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
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