Upload
nen
View
49
Download
0
Embed Size (px)
DESCRIPTION
DOE Course Project. A Study of Factors that Affect Capillarity: a Designed Experiment. Team 1 : 杨路怡 陆泓宇 陈驰. Introduction. Capillarity is pervasive and widely applied. Keen academic interest in HEIGHT Actively researched Theoretical Formula Limitations: Inadequate assumptions - PowerPoint PPT Presentation
Citation preview
A Study of Factors that Affect Capillarity: a Designed Experiment
DOE Course Project
Team 1: 杨路怡 陆泓宇 陈驰
Introduction
Capillarity is pervasive and widely applied.
Keen academic interest in HEIGHT Actively researched Theoretical Formula Limitations:
Inadequate assumptions Inaccurate in characterizing capillarity Fails to consider a number of significant
factors
gdh
cos4
Purpose of the Study
To identify significant factors that affect capillarity height and their potential interactions
To provide insight for practical application and future study
Design of Experiment
Design of Experiment
A 25 (five factors, two levels, 32 tests) full factorial design
Five Factors: Solution type, tube diameter,
experimental method, moisture, angle of inclination
The response variable: Capillarity Height
Design of Experiment
Factor Low Level (-) High Level (+) Note
Solution type water ethanol drink water, pure ethanol
Tube diameter thin thick thin:0.5mm ; thick: 1mm
Experimental method descending ascending
Moisture dry wet
Inclination angle 45 。 90 。
Conducting the Experiment
Date: 2011/5/14Time:19:00-22:00Equipment :pipette, capillary tubes, beaker, Dixie cup, ruler, protractor
Analysis and Results
Main Effects
1-1
40
35
30
25
20
1-1 1-1
1-1
40
35
30
25
20
1-1
溶液
平均值
管直径 上升下降
是否浸润 倾斜角
Hei ght(mm) 主效应图数据平均值
Analysis and Results
Interactions
50
30
10
1-1
1-1 1-1
50
30
1050
30
1050
30
10
1-1
50
30
101-1
溶液
管直径
上升下降
是否浸润
倾斜角
-11
溶液
-11
管直径
-11
下降上升
-11
浸润是否
-11
倾斜角
Hei ght(mm) 交互作用图数据平均值
Analysis and Results
Identify significant factors Solution Type (A), Tube Diameter (B),
Experimental Method (C), AC, ABC
1050- 5- 10- 15- 20- 25
99
9590
80706050403020
105
1
效应
百分比
A 溶液B 管直径C 上升下降D 是否浸润E 倾斜角
因子 名称
不显著显著
效应类型
ABC
AC
BA
效应的正态图(响应为 Hei ght(mm),Al pha = . 05)
Lenth 的 PSE = 2. 83125
C
ABC
AC
B
A
9876543210
项
标准化效应
2. 056A 溶液B 管直径C 上升下降
因子 名称
标准化效应的 Pareto 图(响应为 Hei ght(mm),Al pha = . 05)
Analysis and Results
ANOVA table for the reduced modelSource DF Seq SS SS Adj MS F P
Main effects 3 7306.3 7306.3 2435.43 47.80 0.000
2-factor interaction 1 556.1 556.1 556.11 10.92 0.003
3-factor interaction 1 367.2 367.2 367.21 7.21 0.012
Residual 26 1324.7 1324.7 50.95
Lack of fit 2 360.8 360.8 180.38 4.49 0.022
Pure error 24 963.9 963.9 40.16
Total 31 9554.3
Analysis and Results
Residual Check
20100-10-20
99
90
50
10
1
残差
百分比
604530150
20
10
0
-10
拟合值残差
1680-8
10. 0
7. 5
5. 0
2. 5
0. 0
残差
频率
3230282624222018161412108642
20
10
0
-10
观测值顺序
残差
正态概率图 与拟合值
直方图 与顺序
Hei ght(mm) 残差图
Analysis and Results
Effects of solution type
1- 1
40
35
30
25
20
溶液
平均值
Hei ght(mm) 主效应图数据平均值
1- 1
50
45
40
35
30
25
20
15
溶液
平均值
-11
下降上升
Hei ght(mm) 交互作用图数据平均值
溶液
上升下降
1. 00. 50. 0- 0. 5- 1. 0
1. 0
0. 5
0. 0
- 0. 5
- 1. 0
管直径 - 1是否浸润 - 1倾斜角 - 1
保持值
> – – – < 20
20 3030 4040 50
50
Hei ght(mm)
Hei ght(mm) 与 上升下降, 溶液 的等值线图
120
40
60
- 10
0- 11
Hei ght(mm)
上升下降溶液
管直径 - 1是否浸润 - 1倾斜角 - 1
保持值
Hei ght(mm) 与 上升下降, 溶液 的曲面图
Analysis and Results
Effects of the tube diameter The thinner, the higher Height proportional to the reciprocal of
diameter Consistent with the theoretical formula No two-factor interaction
1- 1
40
35
30
25
20
管直径
平均值
Hei ght(mm) 主效应图数据平均值
Analysis and Results
Effects of the experimental method Higher capillarity achieved by
descending method Interaction with the solution type
1- 1
32
31
30
29
28
27
26
25
上升下降
平均值
Hei ght(mm) 主效应图数据平均值
1- 1
50
45
40
35
30
25
20
15
上升下降
平均值
-11
溶液
Hei ght(mm) 交互作用图数据平均值
Analysis and Results
Effects of moisture No significant effect Conjectures of the unexpectedness▪ Difficult to quantify, limited number of tubes,
hair dryer▪ Descending method nullifies the effect▪ Large measurement error
Analysis and Results
Effects of the angle of inclination 90 。 slightly higher than 45 。 Not significant Practical implication:▪ Incline the tube to let more liquid in
Analysis and Results Three-factor
interaction the best scenario is the
combination of water (inorganic solution), thinner tube and descending method.
The worst case occurs with ethanol (organic solution), thicker tube and ascending method.
Cube plot
Best case
Worst case
Analysis and Results
Regression model R-Sq = 86.14% R-Sq ( Prediction ) = 79.00% R-
Sq ( Adjusted ) = 83.47% Indicate model adequacy
Comments Two outliers with thin tubes Futile Rerun with used tubes: large
variability Impurity and water vacuoles Thick tubes more resistant to such
adverse effects
ABCACCBAy 39.317.410.379.908.1143.28ˆ
Conclusion Mains effects of the solution type, tube
diameter and the experimental method Interaction between solution type and the
experimental method Three-factor interaction of solution type,
tube diameter and experimental method No significant effects of moisture and angle Highlight
identify the experimental method as a significant factor and the interaction effects
THANK YOU!
DOE Course ProjectA Study of Factors that Affect Capillarity: a Designed Experiment
Team 1: 杨路怡 陆泓宇 陈驰