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
advertisement shows
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
时间 的立方图（数据平均值）
246.50
1
247.95
198.55
101.85
205.95
111.35
100.80
108.40
表面积
210.15
188.55
103.30
101.80
1
水量
247.65
216.25
-1
1
-1
112.60
-1
口味
-1
1
水温
97.55
13
Significant factors (2/4)

Main effect
A little bit
Temperature(D)

口味
Not significant
Flavor (A) &
Volume(C)


数据平均值
Surface area (B)


时间 主效应图
quite significant
表面积
200
150
平均值

100
-1
1
-1
水量
1
水温
200
150
100
-1
1
-1
1
14
Significant factors (3/4)
标准化效应的正态图
（响应为 时间，Alpha = .01)
99
AD
95
90
因子
A
B
C
D
80
百 分比
70
60
50
40
30
BCD
20
C
A
10
5
效应类型
不显著
显著
D
1
-50
-40
-30
-20
标准化效应
-10
0
10
名称
口味
表面积
水量
水温
15
Significant factors (4/4)

Main effect

A

C

D

AD

BCD
16
Reduced Model
标准化效应的半正态图
（响应为 时间，Alpha =
标准化效应的 P a r e t o 图
.01)
（响应为 时间，Alpha =
98
因子
A
B
C
D
95
D
85
名称
口味
表面积
水量
水温
A
AD
项
A
70
60
因子
A
B
C
D
D
80
C
AD
BCD
50
C
40
30
20
10
0
BCD
20
绝对标准化效应
30
40
0
10
20
标准化效应
时间 残差图
正态概率图
与拟合值
8
90
4
残差
99
50
0
-4
10
-8
1
-10
-5
0
残差
5
10
100
150
直方图
250
与顺序
8
4.8
4
3.6
2.4
0
-4
1.2
0.0
200
拟合值
残差
10
百分比
0
B
频率
百分比
90
.01)
2.79
效应类型
不显著
显著
-8
-8
-4
0
残差
4
8
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32
观测值顺序
30
40
名称
口味
表面积
水量
水温
17
Effect of factors (1/3)
Flavor

时间 主效应图
数据平均值
Orange tablets
take longer time
to dissolve than
peach ones
175
170
平均值

165
160
155
150
-1
1
口味
18
Effect of factors (2/3)
Volume

Volume of water
increases, the
dissolution time
becomes shorter
时间 主效应图
数据平均值
170.0
167.5
165.0
平均值

162.5
160.0
157.5
155.0
-1
1
水量
19
Effect of factors (3/3)
Temperature

As the
temperature
rises, the
dissolution time
will be shorter
时间 主效应图
数据平均值
220
200
180
平均值

160
140
120
100
-1
1
水温
20
Two-factor interaction
时间 交互作用图
Flavor & Temperature
The two lines are not
parallel, so they have
interaction
口味
-1
1
220
200
平均值

180
160
140
120
100
-1
1
水温
时间 与 水温, 口味 的等值线图
时间 与 口味, 水温 的曲面图
1.0
100
125
150
175
200
225
0.5
水温

数据平均值
240
0.0
时间
<
–
–
–
–
–
–
>
100
125
150
175
200
225
250
250
250
200
时间
150
100
-0.5
-1
0
水温
-1.0
-1.0
1 -1
0
口味
-0.5
0.0
口味
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
数据均值
数据均值
-1
1
time 交互作用图
数据均值
-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
标准序
运行序
水量
口味
水温
表面积（大）
预测
实际
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.

时间 = 162 - 10.2 口味 + 2.72 表面积 - 6.01 水量 - 57.7
水温 + 7.65 口味*水温- 4.28 表面积*水量*水温

The advertisement in Taobao isn’t reliable.
27
Thanks!
Q&A