a designed experiment - tsinghua · pdf filethe full-factorial designed experiment ......
TRANSCRIPT
Factor Analysis for Dissolution
Time of Effervescent Tablets
A Designed Experiment
Niu Jinshu (2010010837)
Wu Xianyu (2010010838)
Cao Liuxing (2010010836)
Wu Yining (2010010835)
Dai Yibo (2010010833)
DOE Project – Factor analysis for dissolution time of effervescent tablets
1
Content
Abstract ....................................................................................................................................................... 3
Experiment Background & Objectives ....................................................................................................... 3
Background ......................................................................................................................................... 3
Objectives ............................................................................................................................................ 3
Experiment Design ...................................................................................................................................... 4
Initial Variable Analysis & Selection .................................................................................................. 4
Variable Table ...................................................................................................................................... 4
Response Variable ....................................................................................................................... 4
Control variable ........................................................................................................................... 5
Constant variable ......................................................................................................................... 5
Noise variable.............................................................................................................................. 6
Fishbone Diagram ............................................................................................................................... 6
Full factorial design .................................................................................................................................... 7
Test matrix ........................................................................................................................................... 7
Factor levels ........................................................................................................................................ 8
Conducting the experiment ......................................................................................................................... 9
Experiment operations ........................................................................................................................ 9
Snapshots of experiments .................................................................................................................. 10
Analysis and result .................................................................................................................................... 10
Experiment data ................................................................................................................................ 10
Effects of factors ............................................................................................................................... 13
Significant factors ..................................................................................................................... 13
Effect of each factor .................................................................................................................. 18
2-factor-interacion ............................................................................................................................. 20
3-factor-interacion ............................................................................................................................. 23
Regression model .............................................................................................................................. 26
Conclusion and discussion ........................................................................................................................ 27
Model validation ....................................................................................................................................... 27
Figure Content
Figure 1 Fishbone diagram of dissolution rate .................................................................................... 7
Figure 2 Snapshot of experiments ..................................................................................................... 10
Figure 3 Result cubes ........................................................................................................................ 12
Figure 4 Main effect plot for the 4 factors ........................................................................................ 13
Figure 5 Interaction plot for the 4 factors.......................................................................................... 14
DOE Project – Factor analysis for dissolution time of effervescent tablets
2
Figure 6 The normality plot for effects ............................................................................................. 14
Figure 7 ANOVA table ...................................................................................................................... 15
Figure 8 Reduced Model Normality plot .......................................................................................... 15
Figure 9 Half normal probability plot ............................................................................................... 16
Figure 10 Pareto plot of the reduced model ...................................................................................... 16
Figure 11 ANOVA for the reduced model ......................................................................................... 17
Figure 12 Residual plot ..................................................................................................................... 17
Figure 13 Main effect plot of flavor .................................................................................................. 18
Figure 14 Main effect plot of volume ............................................................................................... 19
Figure 15 Main Effect Plot of temperature ....................................................................................... 20
Figure 16 Interaction plot for temperature and flavor ....................................................................... 21
Figure 17 The contour plot for flavor and temperature ..................................................................... 22
Figure 18 The response surface ......................................................................................................... 22
Figure 19 Cube plot of three factor interaction ................................................................................. 23
Figure 20 The interactions between BC and D ................................................................................. 24
Figure 21 The interactions between CD and B ................................................................................. 24
Figure 22 The interactions between BD and C ................................................................................. 25
Figure 23 The regression model ........................................................................................................ 26
Figure 24 paired-t test ....................................................................................................................... 28
Table Content
Table 1 Response variable ................................................................................................................... 4
Table 2 Control variables .................................................................................................................... 5
Table 3 Constant variables .................................................................................................................. 5
Table 4 Noise variables ....................................................................................................................... 6
Table 5 Test matrix of experiment ....................................................................................................... 7
Table 6 Factor levels ........................................................................................................................... 8
Table 7 Experiment operations ............................................................................................................ 9
Table 8 Experiment result ................................................................................................................. 10
Table 10 Interactions analysis of three factor .................................................................................... 23
DOE Project – Factor analysis for dissolution time of effervescent tablets
3
Abstract
It is generally accepted that the dissolution rate of effervescent tablets varies with own
properties as well as other environment factors. However, among various possible influential
factors, there are factors, such as volume of water, whose impact on dissolution rate is unclear.
In order to explore the impact of some factors, we design this experiment to gain observations.
Moreover, some factors, such as liquid temperature, are commonly known as a key factor. We
also include it in the experiment to examine its impact. The full-factorial designed experiment
identifies the temperature of water, volume of water, surface area of liquid and flavor of
effervescent tablet as effects. Two-factor interactions and three-factor interactions are involved.
Based on the collected data and result, we have some discussion, and summarize the
implication.
Key words: Dissolution Rate, Effervescent Tablet, Design of Experiment
Experiment Background & Objectives
Background
Effervescent tablets are popular among young people. It contains vitamins and has a pleasant
taste. If dropped into water, the tablet starts effervesce, goes up and down, and gradually
dissolves, and finally disappears. We observe that sometimes it takes only about one minute to
dissolute completely, while it may sometimes take several minutes. Therefore, we are curious
about what factors are having significant effects on the dissolution rate. Thanks to the
opportunity of DOE project, we are able to design a systematic experiment to probe into this
problem.
Objectives
The project aims at determining what the influential factors of effervescent tablets’ dissolution
rate are and their level of influence. Also, we are looking into the correlation between these
factors. Experimental design method is employed to study how response variable reacts to
controllable factors. We collect fairly reasonable amount of data, and then analyze them to find
out the influential factors of dissolution rate of effervescent tablets. Finally, we give our own
explanation on the result and implication presented.
DOE Project – Factor analysis for dissolution time of effervescent tablets
4
Experiment Design
Initial Variable Analysis & Selection
The dissolution rate of the effervescent tablet under the same circumstance varies a lot because
of effervesce, which will release a huge amount of carbon dioxide and lead to the acceleration
of dissolution. Based on the observation of the dissolution of the effervescent tablet, we assume
that the influence of effervesce can be minimized carefully and will not affect the initial
intention of our experiment.
We believe that there may be several factors which will affect the rate of dissolution.
1. Composition of the effervescent tablet
2. Type of liquid
3. Volume of water
4. Temperature of water
5. Surface area of liquid (related to the release of carbon dioxide)
6. Surface area of the effervescent tablet
7. Temperature and air pressure around
8. Experiment method (whether stir is included)
9. Place of experiment
10. Time of ups and downs of the effervescent tablet
Variable Table
Response Variable
Table 1 Response variable
Response
Variable (units)
Normal
Operating
Level & Range
Measure
Precision
Recommended
Experiment
Settings
Relationship with the
Experiment Objective
Dissolution Time
(s) 0 ~ 300 s 0.1 s Stopwatch
Determine the
dissolution rate of the
effervescent tablet
DOE Project – Factor analysis for dissolution time of effervescent tablets
5
Control variable
Table 2 Control variables
Control
Variable
(units)
Normal
Operating
Level & Range
Measure
Precision
Recommended
Experiment Settings Predicted Effects
Volume of
water (ml) 0 ~ 500 ml 1 ml Measuring Pot
Larger the volume
of water is, larger
the rate of
dissolution will be.
Temperature of
water (℃) 0 ~ 100 ℃ 0.1 ℃
Electronic
Thermometer
Higher the
temperature of
water is, larger the
rate of dissolution
will be.
Surface area of
liquid (cm2) 0 ~ 200 cm2 1 cm2
Calculating by
measuring the volume
of water with
measuring pot and the
height of the container
with ruler
Larger the surface
area of liquid is,
larger the rate of
dissolution will be.
Flavor of the
effervescent
tablet
Orange/Peach --- --- ---
Constant variable
Table 3 Constant variables
Control
Variable
(units)
Normal
Operating
Level & Range
Measure
Precision
Recommended
Experiment
Settings
Predicted Effects
Type of liquid --- --- Water ---
Composition of
the effervescent
tablet
--- --- Looking into
the list of
ingredients
effervescent tablet
from the same brand
will have the familiar
composition
Surface area of --- --- Surface area of Larger the surface
DOE Project – Factor analysis for dissolution time of effervescent tablets
6
the effervescent
tablet
the original
effervescent
tablet
area of the
effervescent tablet is,
larger the rate of
dissolution will be.
Experiment
method
--- --- No stir included Stir will accelerate
the dissolution
Place of
experiment
--- --- Fixed place ---
Noise variable
Table 4 Noise variables
Control
Variable
(units)
Normal
Operating
Level & Range
Measure
Precision
Recommended Experiment
Settings
Predicted
Effects
Temperature
around
Fixed Unnecessary Shorten the experiment time
and do the experiment at the
same place to avoid the
change of temperature around
No effect
Air pressure
around
Fixed Unnecessary Ditto No effect
Time of ups
and downs of
the effervescent
tablet
0 ~ 3 times,
length of time
varies
Unnecessary --- No effect
Fishbone Diagram
Factors that could potentially affect the dissolution rate are summarized in the fishbone diagram
below. Based on this, the factors that are considered able to control given the experimental
conditions are selected in the following full factorial design.
DOE Project – Factor analysis for dissolution time of effervescent tablets
7
Figure 1 Fishbone diagram of dissolution rate
Full factorial design
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)
Test matrix
Table 5 Test matrix of experiment
Standard
Sequence
Running
Sequence
Flavor Surface
area
Volume
of water
Temperature
of water
11 1 -1 1 -1 1
1 2 -1 -1 -1 -1
7 3 -1 1 1 -1
32 4 1 1 1 1
27 5 -1 1 -1 1
17 6 -1 -1 -1 -1
19 7 -1 1 -1 -1
31 8 -1 1 1 1
12 9 1 1 -1 1
10 10 1 -1 -1 1
DOE Project – Factor analysis for dissolution time of effervescent tablets
8
13 11 -1 -1 1 1
22 12 1 -1 1 -1
20 13 1 1 -1 -1
18 14 1 -1 -1 -1
23 15 -1 1 1 -1
16 16 1 1 1 1
2 17 1 -1 -1 -1
15 18 -1 1 1 1
24 19 1 1 1 -1
30 20 1 -1 1 1
25 21 -1 -1 -1 1
8 22 1 1 1 -1
14 23 1 -1 1 1
9 24 -1 -1 -1 1
28 25 1 1 -1 1
21 26 -1 -1 1 -1
26 27 1 -1 -1 1
3 28 -1 1 -1 -1
6 29 1 -1 1 -1
29 30 -1 -1 1 1
4 31 1 1 -1 -1
5 32 -1 -1 1 -1
Factor levels
Table 6 Factor levels
-1 1
Flavor Orange peach
Surface area small large
Volume of water 150 ml 450 ml
Temperature of water 25 degrees 70 degrees
DOE Project – Factor analysis for dissolution time of effervescent tablets
9
Conducting the experiment
Experiment operations
Table 7 Experiment operations
Date 2013/5/27 Time 18:00-21:00
Experimenters Girls in ZJ8# 612B and their friend Place Dormitory
Equipment
and materials
500 ml measuring cup; digital thermometer (-50~300 degree); two
transparent cups (with small and large surface areas); effervescent
tablets (orange and peach flavors); hot and cold water
Operation
steps
1. Mixing the hot and cold water in the measuring cup and measure
the current temperature in the cup using the digital thermometer
2. Adding more hot water or cold water according to the degrees
shown on the thermometer
3. When the temperature of the water is appropriate, putting defined
amount of water into the transparent cup needed
4. Putting defined tablets into that cup and then start timing
immediately
5. Stop timing when the tablet completely dissolves
DOE Project – Factor analysis for dissolution time of effervescent tablets
10
Snapshots of experiments
Figure 2 Snapshot of experiments
Analysis and result
Experiment data
Using Minitab, we design the order of each replication. And the experiment was conducted by
the operation order shown in Table 1. The time is the dissolution time of the tablets. More
explanation of the meaning of “-1/1” is shown in table 2. We did 2 replications for each
experiment conditions, and the average time is shown in Figure 1.
Table 8 Experiment result
标准序 运行序 中心点 口味 表面积 水量 水温 时间(s)
11 1 1 -1 1 -1 1 107
1 2 1 -1 -1 -1 -1 254.8
DOE Project – Factor analysis for dissolution time of effervescent tablets
11
7 3 1 -1 1 1 -1 249.1
32 4 1 1 1 1 1 93.2
27 5 1 -1 1 -1 1 115.7
17 6 1 -1 -1 -1 -1 240.5
19 7 1 -1 1 -1 -1 251.9
31 8 1 -1 1 1 1 100.7
12 9 1 1 1 -1 1 107.2
10 10 1 1 -1 -1 1 99.2
13 11 1 -1 -1 1 1 106.9
22 12 1 1 -1 1 -1 189.2
20 13 1 1 1 -1 -1 200.3
18 14 1 1 -1 -1 -1 223.8
23 15 1 -1 1 1 -1 243.9
16 16 1 1 1 1 1 108.4
2 17 1 1 -1 -1 -1 208.7
15 18 1 -1 1 1 1 103
24 19 1 1 1 1 -1 195.4
30 20 1 1 -1 1 1 108.8
25 21 1 -1 -1 -1 1 112.1
8 22 1 1 1 1 -1 201.7
14 23 1 1 -1 1 1 94.8
9 24 1 -1 -1 -1 1 113.1
28 25 1 1 1 -1 1 109.6
21 26 1 -1 -1 1 -1 207.2
26 27 1 1 -1 -1 1 95.9
3 28 1 -1 1 -1 -1 244
6 29 1 1 -1 1 -1 187.9
29 30 1 -1 -1 1 1 99.7
4 31 1 1 1 -1 -1 211.6
5 32 1 -1 -1 1 -1 213.1
DOE Project – Factor analysis for dissolution time of effervescent tablets
12
Figure 3 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)
DOE Project – Factor analysis for dissolution time of effervescent tablets
13
Effects of factors
Significant factors
Figure 4 Main effect plot for the 4 factors
From the figure above, we can see that the surface area have little main effect on the dissolution
time, while the flavor, volume of water, temperature have significant main effects on the
dissolution time. And the temperature has the largest main effect.
For the flavor factor, the peach flavor tablets have shorter resolving time than the orange ones.
And if the volume of the water is large, the resolving time is shorter than that of the small
volume. As temperature rises, the dissolution time gets shorter.
If no interaction is detected between the surface area and other factors, this factor can be
negligible.
1-1
200
150
100
1-1
1-1
200
150
100
1-1
口味
平均
值
表面积
水量 水温
时间 主效应图数据平均值
DOE Project – Factor analysis for dissolution time of effervescent tablets
14
Figure 5 Interaction plot for the 4 factors
From the figure above, we can find there is interaction between the flavor and temperature
factors. To test whether the main effects from each factor and the interaction are significant, we
check the normality plot.
Figure 6 The normality plot for effects
From Figure 6, we get the conclusion that the significant terms are flavor (A), volume(C),
temperature (D), two-factor interaction AD and three-factor interaction B(surface area)CD.
1-1 1-1
200
150
100
200
150
100
200
150
100
1-1
200
150
100
1-1
口味
表面积
水量
水温
-1
1
口味
-1
1
表面积
-1
1
水量
-1
1
水温
时间 交互作用图数据平均值
100-10-20-30-40-50
99
95
90
80
70
60
50
40
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(响应为 时间,Alpha = .01)
DOE Project – Factor analysis for dissolution time of effervescent tablets
15
To confirm the finding, we use ANOVA analysis to check the effects of the factors and the
interaction of the factors. And on a significance level of 99, we get the same result.
Figure 7 ANOVA table
We form a reduced model with only the significant terms, and get the following figures,
including the normality plot, half normal probability plot and Pareto Plot.
Figure 8 Reduced Model Normality plot
0-10-20-30-40
99
95
90
80
70
60
50
40
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(响应为 时间,Alpha = .01)
DOE Project – Factor analysis for dissolution time of effervescent tablets
16
Figure 9 Half normal probability plot
Figure 10 Pareto plot of the reduced model
And the ANOVA result from the reduced model is shown in Figure 9. The left factors and
interactions all have a p<=0.01. The result is quite satisfied.
403020100
98
95
90
85
80
70
60
50
40
30
20
10
0
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(响应为 时间,Alpha = .01)
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
标准化效应的 Pareto 图(响应为 时间,Alpha = .01)
DOE Project – Factor analysis for dissolution time of effervescent tablets
17
Figure 11 ANOVA for the reduced model
Figure 12 Residual plot
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
DOE Project – Factor analysis for dissolution time of effervescent tablets
18
Effect of each factor
Flavor
Figure 13 Main effect plot of flavor
The orange tablets take longer time to dissolve than the peach ones. We checked the content of
each type of the tablets, and found the types of pigment added in the tablets are not the same.
Maybe the dissolving ability of the pigment are not the same, thus causes the difference in the
dissolution time of the two flavors of tablets.
1-1
175
170
165
160
155
150
口味
平均
值
时间 主效应图数据平均值
DOE Project – Factor analysis for dissolution time of effervescent tablets
19
Volume
Figure 14 Main effect plot of volume
From the figure above, we draw conclusion that as the volume of water increases, the
dissolution time becomes shorter. From the research of others, we found little information of
the common relationship between the resolve speed and the volume of water, but from the study
of Shuhong Wang, “Analysis on relationship between Cyclophosphamide dissolving speed and
amount of solvent”, she found that if the amount of solvent is larger, the speed of dissolve is
higher.
And in our experiment, we found a phenomenon that when the tablets were dropped in larger
amount of water, the tablets would go up and down several times in the water, which gave the
tablets more opportunities to contact with the solvent, thus increase the dissolve speed.
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
DOE Project – Factor analysis for dissolution time of effervescent tablets
20
Temperature
Figure 15 Main Effect Plot of temperature
It is clear that as the temperature rises, the dissolution time will be shorter. This result matches
our common sense well. And among the three factors, the temperature plays the most important
role in determination of the dissolution time.
2-factor-interacion
From the interaction plot of the flavor and temperature (the following figure), we detect the
lines are not parallel; there may be interaction between the two factors.
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
DOE Project – Factor analysis for dissolution time of effervescent tablets
21
Figure 16 Interaction plot for temperature and flavor
The contour plot (Figure 15) also confirms the interaction between these two factors. The
contour is curved, so the response is determined by the two factors together. And the response
surface (Figure 16) is a little bit twisted, leads to the same conclusion. The reason why these
two factors have interaction may be the feature of the pigment. We guess the pigment added in
the peach flavor have different dissolving ability against the pigment added in the orange flavor
at different level of temperature. But since the pigments are not the main components, so the
interaction between flavor and temperature is not so obvious.
1-1
240
220
200
180
160
140
120
100
水温
平均
值-1
1
口味
时间 交互作用图数据平均值
DOE Project – Factor analysis for dissolution time of effervescent tablets
22
Figure 17 The contour plot for flavor and temperature
Figure 18 The response surface
口味
水温
1.00.50.0-0.5-1.0
1.0
0.5
0.0
-0.5
-1.0
>
–
–
–
–
–
–
< 100
100 125
125 150
150 175
175 200
200 225
225 250
250
时间
时间 与 水温, 口味 的等值线图
10
100
150
200
250
-1
0
-11
口味
时间
水温
时间 与 口味, 水温 的曲面图
DOE Project – Factor analysis for dissolution time of effervescent tablets
23
3-factor-interacion
Figure 19 Cube plot of three factor interaction
From the cube plot (Figure 17) of the three-factor interaction, we can have a basic conception
of the data, but it is not so obvious that the three-factor terms BCD is significant in the effect of
the dissolution time. So we continue to do the interaction plot of “B and CD”, “C and BD”, “D
and BC” as figure 18, 19, 20.
Table 9 Interactions analysis of three factor
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
1
-1
1-1
水温
水量
表面积
101.325
109.875105.075
102.550
222.525
226.950231.950
199.350
时间 的立方图(数据均值)
DOE Project – Factor analysis for dissolution time of effervescent tablets
24
-1 1 162.5375
-1 -1 166.0125
Figure 20 The interactions between BC and D
Figure 21 The interactions between CD and B
1-1
200
150
100
1-1
200
150
100
BC
D
-1
1
BC
-1
1
D
time 交互作用图数据均值
1-1
165
160
155
150
1-1
165
160
155
150
CD
B
-1
1
CD
-1
1
B
time 交互作用图数据均值
DOE Project – Factor analysis for dissolution time of effervescent tablets
25
Figure 22 The interactions between BD and C
From the above figure, we can perceptional confirm that interactions between B and CD, C and
BD are significant at 5% confidence level. As a result, the three factor interaction is significant.
However,it may require a reasonable explanation of the three factor interaction as the main
effect of the surface area is not significant and the high order interaction is not so much familiar
in the normal experiment. We went back to check the data and find that the response factor is
largely influenced by the factor D (water temperature). And the cross-sectional area of the
experimental cup, namely the factor B surface area, and the water volume has relationship
physically. As we all know,
V = S × h = π𝑟2 × h
S𝑇 = C × h + 2S = 2πrh + 2π𝑟2
Then we guess this may contribute some hidden effects of three factor interaction.
The room temperature is about25𝑜𝐶. The material of the cup is plastic. According to the
previous study of the scientists, water temperature decreases faster with higher differences with
the outer temperature, and the total surface area of the water body experimented may have
larger effect on the cooling process. Checking the interaction plot of BC and D, the difference
of the two lines slopes are not so big, while the interaction between BD and C, CD and B are
much significant.
It is sure that the dissolution time is shorter with high water temperature, the interaction plot
also shows that the response factor also has difference performances under the condition of
different total surface area (BC), and this kind of difference is more obvious when temperature
is higher. So when the water temperature is high, the hidden effect of BC becomes significant.
1-1
170
165
160
155
150
1-1
170
165
160
155
150
BD
C
-1
1
BD
-1
1
C
time 交互作用图数据均值
DOE Project – Factor analysis for dissolution time of effervescent tablets
26
And this kind of interactions cannot be rejected in our data, we try to do normality of the
response time, the BCD is always in the accept family with near the boundary value (p=0.05).
This may be kind of Marginal utility.
Regression model
Figure 23 The regression model
The final model is:
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
Although there are two outliers, we find R-Sq is quite large, and there are only 32 observations,
so we do not eliminate the outliers.
DOE Project – Factor analysis for dissolution time of effervescent tablets
27
Conclusion and discussion
The following conclusions can be drawn from this study:
a. The main effects of flavor, volume of water and temperature of water are significant.
b. The two-factor interactions between flavor and temperature is also significant.
c. Surface area does not show any significant effects at either main effect or two-factor
interactions.
d. The three-factor interaction of flavor, volume of water and temperature of water is
significant.
e. 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
Model validation
From the above test, we form a model of the factors and interactions:
Time = 162 − 10.2 口味 + 2.72 表面积 − 6.01 水量 − 57.7 水温 + 7.65 口味 ∗水
− 4.28 表面积 ∗水量 ∗水温.
To evaluate the model, we conduct 8 more runs to compare the anticipated time and the real
time. The settings of the level of the factors are shown below with the anticipated value and
experiment value:
Table 10 Evaluation of the model
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
Using a 95 significant level paired-t test, we check whether the anticipated value matches the
actual time. From the result, we find the difference of the two sets of data will fall into the
interval (-2.92, 7.19). And we cannot reject the hypothesis that the anticipate value and actual
value are equal.
DOE Project – Factor analysis for dissolution time of effervescent tablets
28
Figure 24 paired-t test