as well as the Normal Probability Plot indicates there is no significant factor when considering
Ra for EN-31. So, no need to refit the model. Now, the Main Effects Plot as well as the Interaction Plot is prepared
for Ra.
0.70.3
0.029
0.028
0.027
0.026
0.025
5030
6.54.0
0.029
0.028
0.027
0.026
0.025
6.55.5
HV
Mean
LV
TON TOFF
Main Effects Plot for Ra
Data Means
Figure XXV. Main Effects Plot of Ra for EN-31 considering all factors.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
28
The main effects plot shows steep slope of means indicating the significance of these factors.
5030 6.54.0 6.55.5
0.032
0.028
0.024
0.032
0.028
0.024
0.032
0.028
0.024
HV
LV
TON
TOFF
0.3
0.7
HV
30
50
LV
4.0
6.5
TON
Interaction Plot for Ra
Data Means
Figure XXVI. Residual Plot of Ra for EN-31 for all factors.
The interaction plot shows nonparallel lines of significance.
Next, the optimized values of significant factors are to be calculated. For optimization of Surface Roughness, we
have set the Target Value to ‘0’ while the Upper Value to ‘0.006 mm’ which is the Minimum value of Surface
Roughness and then the value of Desirability functions is evaluated.
Figure XXVII. Optimization Plot of Ra for EN-31 for significant factors.
d=0 emphasizes that y or response is more away from the target that is “Less emphasis on the Target”, because the
target was taken as “0” and response comes out to be far away from it (rather far from the Upper value that was
taken as 0.006 mm). It could have been d=1 or close to 1, if the target was set close to 0.009 and upper value was
taken as greater than say 0.015.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
29
The Optimized value for LV is 50, HV is 0.7,Ton is 4.0 µs while Toff is 6.5 µs. For these values minimum Ra is
0.018mm.
5.7 Analysis of Results of Base Radius (R) for EN-31. - The ANOVA table for R is prepared in Minitab considering
all factors and then the significant factors are determined having p-value less than 0.05. The goal is kept in mind i.e.
Optimization of Base Radius to the dimensions of electrode.
Table XVII. ANOVA Table of R for EN-31 considering all factors.
Factorial Fit: R versus HV, LV, TON, TOFF
Estimated Effects and Coefficients for R (coded units)
TermEffectCoef SE Coef T P
Constant 1.58946 0.01629 97.57 0.000
HV -0.04275 -0.02137 0.01629 -1.31 0.199
LV -0.03417 -0.01708 0.01629 -1.05 0.302
TON -0.02550 -0.01275 0.01629 -0.78 0.440
TOFF -0.01233 -0.00617 0.01629 -0.38 0.708
HV*LV -0.01850 -0.00925 0.01629 -0.57 0.574
HV*TON -0.00100 -0.00050 0.01629 -0.03 0.976
HV*TOFF 0.01433 0.00717 0.01629 0.44 0.663
LV*TON 0.00492 0.00246 0.01629 0.15 0.881
LV*TOFF -0.00892 -0.00446 0.01629 -0.27 0.786
TON*TOFF -0.00575 -0.00287 0.01629 -0.18 0.861
HV*LV*TON -0.07525 -0.03762 0.01629 -2.31 0.028
HV*LV*TOFF -0.03958 -0.01979 0.01629 -1.21 0.233
HV*TON*TOFF -0.03492 -0.01746 0.01629 -1.07 0.292
LV*TON*TOFF -0.02383 -0.01192 0.01629 -0.73 0.470
HV*LV*TON*TOFF -0.06767 -0.03383 0.01629 -2.08 0.046
S = 0.112858 PRESS = 0.917065
R-Sq = 34.74% R-Sq(pred) = 0.00% R-Sq(adj) = 4.14%
Analysis of Variance for R (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.045567 0.045567 0.011392 0.89 0.479
2-Way Interactions 6 0.008225 0.008225 0.001371 0.11 0.995
3-Way Interactions 4 0.108199 0.108199 0.027050 2.12 0.101
4-Way Interactions 1 0.054945 0.054945 0.054945 4.31 0.046
Residual Error 32 0.407585 0.407585 0.012737
Pure Error 32 0.407585 0.407585 0.012737
Total 47 0.624522
Unusual Observations for R
ObsStdOrder R Fit SE Fit Residual St Resid
46 46 1.86000 1.66700 0.06516 0.19300 2.09R
R denotes an observation with a large standardized residual.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
30
Table XVIII. Coefficient Table of R for EN-31 considering all factors
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99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A HV
B LV
C TO N
D TO F F
F actor N am e
Not Significant
Significant
Effect Type
ABCD
ABC
Normal Plot of the Standardized Effects
(response is R, Alpha = 0.05)
Figure XXVIII. Normal Probability Plot of the standardized effects of R for EN-31 considering all factors.
0.20.10.0-0.1-0.2
99
90
50
10
1
Residual
Percent
1.71.61.51.4
0.2
0.1
0.0
-0.1
-0.2
Fitted Value
Residual
0.160.080.00-0.08-0.16
10.0
7.5
5.0
2.5
0.0
Residual
Frequency
454035302520151051
0.2
0.1
0.0
-0.1
-0.2
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for R
Figure XXIX. Residual Plot of R for EN-31 considering all factors.
The ANOVA table as well as the Normal Probability Plot indicates that the interactions HV*LV*TON and
HV*HV*LV*TON are significant factors when considering R for EN-31. Now, the model is refitted by eliminating
the non-significant values and considering only HV*LV*TON and HV*HV*LV*TON as input factors.
Estimated Coefficients for R using
data in uncoded units
Term Coef
Constant -6.85617
HV 21.4526
LV 0.272280
TON 2.08093
TOFF 1.69079
HV*LV -0.659463
HV*TON -5.05800
HV*TOFF -4.08742
LV*TON -0.0620383
LV*TOFF -0.0520358
TON*TOFF -0.399833
HV*LV*TON 0.147350
HV*LV*TOFF 0.122308
HV*TON*TOFF 0.943000
LV*TON*TOFF 0.0116267
HV*LV*TON*TOFF -0.0270667
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
31
Table XIX. ANOVA Table of R for EN-31 considering significant factors
The p-values from the ANOVA table of refitted MODEL indicate that the models and these factors are significant.
3210-1-2-3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A HV
B LV
C TO N
D TO F F
F actor N ame
Not Significant
Significant
Effect Type
ABCD
ABC
Normal Plot of the Standardized Effects
(response is R, Alpha = 0.05)
Figure XXX. Normal Probability Plot of the standardized effects of R for EN-31 considering significant factors.
Factorial Fit: R versus HV, LV, TON, TOFF
Estimated Effects and Coefficients for R (coded units)
TermEffectCoef SE Coef T P
Constant 1.58946 0.01522 104.41 0.000
HV -0.04275 -0.02137 0.01522 -1.40 0.168
LV -0.03417 -0.01708 0.01522 -1.12 0.268
TON -0.02550 -0.01275 0.01522 -0.84 0.407
TOFF -0.01233 -0.00617 0.01522 -0.41 0.688
HV*LV*TON -0.07525 -0.03762 0.01522 -2.47 0.018
HV*LV*TON*TOFF -0.06767 -0.03383 0.01522 -2.22 0.032
S = 0.105467 PRESS = 0.625079
R-Sq = 26.97% R-Sq(pred) = 0.00% R-Sq(adj) = 16.29%
Analysis of Variance for R (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.04557 0.04557 0.011392 1.02 0.406
3-Way Interactions 1 0.06795 0.06795 0.067951 6.11 0.018
4-Way Interactions 1 0.05495 0.05495 0.054945 4.94 0.032
Residual Error 41 0.45606 0.45606 0.011123
Lack of Fit 9 0.04847 0.04847 0.005386 0.42 0.913
Pure Error 32 0.40758 0.40758 0.012737
Total 47 0.62452
Unusual Observations for R
ObsStdOrder R Fit SE Fit Residual St Resid
46 46 1.86000 1.63771 0.04028 0.22229 2.28R
48 48 1.23000 1.46063 0.04028 -0.23063 -2.37R
R denotes an observation with a large standardized residual.
* NOTE * Estimated regression coefficients in uncoded units are not available
because the model is non-hierarchical.
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
32
0.20.10.0-0.1-0.2
99
90
50
10
1
Residual
Percent
1.741.681.621.561.50
0.2
0.1
0.0
-0.1
-0.2
Fitted Value
Residual
0.20.10.0-0.1-0.2
10.0
7.5
5.0
2.5
0.0
Residual
Frequency
454035302520151051
0.2
0.1
0.0
-0.1
-0.2
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for R
Figure XXXI. Residual Plot of R for EN31 considering significant factors.
After developing the ANOVA tables for significant factors Main Effects Plot and Interaction Plot is prepared for R.
0.70.3
1.61
1.60
1.59
1.58
1.57
5030
6.54.0
1.61
1.60
1.59
1.58
1.57
6.55.5
HV
Mean
LV
TON TOFF
Main Effects Plot for R
Data Means
Figure XXXII. Main Effects Plot of R for EN-31 considering significant factors
The main effects plot shows steep slope of means indicating the significance of these factors.
5030 6.54.0 6.55.5
1.62
1.59
1.56
1.62
1.59
1.56
1.62
1.59
1.56
HV
LV
TON
TOFF
0.3
0.7
HV
30
50
LV
4.0
6.5
TON
Interaction Plot for R
Data Means
Figure XXXIII. Residual Plot of R for EN-31 considering significant factors
M. M. Uz Zaman Siddiqui, S. Amir Iqbal, A. Zulqarnain, A. Tabassum
Memoria Investigaciones en Ingeniería, núm. 30 (2026)
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
33
The interaction plot shows non parallel lines of significance.
Next, the optimized values of significant factors are to be calculated. For optimization of Base Radius value, we
have set the Target Value to ‘1.5’ while the Upper & Lower Values to 1.55 &1.45respectively and then the value of
Desirability function is evaluated.
Figure XXXIV. Optimization Plot of R for EN-31 for significant factors
The Weight of Specific Desirability Function (d) nearly to 1 i.e. emphasis on the Target. The Desirability for a
Response increases linearly.
The Optimized value for HV is 0.6152, LV is 50, Ton is 6.5 and Toff is also 6.5. For these values optimized R is 1.5
mm.