Post on 25-Feb-2016
description
Factor Analysis for Dissolution Time of Effervescent Tablets
NIU JINSHU (2010010837)WU XIANYU (2010010838)
CAO LIUXING (2010010836)WU YINING (2010010835)
DAI YIBO (2010010833)
2Outlines• 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
3Purpose of experiment
Explore how different factors affect dissolution rate
Provide several implications to the dissolution process
Test if the advertisement shows the correct condition
4Experiment design – Factors (1/2) Fishbone diagram
5Experiment design – Factors (2/2)
Response variable Dissolution time:
0~300s Control variable
Volume of water Temperature of water Surface area of water Tablet flavor
Constant variable Composition Place surface area of tablets
Noise variable Temperature around Air pressure Time of ups and downs of
tablets
6Design 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
7Design methodologies (2/3)
Test matrix
8Design methodologies (3/3)
Factor Levels
9Experiment conduction (1/2)
10Experiment conduction (2/2)
Snapshots
11
Analytical procedure
12Significant factors (1/4)
Result cubes
1- 1
1
- 1
1
- 11- 1
水温
水量
表面积
口味
100. 80
101. 80103. 30
101. 85
108. 40
97. 55112. 60
111. 35
198. 55
188. 55210. 15
246. 50
205. 95
216. 25247. 65
247. 95
时间 的立方图(数据平均值)
13Significant factors (2/4)
1-1
200
150
1001-1
1-1
200
150
1001-1
口味
平均值
表面积
水量 水温
时间 主效应图数据平均值
Main effect Surface area (B)
Not significant Flavor (A) &
Volume(C) A little bit
Temperature(D) quite significant
14Significant factors (3/4)
100- 10- 20- 30- 40- 50
99
9590
80706050403020
105
1
标准化效应
百分比
A 口味B 表面积C 水量D 水温
因子 名称
不显著显著
效应类型
BCD
AD
D
CA
标准化效应的正态图 Al pha = . 01)(响应为 时间,
15Significant factors (4/4)
Main effect A C D AD BCD
16Reduced Model
403020100
98
95
908580
706050403020100
绝对标准化效应
百分比
A 口味B 表面积C 水量D 水温
因子 名称
不显著显著
效应类型
BCD
AD
D
C
A
标准化效应的半正态图 Al pha = . 01)(响应为 时间,
B
BCD
C
AD
A
D
403020100
项
标准化效应
2. 79A 口味B 表面积C 水量D 水温
因子 名称
Pareto 标准化效应的 图 Al pha = . 01)(响应为 时间,
1050-5-10
99
90
50
10
1
残差
百分比
250200150100
8
4
0
-4
-8
拟合值
残差
840-4-8
4. 8
3. 6
2. 4
1. 2
0. 0
残差
频率
3230282624222018161412108642
8
4
0
-4
-8
观测值顺序
残差
正态概率图 与拟合值
直方图 与顺序
时间 残差图
17Effect of factors (1/3)
Flavor Orange tablets
take longer time to dissolve than peach ones
1- 1
175
170
165
160
155
150
口味
平均值
时间 主效应图数据平均值
18Effect of factors (2/3)
Volume Volume of water
increases, the dissolution time becomes shorter
1- 1
170. 0
167. 5
165. 0
162. 5
160. 0
157. 5
155. 0
水量
平均值
时间 主效应图数据平均值
19Effect of factors (3/3)
Temperature As the
temperature rises, the dissolution time will be shorter
1- 1
220
200
180
160
140
120
100
水温
平均值
时间 主效应图数据平均值
20Two-factor interaction
Flavor & Temperature The two lines are not
parallel, so they have interaction
1- 1
240
220
200
180
160
140
120
100
水温
平均值
-11
口味
时间 交互作用图数据平均值
口味
水温
1. 00. 50. 0- 0. 5- 1. 0
1. 0
0. 5
0. 0
- 0. 5
- 1. 0
> – – – – – – < 100
100 125125 150150 175175 200200 225225 250
250
时间
, 时间 与 水温 口味 的等值线图
10
100
150
200
250
-10
-11
口味
时间
水温
, 时间 与 口味 水温 的曲面图
21Three-factor interaction (1/2)
BCD is not quite significant Draw the interaction plot of:
B and CD C and BD D and BC
In order to find out BCD’s interaction
BC D Time
1 1 103.21 -1 227.2375-1 1 106.2125-1 -1 213.15CD B Time
1 1 164.1375-1 1 167.251 -1 166.2-1 -1 152.2125BD C Time
1 1 150.33751 -1 170.9125-1 1 162.5375-1 -1 166.0125
22Three-factor interaction (2/2)
Those three pairs of factors all have interaction, so BCD have significant interaction.
C and BD B and CDD and BC
1- 1
170
165
160
155
150
1- 1
170
165
160
155
150
BD
C
- 11
BD
-11
C
t i me 交互作用图数据均值
1- 1
200
150
100
1- 1
200
150
100
BC
D
- 11
BC
-11
D
t i me 交互作用图数据均值
1- 1
165
160
155
150
1- 1
165
160
155
150
CD
B
- 11
CD
-11
B
t i me 交互作用图数据均值
23Regression model
Since R-Sq is quite large, and there are only 32 observations, we do not eliminate the outlier.
24Model validation
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
The evaluation results
25Model validation
95 significant level paired-t test
26Conclusions
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