### Factor Analysis for Dissolution Time of Effervescent Tablets

```Factor Analysis for
Dissolution Time of
Effervescent Tablets
NIU JINSHU (2010010837)
WU XIANYU (2010010838)
CAO LIUXING (2010010836)
WU YINING (2010010835)
DAI YIBO (2010010833)
Outlines
•
Purpose of experiment
•
Experiment design
•
Factors
•
Design mythologies
•
Experiment conduction
•
Analytical procedure
•
Significant factors
•
Effects of factors
•
2-factor interaction
•
3-factor interaction
•
Regression model
•
Model Validation
•
Conclusions
2
3
Purpose of experiment

Explore how different
factors affect
dissolution rate

Provide several
implications to the
dissolution process

Test if the
the correct condition
4
Experiment design – Factors (1/2)

Fishbone diagram
5
Experiment design – Factors (2/2)

Response variable



Dissolution time: 0~300s
Control variable
Constant variable

Composition

Place

surface area of tablets

Volume of water

Temperature of water

Surface area of water

Temperature around

Tablet flavor

Air pressure

Time of ups and downs of tablets

Noise variable
6
Design methodologies (1/3)
Design of experiments


A four-factor two-level design is employed to reveal
the main effects and the interaction effects of four
factors on dissolution time:

Tablet flavor (A)

Surface area of water (B)

Volume of water (C)

Temperature of water (D)
2^4 * 2 = 32 times
7
Design methodologies (2/3)
Test matrix
8
Design methodologies (3/3)
Factor Levels
9
Experiment conduction (1/2)
10
Experiment conduction (2/2)

Snapshots
11
Analytical procedure
12
Significant factors (1/4)

Result cubes

246.50
1
247.95
198.55
101.85
205.95
111.35
100.80
108.40

210.15
188.55
103.30
101.80
1

247.65
216.25
-1
1
-1
112.60
-1

-1
1

97.55
13
Significant factors (2/4)

Main effect
A little bit
Temperature(D)


Not significant
Flavor (A) &
Volume(C)



Surface area (B)



quite significant

200
150


100
-1
1
-1

1

200
150
100
-1
1
-1
1
14
Significant factors (3/4)

（响应为 时间，Alpha = .01)
99
95
90

A
B
C
D
80

70
60
50
40
30
BCD
20
C
A
10
5

D
1
-50
-40
-30
-20

-10
0
10

15
Significant factors (4/4)

Main effect

A

C

D


BCD
16
Reduced Model

（响应为 时间，Alpha =

.01)
（响应为 时间，Alpha =
98

A
B
C
D
95
D
85

A

A
70
60

A
B
C
D
D
80
C
BCD
50
C
40
30
20
10
0
BCD
20

30
40
0
10
20

8
90
4

99
50
0
-4
10
-8
1
-10
-5
0

5
10
100
150

250

8
4.8
4
3.6
2.4
0
-4
1.2
0.0
200

10

0
B

90
.01)
2.79

-8
-8
-4
0

4
8
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32

30
40

17
Effect of factors (1/3)
Flavor


Orange tablets
take longer time
to dissolve than
peach ones
175
170


165
160
155
150
-1
1

18
Effect of factors (2/3)
Volume

Volume of water
increases, the
dissolution time
becomes shorter

170.0
167.5
165.0


162.5
160.0
157.5
155.0
-1
1

19
Effect of factors (3/3)
Temperature

As the
temperature
rises, the
dissolution time
will be shorter

220
200
180


160
140
120
100
-1
1

20
Two-factor interaction

Flavor & Temperature
The two lines are not
parallel, so they have
interaction

-1
1
220
200


180
160
140
120
100
-1
1

1.0
100
125
150
175
200
225
0.5



240
0.0

<
–
–
–
–
–
–
>
100
125
150
175
200
225
250
250
250
200

150
100
-0.5
-1
0

-1.0
-1.0
1 -1
0

-0.5
0.0

0.5
1.0
1
21
Three-factor interaction (1/2)

BCD is not quite significant

Draw the interaction plot of:
BC
D
Time
1
1
103.2
1
-1
227.2375

B and CD
-1
1
106.2125

C and BD
-1
-1
213.15
B
Time

D and BC
CD
1
1
164.1375
-1
1
167.25
1
-1
166.2
-1
-1
152.2125
BD
C
Time
1
1
150.3375
1
-1
170.9125
-1
1
162.5375
-1
-1
166.0125
In order to find out BCD’s
interaction
22
Three-factor interaction (2/2)
C and BD
time 交互作用图
time 交互作用图

-1
1
time 交互作用图

-1
170
165
1
BD
-1
1
-1
200
1
BC
-1
1
165
BC
CD
150
155
155
150
100
C
-1
1
170
165
150
D
-1
1
200
B
-1
1
165
160
160
C
D
150
B
155
155
150
100
-1
1
150
-1

CD
-1
1
160
160
BD
B and CD
D and BC
1
-1
1
Those three pairs of factors all have interaction, so
BCD have significant interaction.
23
Regression model
Since R-Sq is quite large, and there
are only 32 observations, we do not
eliminate the outlier.
24
Model validation

The evaluation
results

6
1
1
-1
1
1
99.28
103.0
4
2
1
1
-1
1
202.84
206.0
5
3
-1
-1
1
1
119.86
112.4
7
4
-1
1
1
1
114.76
104.8
1
5
-1
-1
-1
1
242
246.3
2
6
1
-1
-1
1
238.54
229.9
8
7
1
1
1
1
94.18
90.1
3
8
-1
1
-1
1
206.3
208.2
25
Model validation

95 significant
level paired-t test
26
Conclusions

The main effects of flavor, volume of water and
temperature of water are significant.

The two-factor interactions between flavor and
temperature is also significant.

Surface area does not show any significant effects
at either main effect or two-factor interactions.

The three-factor interaction of surface area, volume
of water and temperature of water is significant.


