MTRL 460-2014-TutRep3-Team9

MTRL 460
Monitoring and Optimization of
Materials Processing
Tutorial 3:
Introduction to Designed Experiments
Group 9:
Muhammad Arshad Hassni
Vishal Sharma
Bennet Lim
Igor Vranjes
Muhammad Harith Mohd Fauzi
Daniel Shim
Date: December 8, 2014

INTRODUCTION
Design of Experiments (DOE) is a class of statistically based techniques to organize
experimentation to obtain the maximum amount of information at the minimum cost
and time expenditure. Among the many different DOE techniques, two-level factorial
experiments (2FD) are amongst the most effective in engineering applications. They can
be easily used to (1) identify the effects and interactions of relatively few (k=2- 4)
variables or to (2) screen many (k>5) variables in order to identify the few (typically 4 or
less) significant ones.
2FD are however NOT the best choice to empirically model the process in terms of the
few important variables; for the modeling we will be using Response Surface Methods
(RSM). These two procedures (i.e. 2FD, RSM) will be aided by use of commercial
software Design Expert (DX8). The best outcome of well-organized experiments is an
empirical (or semi-empirical) model of the process that allows a prediction of the
response Y as a function of the independent variables (factors) Xi at a specified
confidence level.
Some of the features of efficient experiments include:
 The experiments are carefully planned, with a significant portion of time and
resources (~25%) spent at the planning stage. The problem should be well
understood. The right questions should be asked, as even “an approximate
answer to the right question is worth a great deal more than a precise answer to
the wrong question”.
 The objectives of the experimentation are clearly defined and communicated to
everybody involved; the task should focus on the roots of real problems, with
possible numerical targets to be reached as a result of the experimentation
 The process that is experimented on is stable, well defined and understood by
experimenters. In industrial environment focused on process (or product)
optimization, SPC should be introduced, run and utilised to stabilise the process
before attempting experimental program on process optimization

TUTORIAL 3A(i): BLIND BALANCE
 Task (i): Two-level Factorial Design with 2 Variables
OBJECTIVE
To determine the effects of the support and body rotations on body “blind balance”
abilities.
EXPERIMENTAL PLAN
Variables
X1 Surface type X1 (low level {-}): floor X1 (high level {+}: foam
X2 Rotations
X2 (low level {-}): 0
rotations 0R
X2 (high level {+}): 1
rotation 1R
1 Response: Y in-balance time (seconds)
DATA COLLECTION
Exp #
X1
[surface]
X2
[rotations]
X1*X2 Y[sec]A Y[sec]B Y[sec]C
Y[sec]
Average
1 floor {-} 0 rot {-} {+} 51.63 45.38 50.92 49.31
2 foam {+} 0 rot {-} {-} 33.85 41.33 29.18 34.79
3 floor {-} 1 rot {+} {-} 37.08 42.76 16.42 32.09
4 foam {+} 1 rot {+} {+} 73.20 48.75 83.27 68.41
Average 46.15
DATA ANALYSIS
 Square Plot
 Total “effect” L
49.31
34.79
32.09
68.41

The total “effect” L of any given variable on the experiment outcome is calculated as the
difference between all responses when the variable is at high and low levels.
The effect of X1 surface, L1:
LX1 = 34.79 + 68.41 – 49.31 – 32.09 = 21.80 s
47.23% of average: weak positive effect of surface
The effect of X2 rotation, L2:
LX2 = 32.09 + 68.41 – 49.31 – 34.79 = 16.40 s
35.53% of average: weak positive effect of rotations
 Effect of interaction
The effect of the interaction is calculated by taking the difference between (1) the
effects when all variables are the same level (i.e. both at high or both at low level), and
(2) the effects when all variables are at mixed levels (i.e. one at high level and another at
low level).
The effect of interaction of X1 surface and X2 rotation, L12:
LX1X2 = 49.31 + 68.41 – 32.09 – 34.79 = 50.84 s
110% of average: strong interaction effect
CONCLUSIONS
Both variables have weak positive effects. The interaction between the two variables is
strong on the other hand.

TUTORIAL 3A(ii): BLIND COORDINATION
 Task (ii): Two-level Factorial Design with 3 Variables
OBJECTIVE
To determine the effects of the hands and body rotations, on your body “blind
coordination” abilities.
EXPERIMENTAL PLAN
2FD3 with the following variables and response:
Variables
X1 hand-to-target
distance
X1 low level {-}: close X1 high level {+}: far
X2 hand X2 low level {-}: right X2 high level {+}: left
X3 rotations X3 low level {-}: 0 rot 0R X3 high level {+}: 1 rot 1R
“Response” Y: shots at target (%)
DATA COLLECTION
Exp #
Main
Interactions
Group
Data
Factors
Distance Hand Rotation
X1 X2 X3 X1X2 X1X3 X2X3 X1X2X3 Y(%)
1 -1 -1 -1 1 1 1 -1 20
2 1 -1 -1 -1 -1 1 1 90
3 -1 1 -1 -1 1 -1 1 90
4 1 1 -1 1 -1 -1 -1 10
5 -1 -1 1 1 -1 -1 1 10
6 1 -1 1 -1 1 -1 -1 70
7 -1 1 1 -1 -1 1 -1 50
8 1 1 1 1 1 1 1 10
Effects 10 -30 -70 -250 30 -10 50 Ave=44

DATA ANALYSIS
 Cube plot
The results of such 2FD3, with 3-variables at 2 levels (23=8 experiments) factorial design
of experiments can be conveniently plotted on a “cube plot”, with the response values
(i.e. average % of successful hits) at the cube corners.
 Total “effect” L
The effect of X1 distance, L1:
L1 = -20 + 90 – 90 + 10 – 10 + 70 – 50 + 10 = 10
22.7% of average: weak positive effect of distance
The effect of X2 hand, L2:
L2 = -20 - 90 + 90 + 10 – 10 - 70 + 50 + 10 = -30
68.2% of average: weak negative effect of hand
The effect of X3 rotation, L3:
L3 = -20 - 90 – 90 - 10 + 10 + 70 + 50 + 10 = -70
159% of average: strong positive effect of rotation
X3
X2
X1 9020
90
10
10 70
50 10

 Effect of interaction
The effect of interaction of X1 distance and X2 hand, L12:
L12 = 20 - 90 – 90 + 10 + 10 - 70 – 50 + 10 = -250
568% of average: strong negative effect of distance and hand: Strong Interaction Effect
The effect of interaction of X1 distance and X3 rotation, L13:
L13 = 20 - 90 + 90 - 10 – 10 + 70 – 50 + 10 = 30
68.2% of average: weak positive effect of distance and rotation: Weak Interaction Effect
The effect of interaction of X2 hand and X3 rotation, L23:
L23 = 20 + 90 – 90 - 10 – 10 - 70 + 50 + 10 = -10
22.7% of average: weak negative effect of hand and rotation: Weak Interaction Effect
The effect of interaction of X1 distance and X2 hand and X3 rotation, L123:
L123 = -20 + 90 + 90 - 10 + 10 - 70 – 50 + 10 = 50
114% of average: strong positive effect of distance, hand and rotation:
Strong Interaction Effect
CONCLUSION
From the results above, we can see that L12 and L123 have strong interaction effect
whilst L13 and L23 have weak interaction effect to our experiments.

TUTORIAL 3B: FRACTIONAL FACTORIALS FOR VARIABLES SCREENING
 Task #9: Titanium Di-Boride for Composite Aluminum Machining Applications
OBJECTIVE
To design the screening experiments to identify the four significant variables out of the
pool of the tentative seven variables by using DX program.
Tut3B includes the following 4 steps:
1. The Scenario
Advanced Titanium Di-boride (TiB2) ceramic is one of the primary candidates for
applications in high-wear environments, at low and intermediate temperatures and in
contact with corrosive liquid or solid aluminum. The primary advantages of TiB2 are
extremely high hardness, and stability against solid and liquid aluminum. It is presently
being considered as an alternative (to diamond) cutting tool for the highly abrasive
composites based on aluminum, such as SiC-Al and Al2O3-Al. For the metal cutting
applications, the following three properties of TiB2 are required:
R1 Maximum hardness (Target R1T = 27GPa)
R2 Maximum fracture toughness (Target R2T = 7MPa√m
R3 Maximum Weibull Modulus (Target R3T = 13)
The following seven process variables X1 to X7 were tentatively proposed as those
controlling the required properties R1, R2 and R3:
X1 Carbon additive content (2 to 6 wt%)
X2 Heating rate (10 to 30 C/min)
X3 Powder milling time (5 to 10 hr)
X4 Oxygen impurity content in TiB2 (1 to 5 wt%)
X5 Sintering temperature (1,600 to 1,900 C)
X6 Sintering time (1 to 3 hr)
X7 TiB2 powder grain diameter (0.5 to 2 μm)
Using the DX program, design the screening experiments (27-3 fractional factorials) to
identify the 4 significant variables out of the pool of the tentative 7 variables.

2. Screening Experiment using DX8
The tentative 7 variables and their range of variation:
The table of responses (R1, R2, R3):

3. Run the Design Experiment Using MTRL460LABSIM
The data below shows one of the simulations conducted using the LAB program.
Lab 9 Simulation completed on: 16-11-14 at 00:03:30:
Variables Values S.D.
X1: Carbon Content % 3.00 wt% 0.1 %
X2: Heating Rate 25.00 °C/min 0.1 %
X3: Milling Time 7.00 hr 0.1 %
X4: Oxygen Content in TiB2 4.00 wt% 0.1 %
X5: Sintering Temperature 1700.00 °C 0.1 %
X6: Sintering Time 2.50 hr 0.1 %
X7: TiB2 Grain Diameter 0.75 um 0.1 %
Err. of Measurement 0.2 %
Hardness [GPa] Toughness [MPa•√m] Modulus
Average 23.938 5.901 11.754
S.D. 0.395 0.023 0.057
Values Values Values
1 23.086 5.857 11.657
2 23.471 5.859 11.663
3 23.503 5.864 11.672
4 23.523 5.884 11.688
5 23.670 5.888 11.698
6 23.740 5.893 11.724
7 23.774 5.895 11.725
8 23.794 5.896 11.755
9 23.817 5.903 11.758
10 23.853 5.904 11.758
11 24.009 5.905 11.773
12 24.025 5.907 11.774
13 24.069 5.909 11.778
14 24.114 5.909 11.779
15 24.195 5.911 11.781
16 24.251 5.912 11.785
17 24.268 5.922 11.788
18 24.375 5.923 11.819
19 24.453 5.926 11.848
20 24.768 5.947 11.860

The average value of hardness, fracture toughness, and Weibull modulus obtained from
each simulation using LAB program is then transferred into DX8 Data Entry Table as
shown below.
DX8 Data Entry Table:

Design summary:
4. Analysis and the 4 significant variables
Normal probability plots:
Using DX8, we generated a normal probability plot for each of the three response
variables. Outliers on these plots can be identified, showing us the significant variables
in this process.
Design-Expert® Software
Maximum Hardness
Shapiro-Wilk test
W-value = 0.825
p-value = 0.001
A: Carbon Additive Content
B: Heating Rate
C: Powder Milling Time
D: Oxygen Impurity Content in TiB2
E: Sintering Temperature
F: Sintering time
G: TiB2 power grain diameter
Positive Effects
Negative Effects
0.00 0.60 1.21 1.81 2.42 3.02 3.63 4.23 4.84 5.44 6.05
0
10
20
30
50
70
80
90
95
99
Half-Normal Plot
|Standardized Effect|
Half-Normal%Probability
A-Carbon Additive Content
D-Oxygen Impurity Content in TiB2
E-Sintering Temperature
G-TiB2 power grain diameter
AD
AG
DE
DG
Figure 4: Maximum hardness half-normal plot.

Maximum Fracture Toughness
Shapiro-Wilk test
W-value = 0.781
p-value = 0.000
B: Heating Rate
F: Sintering time
Positive Effects
Negative Effects
0.00 0.30 0.61 0.91 1.21 1.52 1.82 2.12 2.43 2.73 3.03
0
10
20
30
50
70
80
90
95
99
Half-Normal Plot
AD
AE
AG
DE
DF
Figure 5: Maximum fracture toughness half-normal plot.
Maximum Weibull Modulus
Shapiro-Wilk test
W-value = 0.960
p-value = 0.508
B: Heating Rate
F: Sintering time
Positive Effects
Negative Effects
0.00 1.52 3.04 4.56 6.08
0
10
20
30
50
70
80
90
95
99
Half-Normal Plot
AD
AE
AG
DE
DF
DG
Figure 6: Maximum Weibull modulus half-normal plot.
From figures 4-6, we can see that the outliers on the half-normal plots are carbon
additive content (A), sintering temperature (E), oxygen impurity content in TiB2 (D), and
TiB2 powder grain diameter (G). Therefore, these 4 variables are significant and they are
the main effects of the process. The other outliers on the half-normal plot are various
combinations of 2 of these main effects. This means that the interaction effects
between these 4 variables are also significant.

Figure 4 shows that the positive effects on maximum hardness are oxygen impurity
content in TiB2 (D), sintering temperature (E), the interaction between oxygen impurity
content in TiB2 and TiB2 powder grain diameter (DG), and the interaction between
carbon additive content and oxygen impurity content in TiB2 (AD). The negative effects
on maximum hardness are carbon additive content (A), TiB2 powder grain diameter (G),
the interaction between oxygen impurity content in TiB2 and sintering temperature (DE),
and the interaction between carbon additive content and TiB2 powder grain diameter
(AG).
Figure 5 shows that the positive effects on maximum fracture toughness are carbon
additive content (A) and interactions AE, AD, DE, and DF. The negative effects on
maximum fracture toughness are sintering temperature (E), oxygen impurity content in
TiB2 (D), TiB2 powder grain diameter (G), and interaction AG.
Figure 6 shows that the positive effects on maximum Weibull modulus are the
interactions AE, AD, DE, DF, and DG. The negative effects on maximum Weibull modulus
are all 4 of the main effects and the interaction AG.
Factor Coding: Actual
Maximum Hardness (GPa)
X1 = A: Carbon Additive Content
X2 = D: Oxygen Impurity Content in TiB2
X3 = E: Sintering Temperature
Actual Factors
B: Heating Rate = 20
C: Powder Milling Time = 8
F: Sintering time = 2
G: TiB2 power grain diameter = 1.125
Cube
Maximum Hardness (GPa)
A: Carbon Additive Content (wt%)
D:OxygenImpurityContentinTiB2(wt%)
E: Sintering Temperature (oC)
A-: 3 A+: 5
D-: 2
D+: 4
E-: 1700
E+: 1800
23.3469
28.5839
22.3922
24.9181
16.2389
21.4759
20.0308
22.5567
Figure 7: Cube plot for A, D, E and their interactions affecting maximum hardness.

Maximum Fracture Toughness (MPa*sqrt(m))
Actual Factors
Cube
D:OxygenImpurityContentinTiB2(wt%) E: Sintering Temperature (oC)
A-: 3 A+: 5
D-: 2
D+: 4
E-: 1700
E+: 1800
9.13019
7.51006
5.14231
4.84394
8.72181
7.41894
5.31819
5.33706
Figure 8: Cube plot for A, D, E and their interactions affecting maximum fracture
toughness.
Actual Factors
Cube
A-: 3 A+: 5
D-: 2
D+: 4
E-: 1700
E+: 1800
13.4728
10.4799
9.60641
8.48684
12.0567
9.68084
9.57859
9.07616
Figure 9: Cube plot for A, D, E and their interactions affecting Weibull modulus.

Figures 7-9 show the cube plots for A, D, E significant variables and their interactions
and their effects on the three response variables. All three cube plots confirm the half-
normal plots findings on which main effects and interactions cause positive effects and
which main effects and interactions cause negative effects. However, our process has 4
significant variables and cube plots can only show the effects of 3 significant variables.
Therefore, several more cube plots would have to be made with different combinations
of 3 significant variables. The results would show the same as the half-normal plots.
TUTORIAL 3C: RESPONSE SURFACE METHOD FOR PROCESS MODELLING AND
OPTIMIZATION
OBJECTIVE
 Using Response Surface Methodology (RSM) principles, Central Composite
Design CCD of DX8 software, and the LAB simulation program, empirically model,
plot and examine the response surfaces for R1, R2 and R3 as a function of the
four significant variables.
 Examine and discuss the statistical significance tests for the models
 Optimize the process using the model: identify the optimum conditions of the
process, that would result in a combination of the responses R1, R2 and R3
closest to the target values R1T, R2T and R3T; verify the optimum processing
and/or use conditions through running LAB simulation program.
In tutorial 3B, the 4 significant variables that affect the 3 responses were determined to
be carbon additive, oxygen impurity, sintering temperature and titanium diboride (TiB2)
MaximumFractureToughness(MPa*sqrt(m))
X1= A: CarbonAdditiveContent
X2= D: OxygenImpurityContent inTiB2
X3= E: SinteringTemperature
ActualFactors
B: HeatingRate= 20
C: Powder MillingTime= 8
F: Sinteringtime= 2
G: TiB2power graindiameter = 1.125
Cube
A-: 3 A+: 5
D-: 2
D+: 4
E-: 1700
E+: 1800
9.13019
7.51006
5.14231
4.84394
8.72181
7.41894
5.31819
5.33706

powder grain diameter. Using these variables and the DX9 program, we are able to plan
a Central Composite Design (CCD) to model the process. The CCD will run 30
experiments providing different sets of data for the 4 variables.
The new series of CCD experiments are run again using the LAB simulation program with
the previously determined values for the 4 variables. Each simulation will occur at
various values for the 4 variables while the 3 minor variables will be kept at constant
values at the midpoint of their respective ranges. The LABSIM program will generate
averaged values for the 3 responses (hardness, fracture toughness and Weibull
modulus) for each individual experiment.
The following is the design summary of the CCD experiments

The CCD table for the 30 experiments is shown below.

Now that we have our data we can obtain empirical models of the process with the CCD
module in DX9. We will be producing 3 models, one for each response that we want to
maximize.
Response 1: Hardness
The following is the model for maximizing hardness.

The following is the ANOVA table generated in the CCD module.

With this ANOVA table we can assess the quality of the model. As indicated, the F-ratio
has a value of 229.93 and the correlation coefficient r2 has a value of 0.9954. The
standard requirement of a qualified model is a F-ratio larger than 10 and correlation
coefficient larger than approximately 0.9.
Since this model qualifies, we do not need to perform further re-evaluation such as
using transformations or different ranges of insignificant variables.
We can now proceed to observe some of the plots of this model.

Response 2: Fracture Toughness
The following is the model for maximizing fracture toughness.

The generated ANOVA table for model 2 is shown below.

With this ANOVA table we can assess the quality of the model. As indicated, the F-ratio
has a value of 1173.81 and the correlation coefficient r2 has a value of 0.9991. The
values are well above the requirements and compared to model 1, as the quality of the
model can be considered to be much higher. Therefore, no further action needs to be
taken.
The following are graphical representations of the model.

Response 3: Weibull Modulus
The following is the generated model for our third response: Weibull modulus.

Correspondingly, the ANOVA table of the model is shown below.

As indicated in the table, the F-ratio has a value of 674.46 and the correlation coefficient
r2 has a value of 0.9984. We can confirm the quality of the model as these two values
exceed the standard requirement.
Finally we represent our model graphically for the third response.

Optimization of CCD
We set the 4 significant variables in the range and the goal is to maximize the 3
responses. This is done in the “Criteria” tab under optimization in DX9.

We order the solutions in terms of desirability, which means that the underlined set of
data is providing the best data that maximizes our target responses. The ideal solution is
shown below:
The red dots indicate the 4 significant variables whereas the blue dots indicate the our
maximized responses. The desirability is 86.7%, which means that we are 86.7% certain
that the values for the 4 variables gives us the best end result. Since there are other
non-identified errors in statistics, it would be rather difficult to approach a perfect
desirability of 100%. Therefore, we can still be satisfied with these results as it is
relatively close to a perfect 100% desirability. An alternative representation is shown
below as a bar graph

Consequently, we can obtain contour and cube plots of the results from the ideal
solution. Below is the contour plot of the 4 significant variables, showing the ranges of
different desirability.

We can also express our results as a cube plot, again in terms of the 4 variables.

A summary of our optimization results is shown below, 3 confirmation runs were run to
ensure consistent results.
Finally, we use LABSIM again at the predicted optimum level of the 4 variables, to verify
the model predictions.
Hardness [GPa] Toughness [MPa•m^(1/2)] Modulus Variables Values S.D.
Average 28.190 9.724 17.302 X1: Carbon Content % 3.49 wt% 0.1 %
S.D. 0.177 0.033 0.069 X2: Heating Rate 25.00 °C/min 0.1 %
X3: Milling Time 7.00 hr 0.1 %
Values Values Values X4: Oxygen Content in TiB2 2.00 wt% 0.1 %
1 27.803 9.653 17.172 X5: Sintering Temperature 1725.82 °C 0.1 %
2 27.968 9.673 17.184 X6: Sintering Time 2.50 hr 0.1 %
3 28.015 9.680 17.216 X7: TiB2 Grain Diameter 0.75 um 0.1 %
4 28.037 9.685 17.236 Err. of Measurement
5 28.074 9.700 17.255
0.2 %

Our model has presented that the average for hardness; toughness and modulus are
given as below:
1) Hardness= 28.2818 GPa
From the data obtained in the model, our mode averagel is about 0.32% closed to
the lab simulation result for hardness value. According to the graph above, the lab
data is within the range of specification and its average is reliable to verify our
model.
2) Fracture toughness = 9.6739MPa*m0.5

From the data obtained in the model, our model average is about 0.52% closed to
the lab simulation result for fracture toughness value. According to the graph above,
the lab data is within the range of specification and its average is reliable to verify
our model
3) Weibull Modulus = 17. 1969 MPa
From the data obtained in the model, our model average is about 0.61% closed to
the lab simulation result for Weibull Modulus value. According to the graph above,
the lab data is within the range of specification and its average is reliable to verify
our model
The lab data average is approximately equal to the model data average as the
changes are just less than 1% differences. The changes are maybe due to the
systematic and random error occurring during measurement. For the experiment,
you can optimize the data value by having a well-calibrated high quality measuring
tool.

MTRL 460-2014-TutRep3-Team9

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