Group 9 Project Report of DOE Course

Group 9:HOU Xiangyu 2008010881

YU Guo 2008010884TU Mengyuan 2008010844TAO Jianping 2008010870

MENG Xiangnan 2007010832

ContentAbstract.................................................................................................................................2

1. Introduction of Idea...................................................................................................2

1.1 Flour and Cooked-wheaten-food....................................................................2

1.2 Yeast versus Baking-soda................................................................................3

1.3 Material and Apparatus.....................................................................................4

Material............................................................................................................................4

Apparatus.........................................................................................................................4

1.4 Procedures of Fermentation............................................................................5

1.5 Criteria of Fermentation...................................................................................5

Under fermented..............................................................................................................5

Well fermented.................................................................................................................6

Over fermented................................................................................................................6

2. Problem Definition.....................................................................................................6

2.1 Variable Definition..............................................................................................6

2.2 Factors Decomposition......................................................................................7

2.3 Noise Factors........................................................................................................7

2.4 Constant Factors.................................................................................................7

3. Design of Experiment...............................................................................................8

4. Implementation of Experiment..............................................................................9

5. Data analysis.............................................................................................................11

5.1 Intuitive Observation.......................................................................................11

5.2 Model Formulation............................................................................................12

5.3 Model Verification.............................................................................................14

5.4 Plan Optimization..............................................................................................18

6. Conclusion and Future Direction.........................................................................18

7. References..................................................................................................................19

1

Abstract

Cooked-wheaten-food is the major part of people’s daily recipe. The most technical part of this cuisine is the process of fermentation. Using yeast to ferment can produce delicious dough with rich nutrition. This report presents the results of finite elements analysis for the yeast-fermentation. In this investigation, a N-factor Two-level, Quarter-Factorial Design is employed to reveal the main effects as well as the interactions of N factors (yeast amount, water amount, temperature, salt, cover) on effectiveness of fermentation. The optimum-design is also discussed.

Keywords: yeast, fermentation, factorial design, finite element analysis

1. Introduction of Idea

1.1 Flour and Cooked-wheaten-food

Wheat and barley are the most common crops in the northern China, and people eat them as the staple food for thousands years. People discovered that pulverizing the wheat groats and barleycorn into powder can produce delicious food with totally different tastes while satisfying people’s hungers. Then the powder called “flour” entered the recipe of people’s daily life.

With the help of water and animal, people invented water-mill and stone-mill to pulverize wheat and barley into finer flour, thus popularize the flour-made food.

There are several ways to cook the flour, such as boiling, steaming, frying, and so on. However, different cuisine methods need different type paste.

For instance, all the food required to be cooked by steaming, steamed-stuff-bums, steamed-buns or steam-twisted-rolls, should be made of leaven dough.

2

While all the food cooked by boiling water, such as noodles and dumplings, can be made of common crude dough.

Pour water into the flour, and we can get the crude dough by stirring and rubbing and start to make dumpling or noodles directly.

In order to make the dough fermented, people usually blend some yeast into the flour before pouring the water. Under certain conditions, the crude dough can become leaven and be used to make stuffed-bums or buns.

In some way, cooking steamed-stuffed-bums are much more technical than dumpling, since the quality and taste of bums depends on the quality of fermented dough while the “certain conditions” are quite uncertain to some degree. People usually make the dough according to their own experience or under instruction of experienced cooks, thus resulting in a significant fluctuation of quality and taste, sometimes each leading to unnecessary waste of flour and yeast.

Our research is aiming to find the factors that affect the fermentation of dough by analysis the effect of each factor as well as the interaction of multiple factors, hence present the relatively desirable and practical settings to get dough fermented.

3

1.2 Yeast versus Baking-soda

To make the dough fermented, 2 methods are used most frequently: one is blending yeast in to the flour, the other one is blending baking-soda.

The yeast in the dough will proceed aerobic respiration using the organics of the dough during the fermentation, thus producing CO2 which would inflate the dough. (And that’s also the reason why stuffed-bum is softer than dumpling.) The reaction equation is shown below:

C6H12O6→2C2H5OH+2CO2↑+EnergyIf we choose to make leaven dough with baking-soda, the

scheme of fermentation is different. NaHCO3is the basis of baking-soda, which is very unstable under heated condition. It can also produce CO2when it disintegrates and make the dough swelled. The reaction equation is shown below:

2NaHCO3→Na2CO3+H2O+CO2↑

The dough fermented by baking-soda is whiter and softer than yeast-dough, and the fermenting process is much faster than yeast-fermentation, therefore most restaurants and refectories use baking-soda to make leaven dough. Yet the yeast is still preferred in making home-made food, since the baking-soda will destroy the Vitamin B of the flour, while the yeast won’t be harmful to the nutrition of flour. What’s more, the yeast itself is of great benefit to human’s health. Therefore, yeast-fermentation is still very popular, although it’s more slowly and more possible to fail.

We must ensure that the fermentation environment is suitable for yeast to survive. The main factors affecting the activeness of yeast are nutrition, water, pH, temperature and oxygen.

The fermenting dough can provide the organic nutrition and water for the metabolism of yeast. Yeast can survive in the pH environment of 3.0~7.5, and the optimum range is 4.5~5.0. (That’s why yeast cannot survive

4

together with baking-soda.) As for the temperature, the yeast will die when it is hotter than 47℃, will lose activeness when it is under 0℃, and the suitable range is 20℃~35℃.

Our research is based on the environmental settings descripted above.

1.3 Material and Apparatus

Material

Flour (whole-meal flour)Yeast (Brand: AnQi)Water (tap water)NaCl (pure)

Apparatus

Beaker (50mL, precision: 5ml)Graduated cylinder (10mL, precision: 0.5mL)Thermometer (-10℃~100℃, precision 1℃)Electronic balance (precision 0.01g)Watch (precision: 1s)Ruler (precision: 1mm)Chopsticks (for stirring)Basin (for heating in water bath)

1.4 Procedures of Fermentation

As the cooking experience accumulated and spread, the common procedures of making leaven dough is summarized:

5

1.5 Criteria of Fermentation

Under fermented

Small dough sizeCoarse grains insideNon-elastic and dark surface

Well fermented

Larger dough sizeFine and smooth insideElastic, smooth and white surface

6

Over fermented

Small and flat dough sizeLarge air hole insideNon-elastic, wrinkled surfaceSour taste

2. Problem Definition

2.1 Variable Definition

To measure the quality of fermentation, there’re many indices reflecting different respects. Generally speaking, we considered three directions to describe that: the volume change, the elasticity of pasta and the porosity of pasta. These three directions reflects three dimensions of fermentation quality, however, they are closely related: the elasticity is poor when flour doesn’t fully ferment and the volume won’t change much, and obviously, the porosity is closely related to the volume change. So we though only one dimension is enough to describe the phenomenon. To make it easy to measure, we select the volume change as our criterion, and to measure that, we fix the container of experiment to make the shape of pasta fixed and make the height change as the response variable. This variable is easy to measure and can well reflect the quality of fermentation.

7

2.2 Factors Decomposition

According to the guidelines of fermentation, we thought water volume, water temperature, amount of inoculation, sealing, fermentation time and whether treated with salt are six factors which are important to fermentation. The water volume, temperature, sealing and salt determine the growing environment of yeast, the amount of inoculation determines the efficiency, and time is important because fermentation is a process of yeast growing which will consume flour, it’s important to control the degree of yeast growing.

We considered: Water volume: too much water will destroy the shape of pasta, too little will influence the growing of yeast. Water temperature: high temperature is good for yeast growing but too hot will kill yeast, with low temperature, yeast will not be active. Amount of inoculation: too much will consume too much flour, too less will lead to insufficient fermentation. Sealing: it seems that yeast can survive with or without oxygen, but the pasta expands with the help of CO2 released by yeast, so we thought sealing may be important to the process. Fermentation time: time determines the degree of the process. Salt: it is an empirical rule; maybe this factor influences the growing environment of yeast.

2.3 Noise Factors

Factors that couldn’t be handled and may influence the result are called noise; we will try to reduce the effects of noise by randomizing the sequence of processes with different treatment, those noise factors considered which may influence the result of experiment are:

The process of kneading dough may vary because of operator’s variation.The measurement of pasta’s height needs an estimation of an average height. The temperature may vary with time

8

2.4 Constant Factors

For those factors we can control, we will try to make them fixed. The shape and size of containers.The lot of flour

3. Design of Experiment

To study the influences of 6 factors, we want to experiment in a way convenient and cost-effective.

First we set our treatments according to the given guidelines, and then adjust them slightly lower or higher; those influences of slight changes in a small region can be considered to be linear. So it’s reasonable to fit those factors with simple linear model.

Then we considered that if we use a full factorial design, we will have 26=64 treatments, those experiments will be too hard to complete. So we select a 1/4 fractional factorial design, only 16 treatments are needed, and we can also fit a model for those 6 factors.

Because the fermentation takes long time to get the result, we determined an experiment without replication. We also considered that among the 6 factors, some may be insignificant, we can screen the important factors out, if 2 factors are insignificant, we can analyze the remaining 4 factors again and we can regard the data as the result of 4 replication experiment, in this way we can make full use of the data and avoid to waste the experiment resources.

And the factors’ level settings are as following: Cod

eFactors Low

LevelHigh

LevelA Water volume 23ml 35mlB Water temperature 23°C 37°CC Amount of inoculation 2g 4gD Sealing sealed Not

sealedE Fermentation time 1.5h 2.5hF Salt 0g 0.06g

Table 1: Factors and Level SettingsAnd the experiment configurations are generated based on a full

9

factorial design, we let A, B, C, D generate a full factorial design, and make E=ABC, F=BCD. So we have I=ABCE=BCDF=ADEF. And we should also notice the aliases are:

Table 2: Aliases of Fractional Factorial DesignThis is a design with IV resolution, and we thought those three-

order interactions are not as significant as one and two orders items, so we only should be careful about those two-order aliases.

And based on this plan, we randomize the sequence of experiments, the final plan is as following table:

标准序

运行序

中心点

区组 加水量

初始水温

酵母用量

密封 发酵时间

盐

13 1 1 1 -1 -1 1 1 1 -115 2 1 1 -1 1 1 1 -1 12 3 1 1 1 -1 -1 -1 1 -1

14 4 1 1 1 -1 1 1 -1 -116 5 1 1 1 1 1 1 1 19 6 1 1 -1 -1 -1 1 -1 14 7 1 1 1 1 -1 -1 -1 16 8 1 1 1 -1 1 -1 -1 17 9 1 1 -1 1 1 -1 -1 -1

12 10 1 1 1 1 -1 1 -1 -110 11 1 1 1 -1 -1 1 1 111 12 1 1 -1 1 -1 1 1 -18 13 1 1 1 1 1 -1 1 -13 14 1 1 -1 1 -1 -1 1 15 15 1 1 -1 -1 1 -1 1 11 16 1 1 -1 -1 -1 -1 -1 -1

Table 3: Experiment Plan

10

A=BCE=DEF AB=CEB=ACE=CDF AC=BEC=ABE=BDF AD=EFD=BCF=AEF AE=BC=DFE=ABC=ADF AF=DEF=BCD=ADE BD=CFABD=CDE=ACF=BEF

BF=CDACD=BDE=ABF=CEF

4. Implementation of

Experiment

Thanks a fellow student from department of chemistry then we take out our experiment at the chemical laboratory with precise instrument: electronic balance, measuring cylinder, and glass bar.

We have 6 factors in the experiment. Before the experiment we know little about fermentation, so we have to take it three times to get the suitable data in the experiment. Before the experiment we have to get the volume of water, the weight of the flour, the weight of the yeast, the temperature, and the suitable time. We did those in our dormitory, we take plastic cup to ferment, so we don’t get a suitable data for each, for each item we just mark a sign on the plastic cup and get a suitable data as our basic setting.

In the experiment we take the weight of the flour as constant, from the sign of the plastic cup we make it 40g. And we determined our factors’ settings according to our prior trials, see Table 1:Factors and Level Settings.

Then I will introduce the process of the experiment. At first we get 16 pieces of flour with electronic balance and the weight of each piece is 40g, we have the cup on the electronic balance to get the weight of it then we reset it and then put flour in it until it is 40g. Then we take out a scrap of paper to weigh the inoculation we have 8 cups with 2g and another 8 cups with 4g. After this we mixed the flour and the inoculation. The next step is putting the water in and making the mixed flour to be a ferment state and have a sign on it to get the initial height of the flour, because we decide which setting is better by the altitude intercept. As the process need a certain time so we recorded the start time alone and got the finish time of each setting. Then we put the cups with the two temperature level into two kinds of water bath. At last we observe the result and get the altitude intercept on time. And our result is as Table 4:Experiment Result.

标准序 运行序 加水 初始 酵母 密封 发酵 盐 初始 结束 响

11

量 水温 用量 时间 高度 高度 应13 1 -1 -1 1 1 1 -1 2.5 5.6 3.115 2 -1 1 1 1 -1 1 2.6 6.2 3.6

2 3 1 -1 -1 -1 1 -1 2.6 4.8 2.214 4 1 -1 1 1 -1 -1 2.5 5.8 3.316 5 1 1 1 1 1 1 2.5 5.9 3.4

9 6 -1 -1 -1 1 -1 1 2.2 2.9 0.74 7 1 1 -1 -1 -1 1 2.3 4.9 2.66 8 1 -1 1 -1 -1 1 2.6 5.5 2.97 9 -1 1 1 -1 -1 -1 2.4 5.9 3.5

12 10 1 1 -1 1 -1 -1 2.4 4.7 2.310 11 1 -1 -1 1 1 1 2.7 4.3 1.611 12 -1 1 -1 1 1 -1 1.9 4.1 2.2

8 13 1 1 1 -1 1 -1 2.2 5.6 3.43 14 -1 1 -1 -1 1 1 2.4 4.2 1.85 15 -1 -1 1 -1 1 1 2.1 4.7 2.61 16 -1 -1 -1 -1 -1 -1 2 3.6 1.6

Table 4: Experiment Result

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5. Data analysis

5.1 Intuitive Observation

To understand the result of experiment, we should observe the data intuitively first.

Before we analyze the property of data, we draw a probability plot in Figure 1 and find the response is normally distributed with P value = 0.415. This normality makes our later regression and analysis more convinced.

6543210

99

9590

80706050403020

105

1

响应

百分比

均值 2. 55标准差 0. 8383N 16AD 0. 355P 值 0. 415

响应 的概率图 - 95% 正态 置信区间

Figure 1 Probability Plot of Response

The main effects are as Figure 2, we can say whether sealed and fermentation time will not influence the response, and the volume, temperature of water, the amount of inoculation, and whether with salt, make the result vary (more water, higher temperature, more yeast, and less salt make the response more obvious). And we found the effect of the amount of inoculation is especially significant.

13

1-1

3. 2

2. 8

2. 4

2. 0

1-1 1-1

1-1

3. 2

2. 8

2. 4

2. 0

1-1 1-1

加水量

平均值

初始水温 酵母用量

密封 发酵时间 盐

响应 主效应图数据平均值

Figure 2 Main Effect PlotAnd we also want to know their interactions, observe the plot in

Figure 3, we can find that AB, AC, BE, BF, CD and CE seem to have significant interactions.

1- 1 1- 1 1- 1 1- 1 1- 1

3. 2

2. 4

1. 63. 2

2. 4

1. 63. 2

2. 4

1. 63. 2

2. 4

1. 63. 2

2. 4

1. 6

加水量

初始水温

酵母用量

密封

发酵时间

盐

-11

加水量

-11

水温初始

-11

用量酵母

-11

密封

-11

时间发酵

响应 交互作用图数据平均值

Figure 3 Interactions Plot

5.2 Model Formulation

Then we analyze the experiments. Beginning with all main effects and the selected intuitively

significant two-order interactions, we have 12 variables, and among those 6 two-order items, there’re 3 groups of aliases, so this requires 9 degrees of freedom, which is less than 15 degrees of freedom (altogether 16 records).

14

Then we have the half-normal plot in Figure 4. We found that factors: A, B, C, F, BF, AC are significant.

14121086420

98

95

908580

706050403020100

绝对标准化效应

百分比

A 加水量B 初始水温C 酵母用量D 密封E 发酵时间F 盐

因子 名称

不显著显著

效应类型

BF

ACF

C

B

A

标准化效应的半正态图 Al pha = . 05)（响应为 响应，

Figure 4 Half Normal PlotAnd to analyze their relative significance, we draw the Pareto

chart in Figure 5, we find factor C has a dominating influence than other factors.

ED

ABACF

BFABC

14121086420

项

标准化效应

2. 45A 加水量B 初始水温C 酵母用量D 密封E 发酵时间F 盐

因子 名称

Pareto 标准化效应的 图 Al pha = . 05)（响应为 响应，

Figure 5 Pareto ChartThen we can delete the factors insignificant. And we have the

new model with six factors, and all of the factors are significant.

15

14121086420

99. 8

98

95

908580706050403020100

绝对标准化效应

百分比

A 加水量B 初始水温C 酵母用量F 盐

因子 名称

不显著显著

效应类型

BF

ACF

C

B

A

标准化效应的半正态图 Al pha = . 05)（响应为 响应，

Figure 6 Half Normal Plot

Then we analyze the variance; see the ANOVA in Table 5. We found this model is well fitted with high R value and all the factors are significant with P value<0.05.

拟合因子: 响应 与 加水量, 初始水温, 酵母用量, 盐 响应 的效应和系数的估计（已编码单位）项 效应 系数 系数标准误 T P常量 2.5500 0.05035 50.65 0.000加水量 0.3250 0.1625 0.05035 3.23 0.010初始水温 0.6000 0.3000 0.05035 5.96 0.000酵母用量 1.3500 0.6750 0.05035 13.41 0.000盐 -0.3000 -0.1500 0.05035 -2.98 0.015加水量*酵母用量 -0.2750 -0.1375 0.05035 -2.73 0.023初始水温*盐 0.3000 0.1500 0.05035 2.98 0.015

S = 0.201384 PRESS = 1.15358R-Sq = 96.54% R-Sq（预测） = 89.06% R-Sq（调整） = 94.23%

对于 响应 方差分析（已编码单位）来源 自由度 Seq SS Adj SS Adj MS F P主效应 4 9.5125 9.5125 2.37813 58.64 0.000

16

2 因子交互作用 2 0.6625 0.6625 0.33125 8.17 0.009残差误差 9 0.3650 0.3650 0.04056合计 15 10.5400

Table 5 ANOVA

5.3 Model Verification

We also have to consider the residuals of the model. With Figure7, we can conclude the residual is normal distributed with constant standard deviation and not related to observation order, this normality can also be tested and we found the P value is 0.614 (in Figure 8), which means the normality is significant.

0. 40. 20. 0-0. 2-0. 4

99

90

50

10

1

残差

百分比

321

0. 4

0. 2

0. 0

-0. 2

拟合值

残差

0. 30. 20. 10. 0-0. 1-0. 2-0. 3

4. 8

3. 6

2. 4

1. 2

0. 0

残差

频率

16151413121110987654321

0. 4

0. 2

0. 0

-0. 2

观测值顺序

残差

正态概率图 与拟合值

直方图 与顺序

响应 残差图

Figure 7 Residual Plots

0. 500. 250. 00- 0. 25- 0. 50

99

9590

80706050403020

105

1

1残差

百分比

均值 2. 289835E- 16标准差 0. 1560N 16AD 0. 274P 值 0. 614

1 残差 的概率图 - 95% 正态 置信区间

Figure 8 Probability Plot of Residual

17

Then we plot the residual versus each factor in Figure 9 Residualversus Factors, trying to explore the factors’ influence to variance. We can see that for factor sealing or salt, the residuals seems to be larger in high level, so we have to verify whether that tendency is significant.

10-1 10-1 10-1

0. 4

0. 2

0. 0

-0. 2

10-1

0. 4

0. 2

0. 0

-0. 2

10-1 10-1

加水量

残差

1

初始水温 酵母用量

密封 发酵时间 盐

1 , , , , , 残差 与 加水量 初始水温 酵母用量 密封 发酵时间 盐 的散点图

Figure 9 Residual versus Factors

Then we consider the dispersion of the data, for each factor, calculate the standard deviation of residuals at the low and high level, and then use statistic

F i¿=ln S2¿¿¿

to present the dispersion. Theoretically, F i¿ should be normal

distributed, if one factor has large variability effect, F i¿ will be an

outlier of those group of data. We should notice: this method measures dispersion effect without eliminating the location effects, however, we consider there isn’t significant location effect according to the ANOVA table (see Table 5 ANOVA), so we use this method. More methods about distinguishing dispersion effects will not be

presented in this report. We calculated the value of F i¿ as following

table: No.

A B C D E F Residual

1 -1 -1 1 1 1 -1 -0.12 -1 1 1 1 -1 1 0.13 1 -1 -1 -1 1 -1 0.0254 1 -1 1 1 -1 -1 0.05

18

5 1 1 1 1 1 1 -0.156 -1 -1 -1 1 -1 1 -0.2757 1 1 -1 -1 -1 1 0.1258 1 -1 1 -1 -1 1 0.259 -1 1 1 -1 -1 -1 -4.4E-

1610 1 1 -1 1 -1 -1 -0.17511 1 -1 -1 1 1 1 0.02512 -1 1 -1 1 1 -1 0.32513 1 1 1 -1 1 -1 -0.1514 -1 1 -1 -1 1 1 -0.07515 -1 -1 1 -1 1 1 016 -1 -1 -1 -1 -1 -1 0.025S+ 0.15 0.1742

330.1362

770.1899

250.1541

10.1658

31S- 0.1721

710.1476 0.1832

250.1210

080.1674

390.1569

8F -

0.27571

0.331777

-0.5920

5

0.901548

-0.1659 0.109699

No.

AB=CE AC=BE AD=EF AE=BC=DF

AF=DE BF=CD BD=CF Residual

1 1 -1 -1 -1 1 1 -1 -0.12 -1 -1 -1 1 -1 1 1 0.13 -1 -1 -1 1 -1 1 1 0.0254 -1 1 1 -1 -1 1 -1 0.055 1 1 1 1 1 1 1 -0.156 1 1 -1 1 -1 -1 -1 -0.2757 1 -1 -1 -1 1 1 -1 0.1258 -1 1 -1 -1 1 -1 1 0.259 -1 -1 1 1 1 -1 -1 -4.4E-

1610 1 -1 1 -1 -1 -1 1 -0.17511 -1 -1 1 1 1 -1 -1 0.02512 -1 1 -1 -1 1 -1 1 0.32513 1 1 -1 1 -1 -1 -1 -0.1514 -1 1 1 -1 -1 1 -1 -0.07515 1 -1 1 -1 -1 -1 1 016 1 1 1 1 1 1 1 0.025S+ 0.1288

690.2061

550.0855

650.1267

730.1631

170.0981

980.1742

33

19

S- 0.134297

0.098198

0.203978

0.174233

0.128869

0.206155

0.126773

F -0.0825

2

1.483287

-1.7374

7

-0.6359

9

0.471347

-1.4832

9

0.635989

Table 6 Dispersion EffectAnd the probability plot of F value is as Figure 10.

3210- 1- 2- 3

99

9590

80706050403020

105

1

分散效应

百分比

均值 - 0. 07994标准差 0. 9020N 13AD 0. 176P 值 0. 903

分散效应 的概率图 - 95% 正态 置信区间

Figure 10 Probability Plot of DispersionThis result means, for all of the one-order, two-order factors in

different levels, there’s no obvious tendency to have a dispersion effect, means, the factors are not significant to the variance and we can adjust our settings, that won’t largely influence the variability of fermentation.

Finally we can get our model: RESPONSE=2.5500+0.1625*A+0.3000*B+0.6750*C-0.1500*F-0.1375*AC+0.1500*BF

We should notice the aliases of the fractional factorial design, AC=BE and BF=CD should be considered. When we consider this model, it’s hard for us to distinguish the actual interactions. But we can draw the contour plots to observe the interactions (Figure 11). We found only AC and BF plots appears curved, that means, the interactions AC and BF are significant rather than BE and CD.

20

加水量

酵母用量

1.00.50.0-0. 5-1. 0

1.0

0.5

0.0

-0. 5

-1. 0

初始水温 - 1密封 - 1发酵时间 - 1盐 - 1

保持值

> – – – – < 1. 6

1. 6 2. 02. 0 2. 42. 4 2. 82. 8 3. 2

3. 2

响应

初始水温

发酵时间

1.00.50.0-0. 5-1. 0

1.0

0.5

0.0

-0. 5

-1. 0

加水量 - 1酵母用量 - 1密封 - 1盐 - 1

保持值

> – – – < 1. 50

1. 50 1. 651. 65 1. 801. 80 1. 95

1. 95

响应

初始水温

盐

1.00.50.0-0. 5-1. 0

1.0

0.5

0.0

-0. 5

-1. 0

加水量 - 1酵母用量 - 1密封 - 1发酵时间 - 1

保持值

> – – – – – – < 1. 00

1. 00 1. 151. 15 1. 301. 30 1. 451. 45 1. 601. 60 1. 751. 75 1. 90

1. 90

响应

酵母用量

密封

1.00.50.0-0. 5-1. 0

1.0

0.5

0.0

-0. 5

-1. 0

加水量 - 1初始水温 - 1发酵时间 - 1盐 - 1

保持值

> – – – – – – < 1. 50

1. 50 1. 751. 75 2. 002. 00 2. 252. 25 2. 502. 50 2. 752. 75 3. 00

3. 00

响应

, 响应 与 酵母用量 加水量 的等值线图 , 响应 与 发酵时间 初始水温 的等值线图

, 响应 与 盐 初始水温 的等值线图 , 响应 与 密封 酵母用量 的等值线图

Figure 11 Contour Plots of Response

5.4 Plan Optimization

Then we can use response optimization to get the best configuration. From the result, we know that this configuration doesn’t reach the peak of the response, for A, B and C are need to be the high level to get the largest response, this means our recipe is not the best one and we can determine our improvement direction is to increase the volume of water, increase the temperature of water and put more yeast. For this linear model is valid only in this small interval, it’s hard for us to predict the peak value of response, but on the other hand, we can get the direction easily with the results of these experiments.

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曲线高

低0. 71000D优化

d = 0. 71000

望大响应

y = 3. 550

0. 71000合意性复合

- 1. 01. 0

- 1. 01. 0

- 1. 01. 0

- 1. 01. 0

初始水温 酵母用量 盐加水量

[1. 0] [1. 0] [1. 0] [ - 0. 7374]

Figure 12 Response Optimization

6. Conclusion and Future

Direction

Our experiment proved that factor water volume, water temperature, amount of inoculation and salt are significant to the effect of fermentation. And the interactions between water volume and amount of inoculation, water temperature and salt are also significant.

There isn’t significant dispersion effect in any factors in the model, so we can consider the variation won’t change too much in any treatment, this property provides convenience for our further improvement.

We tried to improve our settings with our model. Using the response optimization we found that the best result will come when the water volume is in high level, the temperature is high, and the amount of yeast is large. This means the optimal solution is far away from our current area, our experiment can only provide a direction of improvement. So, further studies can continue based on the result and the direction given by the response optimization.

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7. References

Design and Analysis of Experiments , Douglas C. Montgomery

Dispersion Effect From Fractional Designs, George E. P. Box, R. Daniel Meyer, 1986

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