Project Report of DOE

Course -- Research on Factors Affecting the Stickiness of

Home-made Paste

Group Leader：曾夏明

Group Members：刘宝龙，赵妤婕，毛茅，闫博，权

宣亨

2010/6/20

Contents

1. Motivation ................................................................................................................................. 2

2. Literature Review ...................................................................................................................... 2

2.1 The history of home-made paste .................................................................................. 2

2.2 Principle of making paste: ............................................................................................ 3

2.3 Common methods of making paste .............................................................................. 3

2.4 Procedure of making paste ........................................................................................... 4

3. Factor Decomposition ............................................................................................................... 4

3.1 Assumption .................................................................................................................. 4

3.2 Variable definition ........................................................................................................ 4

3.2.1 Response variable ................................................................................................ 4

3.2.2 Factors interested ................................................................................................. 5

3.2.3 Noise factor .......................................................................................................... 5

3.2.4 Constant factor ..................................................................................................... 5

4. Design of experiment ................................................................................................................ 5

4.1 Sample size analysis ..................................................................................................... 6

4.2 Factor level definition .................................................................................................. 6

4.3 Implementation of the experiments .............................................................................. 7

4.4 The results of the experiment ....................................................................................... 9

5. Data analysis ........................................................................................................................... 10

5.1 Basic analysis ............................................................................................................. 10

5.1.1 Main Effects ....................................................................................................... 10

5.1.2 Interaction Plot ................................................................................................... 11

5.1.3 Half Normal Plot ................................................................................................ 11

5.1.4 Pareto Plot .......................................................................................................... 12

5.1.5 Half Normal Standardized Effects: .................................................................... 13

5.1.6 ANOVA ............................................................................................................. 13

5.1.7 Residual Plot ...................................................................................................... 14

5.1.8 Contour Plots of Result ...................................................................................... 15

5.1.9 Response Surface Plot ....................................................................................... 15

5.2 Further analysis .......................................................................................................... 16

5.3 Optimization design ................................................................................................... 17

6. Conclusion .............................................................................................................................. 18

7. Possible improvement for our experiment .............................................................................. 18

8. Reference ................................................................................................................................ 18

1. Motivation

Home-made paste is a Chinese tradition which could date back to ancient times.

The use of paste is to paste couplets and framed painting.

The reason that we choose home-made paste for the prototype of the Design of

Experiment project is that the theorem and process of making paste is relatively

simple and easy to handle. Moreover, the procedure of manufacturing is convenient to

control for the reason that there’re relatively fewer noise factors. As a result we form

the process of making home-made paste as a manufacturing process, and are trying to

explore some of the factors that affect the quality and feasibility of paste.

2. Literature Review

2.1 The history of home-made paste

Home-made paste is mostly used as the adhesion of framed painting throughout

Chinese history. The techniques for making paste have had received great

achievements in the ancient times. The most famous pieces are:

“Famous Paintings in History” (《历代名画记》) from Yanyuan Zhang in

Tang Dynasty

“Evaluation of Ancient Framed Painting” (《论鉴赏装裱古画》) in Song

Dynasty

“Record of Framing” (《装潢志》) from Jiazhou Chou in Ming Dynasty

It is said in “Zhuang Huang Zhi” that:

We know that the techniques of making paste do not only focus on the quality of

adhesion, but also on the maintenances of it. Moreover, the level of paste that is

pleasing to the eye is also an important criterion of home-made paste for framed

paintings.

“表于之糊,犹墨之于胶。墨以胶成,表以糊就。胶用善则灵液清虚, 糊用仁则卷舒温

适。调用之宜,妍媸攸赖。良之用糊如水,止在多刷,刷多则水泌透纸。凝结如抄成者,不全

恃糊力矣。”

2.2 Principle of making paste:

The material of making paste is flour. When flour is solved in water and formed

as glue, the original phase of paste is achieved. Of course, the addictive to paste varies

greatly corresponding to the purpose of paste. It is obvious that paste for framed

painting is more refined than that of daily use. In order for the feasibility of making,

we simplified the components of paste:

Starch

It is insoluble in water, alcohol and ether, but its cell membrane will rupture

when heated together with water, swelling into a transparent paste.

NaOH

It vaginally discharges the water molecules in starch granules, producing

expansion of the viscosity of starch as well as lowering the gelatinization

temperature.

Phenol

Pest control, anti-corrosion

Water

The environment for the starch to get paste.

2.3 Common methods of making paste

There’re many kinds of methods to make paste. The most commonly used four are:

Water washing Method

Use water in to dissolve the flour and form the glue phase of the paste.

And it is used in our experiment.

Steam Blowing Method

Blowing steam into the flour with water

Boiling in the Pot Method

Boling the paste of flour and water in the pot, the high temperature may lead to

the form of paste.

Agar-paste Method

Agar is a kind of expensive but exquisite material for making paste. The paste

made from Agar is relatively with better quality and appearance. However, the

cost of it is high, which is not suitable for common experiments.

2.4 Procedure of making paste

According to the knowledge of making paste and some chemical principles, we

generate our procedure of making paste.

Figure 1 the procedure of making paste

At first we dissolve NaOH into water and form the NaOH solution, than add flour

to the solution and at the same time pour hot water into it. After that, we add in phenol

and stir the mixture always in the same direction until the paste cools off.

Since we have already made our paste, the next procedure is to add weight and

measure the strength and viscosity of paste correspond to the magnitude of weight.

3. Factor Decomposition

3.1 Assumption

When considering the viscosity of paste, the four factors: temperature of water,

mess ratio of water and flour, value of NaOH, and Phenol are of the interests to

research. According to the literature we found, the addition of Phenol is used for

anti-corrosion, and perhaps has nothing to do with the viscosity.

3.2 Variable definition

3.2.1 Response variable

The viscosity (stickiness) of home-made paste

NaOH SolutionAdd flour to the solution

Add hot water

Add PhenolStir the paste

and let the paste cool off

Add weight and measure

the weight

We measure the viscosity of paste by measuring the strength of paste to bear

pulling force. Namely, we use some force to stretch the paste and see how much the

extreme forces are that the paste can bear. Specifically, we stick a pocket under to the

pasted papers. And then we add coins in the pocket to increase the weights that apply

to the paste. Accordingly, we can convert the force into the weight of coins that

correspond to the force.

3.2.2 Factors interested

Concentration of NaOH Solution

Water Temperature

Mass ratio of Water to flour

Whether or not to Phenol

3.2.3 Noise factor

Factors that we could not handle are the noise factors, and we try to eliminate their

effects on our experiment. The ways that we use generally are blocking and

randomization. The followings are the noise factors in our experiment as far as we

concerned.

Operator variation

Measurement of force

Way to paint the paste

3.2.4 Constant factor

Factors that we are not interested in and can be controlled are set to be constant.

This is a good way to simplify our experiment. The followings are the constant factors

in our experiment as far as we concerned.

Stirring time

The room temperature

Flour lot

Time after pasting

4. Design of experiment

After defining the factors, we continue to come up with a feasible and effective

experiment design. We thought that a full factorial design is good one based on

the following reasons:

a) there are in total four factors, not too much;

b) relationships among all factors are to be identified;

c) all main effects and all interactions are to be estimated;

We can measure the responses by using various combinations of factors and levels in

order to determine the large-effect factors and distinct interactions between factors.

4.1 Sample size analysis

Sample size analysis is important in the design of experiments. However, we can’t

find a way to determine sample size for a four factor experiment.

So intuitively we finally choose an unreplicated full factorial design for the

following reasons:

a) The experiment takes relative a long time;

b) Caustic materials are used, such as NaOH and Phenol, the more trials, the

more risk.

4.2 Factor level definition

In order to take a full factorial design, we need to set all the factors at two

levels—low and high. Considering it is an unreplicated experiment, we do not want

the noise to overwhelm the signal in data. Thus the distance between two levels of

factors should be appropriately increased. The problem comes that how to determine

it? Since there is no data to be referred to, we do it by ourselves. Some tentative

experiments are done for the purpose to find a relatively accepted distance. We try

several levels of concentration of NaOH, water temperature and mass ratio of water to

flour, and obvious difference of the pastes is obtained to increase the span between

two levels. The result is shown in the following diagram:

Factor\level Low High

NaOH 0.00001mol/L 1mol/L

Water_Temp 60°C 80°C

Water_to_flour 4:3 2:1

Phenol 0g 5.0g

Table 1 Low-high levels of factors

4.3 Implementation of the experiments

With the help of Minitab, we create a factorial design. The combination of factors

and orders, the run order are given by Minitab.

StdOrder RunOrder NaOH Water_Temp Water_to_Flour Phenol

15 1 1 1 1 -1

1 2 -1 -1 -1 -1

5 3 -1 1 -1 -1

7 4 -1 1 1 -1

13 5 1 1 -1 -1

12 6 1 -1 1 1

14 7 1 1 -1 1

8 8 -1 1 1 1

10 9 1 -1 -1 1

2 10 -1 -1 -1 1

4 11 -1 -1 1 1

6 12 -1 1 -1 1

16 13 1 1 1 1

9 14 1 -1 -1 -1

3 15 -1 -1 1 -1

11 16 1 -1 1 -1

Table 2 2^4 full factorial design given by Minitab

After the design is finished, some detailed methods of operation are then taken

into account.

1) Measurement methods. For good accuracy and experiment result, a set of

fine measurement methods are critical. Some of the factors can be well

measured by specific instruments, but some cannot. How to measure the

stickiness of pastes is a difficult problem which confuses us for long time.

The conclusion of discussion is using a cardboard which is attached to a

receptacle which can hold numbers of coins and give a controllable load to

the cardboard. We smear the paste on one side of the cardboard and stick it to

the table. After a several minutes the paste becomes dry and it’s time for

measuring the stickiness.

Factor Method

Stickiness: Force Needed to

make the cardboard fall

Coins Number and the

Weight of the Coins

Concentration of NaOH Solution PH Meter

Temperature of the Water Thermometer

The Ratio of Water to Flour Graduated Cylinder

The Weight of Flour Balance(30.0g)

Table 3 Measurement of factors

2) Preparation of experiment. According to the design plan of the experiment

execution, we prepare necessary materials, including Flour, NaOH, Phenol,

Hot and Cold Water, as well as experiment and measurement instruments:

Plastic cup

50ml Graduated cylinder

100°C Thermometer

Balance

pH meter

Pencil

Rope

Cardboard

Thermos bottle

3) Since we use plastic cups as the receptacle for making paste, we write the

combinations and levels of factors on the lateral of cup in order to

differentiate every paste and the result, as the following picture shown.

4) We perform the experiment Performance according to the experiment flow

chart shown in Figure1. And it is worth notice that the stir of paste should be

consistent in direction for a good result.

Figure 2: The proces of our experiment

4.4 The results of the experiment

After the construction of the experiment, we got the 16 different pastes and then

tested the stickiness of them, and get the following raw data.

The original data set is listed below.

StdOrder RunOrder CenterPt Blocks Phenol Water_to_Flour Water_Temp NaOH result

1 1 1 1 -1 -1 -1 -1 500.2

2 2 1 1 1 -1 -1 -1 636.5

3 3 1 1 -1 1 -1 -1 1023.1

4 4 1 1 1 1 -1 -1 628.9

5 5 1 1 -1 -1 1 -1 651.7

6 6 1 1 1 -1 1 -1 640.3

7 7 1 1 -1 1 1 -1 1090.3

8 8 1 1 1 1 1 -1 847.1

9 9 1 1 -1 -1 -1 1 530.7

10 10 1 1 1 -1 -1 1 741.6

11 11 1 1 -1 1 -1 1 1101.1

12 12 1 1 1 1 -1 1 812.4

13 13 1 1 -1 -1 1 1 736.5

14 14 1 1 1 -1 1 1 884.7

15 15 1 1 -1 1 1 1 1267.5

Figure 3: Results

16 16 1 1 1 1 1 1 1653.5

17 17 0 1 0 0 0 0 832.9

18 18 0 1 0 0 0 0 964.5

19 19 0 1 0 0 0 0 821.3

Table 4: Original Data Set

5. Data analysis

We want to achieve a model between the mass of coins (response variable) and the

4 factors to interpret the relationships of them and find the effects which influenced

the stickiness of paste.

5.1 Basic analysis

5.1.1 Main Effects

With the help of Minitab, we got the Main Effect Plot：

Figure 4 Main Effects Plot for the Mass of Coins

We can find that all the factors except Phenol have significant affects to the

response variable. And the high level of all the three factors will result in high

stickiness of paste. To get more information of the interaction effects, we had the

interaction plot for result.

5.1.2 Interaction Plot

Figure 5 Interaction Plot among the factors

There are no obvious interactions from the plot even though NaOH and

Water_Temp, NaOH and Phenol have weak interactions. To select key factors which

have great effects on stickiness of the paste, we formed the Half Normal Plot of the

effects.

5.1.3 Half Normal Plot

Figure 6 Half Normal Plot of the Effects

Only C (Water_to_Flour) is significant. But the other factors and interactions

don’t fit the normal probability plot well; maybe there are some other main effects or

interactions. Therefore we had the Pareto Plot to help us to find significant factors.

5.1.4 Pareto Plot

Figure 7 Pareto Chart of the Effects

Then we abandoned some insignificant factors like D, high order terms like

ABCD and so on. In the end, we got the following Half Normal Standardized Effets.

5.1.5 Half Normal Standardized Effects:

Figure 8 Half Normal Standardized Effects

We can find that NaOH, Water_Temp and Water_to_Flour are significant factors,

and no interaction left.

5.1.6 ANOVA

Next figure is our ANOVA table of the experiment：

Figure 9 ANOVA Table

In the ANOVA Analysis, the three factors are significant according to the P value

of them. Then we can formulate our model of the experiment:

To replace the binary variable with the actual ones, we get:

The P value of “Lack of Fit” indicates that our model fit the linear model well

since it isn’t significant.

5.1.7 Residual Plot

Next step is to analyze the residual of our model and see whether our model is

good or not.

Figure 10 Residual Plots for the model

The residual plots tell us that even though our sample size isn’t large, our residual

is good and our model fits well.

5.1.8 Contour Plots of Result

In order to further explain there is no significant interaction among the factors,

we have the contour plot and the response surface plot below:

Figure 11 Contour Plots of the Response Variable

All the three plots indicate that there aren’t significant interactions so in our

model we can abandon them without hesitation.

5.1.9 Response Surface Plot

Figure 12 Response Surface Plot between NaOH and Water_Temp to Response

The surface plot is generally a plane plot, no significant curvature is available.

This also means that interactions among factors are not significant.

5.2 Further analysis

According to our previous data analysis, there are two interesting findings. First

is that the coefficient of NaOH solution’s concentration is positive. This implies that

more condensed NaOH solution will increase the stickiness of our home-made paste.

However, this contradicts with our research result of literature review. Most literature

recommends us to use dilute resolution. One possible explanation is that the linear

assumption is not satisfied. Our experiment data need to be analyzed more carefully.

Besides, the levels’ setting of phenol is similar to that of a categorical variable.

However, we regard it as a continuous variable in our data analysis.

Thus, we add three center points in our experiment to check the linear assumption

of the factors’ levels. Though new data were collected several days later after the first

16 observations, we still assume these data are supportive for our assumption

checking as the experiment condition was generally the same. The original data set in

the previous sections have already contained the center points obtained afterwards.

The data analysis output from Minitab is listed below.

Figure 13 ANOVA table after adding three points

The p value of curvature shows that the quadratic is not significant. Our linear

assumption is generally satisfied.Our explanation for why literature recommends

dilute solution is that it is safer to use as condensed NaOH solution is corrosive.

More words to add for the follow up experiment. Actually when we have more

data, we generally need to incorporate them in our model construction. However as

they were not collected at the same time, we drop them in our model construction.

The final model is only based on the previous 16 observations.

5.3 Optimization design

Our experiment is not intended for an optimization research. Specifically, there

are several optimization criteria for the home-made paste, such as low manufacturing

cost at a target stickiness level, high stickiness etc. Different optimization criterion

requires different experiments. However, our collected observations are appropriate

for us to analyze the optimized treatment combination for higher stickiness.

The output from Minitab is listed below.

Figure 14 Response optimization

Figure 15 Response optimization with desirability

We can imply that the treatment of high level of NaOH, Water_temp,

Water_to_Flour provides highest stickiness.

6. Conclusion

From our experiment, several useful conclusion can be obtained.

The concentration of NaOH, temperature of the water and mass of water to

flour affects the stickiness of home-made paste a lot.

One of the best way to produce high stickiness of the paste is use high level of

NaOH, temeperature of water and mass of water to flour.

7. Possible improvement for our experiment

Our experiment follows the basic design method of full factorial. However,

basically it can be regarded as a DIY experiment as resources are limited. Several

improvements can be made to gain better result for our research.

Better Gauge R&R System

Initial Design with center points

Besides, what we want to emphasize is that safety is the most important issue in

experiments, especially when chemicals are involved.

8. Reference

Design and Analysis of Experiments (2005), Sixth Edition, Douglas C. Montogomery,

John Wiley

实验设计与分析及参数优化 (2003), C. F. Jeff Wu, Michael Hamada 著 张润楚等

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