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

- 1

1- 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

95

90

80

70

605040

30

20

10

5

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

C

A

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

90

85

80

70

60

50

403020100

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. 79

A 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 1 103.2

1 -1 227.2375

-1 1 106.2125

-1 -1 213.15

CD B Time

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

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