Helicopter Paper

Helicopter

BY:

RENDY 004201200003

RIFI PRASETYO 004201200033

GANDI SUHARTINAH 004201200036

INDUSTRIAL ENGINEERING DEPARTMENT

ENGINEERING FACULTY – PRESIDENT UNIVERSITY

2015

Table of Contents

CHAPTER I.........................................................................................................................2

INTRODUCTION...............................................................................................................2

1.1. Background...............................................................................................................2

1.2. Objective...................................................................................................................3

1.3. Tools and Equipment................................................................................................3

1.4. Steps..........................................................................................................................3

CHAPTER II........................................................................................................................3

LITERATURE STUDY.......................................................................................................8

Experiment with Three-level, mixed-level and fractional factorial designs..........Error! Bookmark not defined.

Experiment with Generating a Mixed Three-Level and Two-Level Design.........Error! Bookmark not defined.

CHAPTER III......................................................................................................................8

DATA COLLECTION......................................................................................................18

3.1. Experiment Procedure.............................................................................................18

3.2. Response Measurement...........................................................................................19

3.3. Experiment Hypothesis...........................................................................................21

CHAPTER IV....................................................................................................................21

DATA ANALYSIS............................................................................................................26

4.1. Pre Test...................................................................................................................26

4.2. Effect Plot................................................................Error! Bookmark not defined.

4.3. Interaction Plot........................................................................................................28

4.4. ANOVA Test..........................................................................................................29

4.5. Residual Plot and Model Adequacy........................................................................32

4.6. Hypothesis Testing..................................................................................................33

4.7. Regression Model...................................................................................................35

CHAPTER V......................................................................................................................36

CONCLUSION..................................................................................................................36

REFERENCE.....................................................................................................................37

APPENDIX 1: Documentation of Experiment..................Error! Bookmark not defined.

APPENDIX 2: Minitab Output..........................................Error! Bookmark not defined.

CHAPTER I

INTRODUCTION

Helicopter Project | Design of Experiment Page 1Industrial Engineering 2012 | President University

1.1. Background

Design of Experiment is a method to determine the relationship between

factors that affecting the process and the output of that process. In other words, it

is used to find cause-and-effect relationships between factors to the output or

mostly known as response. Design of Experiment can be done in many aspects

including the daily life operation.

One application of experimental design is by doing an experiment to

measure downward speed of the paper helicopter. In this occasion, the

experiments used paper helicopter as the material of the experiments and then

give different treatment to measure the differences. The paper helicopter is a

simple construction that shares this property of autorotation when falling to the

ground and the objective of the project is to build a paper helicopter that takes the

longest time to fall to the ground from a given height. Helicopters rely on a

phenomenon called autorotation to slow their descent to the ground when they

lose power. The air-flow past the rotors generated by the downward speed causes

the rotor to spin and generate drag that slows down the fall. However, there are

several factors that might be effecting the downward speed time to fall faster, such

as: body lenghts size, tail width size, tail lenght size and paperclip size. Thus, this

experiment aims to analyze which factors that have significant effect to the

downward speed time.

This experiment is using 4 factors that believe as the factors that have

significant effect to the growth rate (response); those factors are Size of Body

Lenght, Size of Tail Widht, Size of Tail Lenght and Size of Paper Clip. The size

of body length are differing into two (small size and large). The tail width is

divided into two; one small size and large large. The tail lenght is divided into two

levels (small size and large size). By using three replications, so there are 48

experiments.

This experiment is using the method of full factorial design. The

experiments used that method as experimental units of homogeneous materials or

being considered homogeneous and different treatment, which was the diversity

of the response brought about only through by the treatment. The observation is


noted every day and being compared whether there is any influence that was due

to the provision of the treatment against heavy and high of the mung bean.

This report contains of six main chapters, which are: Introduction,

Literature Study, Data Collection, Data Analysis, Conclusion, and References.

1.2. Objective

The main objective of this study is to analyze which factors that might be

affecting measure of downward speed of the paper helicopter. There are several

objectives of this experiment, which are:

1. To conduct hypothesis testing

2. To analyze the residual and main effect plot between factors

3. To analyze ANOVA between factors using Minitab

4. To create regression model

1.3. Tools and Equipment

There are several tools and equipment that are being used for this analysis.

The main tool is Minitab Software. Minitab is being used to analyze the data that

is given. The others software are Ms. Office and Ms. Excel. These tools are being

used to do administration thing.

1.4. Steps

Minitab is being used to solve the problem. Generally, the Factorial

Design Analysis is used to solve all those problems. The steps of to analyze the

problem is clearly seen for each problem below.

The steps are:

1. Open the Minitab software → Click Stat on menu bar → DOE →

Factorial → Create Factorial Design as shown in Figure 1.1.


Figure 1.1 Create Factorial Design

2. Choose 2-level Factorial (default Generators) → Number of Factor = 4 →

Change the Factor name (Factor A = Paper Clip, Factor B = Tail

Length, ,Factor C = Tail Width and Factor D = Body Length) →

Determine the Number of Levels for each Factor (Factor A = 2 Level,

Factor B = 2 Levels, Factor C = 2 Levels and Factor D = 2 Levels) →

Determine the Number of Replicates = 3 → OK. These steps are shown in

Figure 1.2.

Figure 1.2 Determinations of Factors and Replications

3. Click Factors → Determine the Level Values for the Factors (Ascending

number is required or from Low to High) → OK. These steps are shown in

Figure 1.3.


Figure 1.3 Determination of Level Value

4. The Sessions Panel and Worksheet panel will appear as shown in Figure

1.4. Create a new column which is Response Column. Fill in the response

value based on level of factos.

Figure 1.4 Response Columns on Worksheet Panel

5. To analyze the data, click stat on the Menu Bar → DOE → Factorial →

Analyze Factorial Design, then the panel will appear as shown in Figure

1.5. Fill the Response box with C9 downward speed of the paper

helicopter (Response column) → Click Graph → Choose “Four in One”

on Residual Plots. This aims to shows all plots (Histogram, Normal plot,

Residual vs fits, and Residual vs order) into one panel.


Figure 1.5 Analyze Factorial Design

6. Figure 1.6 shows the analysis of factorial design in Session panel and the

Residual Plots for Response in one panel. From this, the deeper analysis

can be conducted.

Figure 1.6 Result of Factorial Design Analysis


7. To show the effect plot, click stat on the Menu Bar → DOE → Factorial

→ Factorial Plot, then the panel will appear as shown in Figure 1.7. Click

Graph → Check Main Effect Plot and Interaction Plot → OK

Figure 1.7 Factorial Plots Graphs


CHAPTER II

LITERATURE STUDY

Factorial Experiment

Factorial experiment is experiments that investigate the effects of two or

more factors or input parameters on the output response of a process. Other

definition is about factorial experiments is a treatment arrangement in which the

treatments that are consist of all combinations of all levels of two or more factors.

Usually factorial experiment is called simply factorial design because it is a

systematic method for formulating the step needed to successfully implement a

factorial experiment and estimating the effect of various factors on the output of a

process with a minimal number of observations that function to optimize the

output of the process.

In a factorial experiment, the effects of varying the levels of the various

factors affecting the process output are investigated. Each complete trial or

replication of the experiment takes into account all the possible combinations of

the varying levels of these factors. Then for effective factorial design can ensures

that the least number of experiment runs are conducted to generate the maximum

amount of information about how to input the variable affect the output of the

process.

There are some advantages and disadvantages of Factorial experiment, which are:

Advantages

1. More precision on each factor than with single factor experimentation.

2. Broadening the scope of an experiment.

3. Possible to estimate the interaction effect.

4. Good for exploratory work where it wish to find the most important factor

or the optimal level of a factor.

Disadvantages

1. Some people says it`s complex, but in the reality it is all not complex and

it`s the phenomenon which is complex.

2. With a number of factors each for several levels, the experiment may be

become very large.


Interaction is the failure of the differences in response to changes in levels

of one factor, to retain the same order and magnitude of performance through all

the levels of other factor OR the factors are said to interact if the effect of one

factor changes as the levels of the other factors changes.

For the running of factorial combinations and mathematical interpretation

of the output responses of the process combinations because it is the essence of

the factorial experiments and it allows to understand which factor the process that

improvement or corrective actions may be geared towards these. The experiments

in which numbers of levels of all the factors are equal are called symmetrical

factorial experiments and the experiments in at least two are different are called as

asymmetrical factorial experiments.

Factorial also provides an opportunity to study not only the individual

effects of each factor but also their interactions. It have the further advantages of

economizing on experimental resources and the experiments are conducted factor

by much more resources are required for the same precision than when there are

tried in factorial experiments.

Experiments with Factor Each at Two levels

The simple of the symmetrical factorial experiments are with each of the

factors at 2 levels. If there are “n” factors each at 2 levels it called as 2 n factorial

where the power stands for the number of factors and the base the level of each

factor. For make it simple the symmetrical factorial experiments is the 22 factorial

experiment where i.e. 2 factor are A and B, A and B have two levels lower (0) and

High (1). In a 22 factorial experiment has r or replicates were run for each

combination treatment, the main and interactive effect of A and B on the output

may be mathematically expresses such as:

A= [ab+a-b-(1)] / 2r (main effect for factor A) (2-1)

B= [ab+b-a-(1)] / 2r (main effect for factor B) (2.2)

AB= [ab+(1)-b-a] / 2r (main effect for factor AB) (2-3)


Where r is the number of replicates per treatment combination and A is the

total of outputs of each of the r replicates of the treatment combination A because

A is high and B is low. For B is the total output for then n replicates of the

treatment B because B is high and A is low. And then for AB, it is the total output

for the r replicates of the treatment combination AB where both A and B are high

and the last is (1), it is the total output for the r replicates of the treatment

combination (1) where A and B are low.

Two factor had been independent because [ab+(1)-a –b ] /2n will be of

the order of zero. If not then it will give an estimate of interdependence of the two

factors and it is called the interaction between A and B. it is easy to verify because

the interaction of the factor B with factor A is BA which will be same as the

interaction AB and hence the interaction does not depend on the order of the

factors. It`s also easy to verify the main effect of factor B because a contrast of the

treatment total is orthogonal to each of A and AB.

There are several steps for analyze experiments with factor each at two

levels:

Step 1 : Calculating the Sum of Squares or SS due to the SS treatment, SS rows

and columns, SS error and the last SS total.

Step 2 : Calculating the DF between treatment, rows and columns, error and total.

Step 3 : After calculating SS and DF it can find to calculate the Mean Square

(MS), formulate to calculate MS is SS / DF.

Step 4 : The last is calculating the F value. Formulate F value is MS/ MSerror.

For example calculating F value is MSa /MSerror.

Step 5 : After calculating all of F value, after that analyze the hypothesis all of F-

value if the F value > α it means reject H0 or Accept H1 but if F value < α it means

do not reject H0 or accept H0.

Step 6 : Calculating the standard errors for main effect and two factor

interactions.

SE of difference between main effect means = √ 2 MSEr .2n−1 (2-4)

Helicopter Project | Design of ExperimentPage 10Industrial Engineering 2012 | President University

SE of difference between A means at the same level of B= SE of difference

between B means at same level of A = √ 2 MSEr . . 2n−2

So, for general SE for testing the difference between means of r-factor

interactions is

√ 2 MSEr .2n− y

The table below has shown the sources of variation for solving with

ANOVA for 2 factors.

Table 2.1 Sources of Variation Is About 2 Factors (A and B)

Sources of variation DF SS MS F-value

Between

replicationsr-1 SSR

MSR = SSR /

DFreplicationMSR / MSE

Between Treatments 22-1 = 3 SSTMST = SST /

DFtreatmentMST / MSE

A 1 SSA = [A]2 / 4rMSA =

SSA / DFaMSA / MSE

B 1 SSB = [B]2 / 4rMSB = SSB /

DFbMSB / MSE

AB 1 SSAB = [AB]2 /4rMSAB =

SSAB / DFab

MSAB /

MSE

Error

(r-1) (22 -

1) = 3 (r-

1)

SSEMSE = SSE /

DFerror

Totalr. 22 -1 =

4r-1TSS

The table below has shown the sources of variation for solving with

ANOVA for 3 factors.


Table 2.2 Sources of Variation Is About 3 Factors (A, B and C)

Sources of

variationDF SS MS F-value

Between

replicationsr-1 SSR

MSR = SSR /

DFreplicationMSR / MSE

Between

Treatments22-1 = 3 SST

MST = SST /

DFtreatmentMST / MSE

A 1 SSA = [A]2 / 4rMSA = SSA /

DFaMSA / MSE

B 1 SSB = [B]2 / 4rMSB = SSB /

DFbMSB / MSE

C 1 SSC = [C]2 / 4rMSC = SSC /

DFcMSC / MSE

AB 1SSAB = [AB]2

/4r

MSAB =

SSAB / DFabMSAB / MSE

AC 1SSAC = [AC]2

/4r

MSAC =

SSAC / DFacMSAC / MSE

BC 1SSBC = [BC]2

/4r

MSBC =

SSBC / DFbcMSBC / MSE

ABC 1SSABC =

[ABC]2 /4r

MSABC =

SSABC /

DFabc

MSABC /

MSE

Error(r-1) (23 -1) = 7

(r-1)SSE

MSE = SSE /

DFerror

Total r. 23 -1 = 8r-1 TSS

Experiments with Factor 2k Designs

The factorial experiments, where all combination of the levels of the

factors is run, are usually referred to as full factorial experiments. Factorial two

level experiments are also referred to as 2k designs where k is the number of

factors being investigated in the experiment. A full factorial two level design

with k factors requires 2k runs for a single replicate. For example, a two level


experiment with three factors will require 2 x 2 x 2 = 23 = 8 runs. The choice of

the two levels of factors used in two level experiments depends on the factor;

some factors naturally have two levels. For example, if gender is a factor, then

male and female are the two levels. For other factors, the limits of the range of

interest are usually used.

The two levels of the factor in the 2k design are usually represented as -

1 (for the first level) and 1 (for the second level). For note about the representation

is reversed from the coding used in General Full Factorial Designs for the

indicator variables that represent two level factors in ANOVA models. For

ANOVA models, the first level of the factor were represented using a value

of 1 for the indicator variable, while the second level was represented using a

value of -1.

Experiments with Factor 22 Design

The simpler of the two level factorial experiments is the 22 design where

two factors (say factor A and factor B) are investigated at two levels. A single

replicate of this design will require four runs (2 x 2 = 22 = 4). The effects

investigated by this design are the two main effects, A and B and the interaction

effect AB. The presence of a letter indicates the high level of the corresponding

factor and the absence indicates the low level.

Table 2.3 Experiments with Factor 22 Design

Treatment NameFactor

A B

(1) -1 -1

A 1 -1

B -1 1

Ab 1 1

For example, the first is represents the treatment combination where all factors

involved are at the low level or the level represented by -1 and α represents the

treatment combination where factor A is at the high level or the level of 1, while

the remaining factors in this case, factor B are at the low level or the level of -1.

Similarly, b represents the treatment combination where factor B is at the high


http://reliawiki.org/index.php/General_Full_Factorial_Designs

level or the level of 1, while factor a, is at the low level and AB represents the

treatment combination where factors A and B are at the high level or the level of

the 1.

Experiments with Factor 23 Design

The 23 design is a two level factorial experiment design with three factors

(factors A, B and C) and this design will design tests three where k = 3 and also

main effects, A, B and C , two factor interaction effects, AB, BC, AC ; and one

three factor interaction effect is ABC. The design requires eight runs per replicate.

The eight treatment combinations corresponding to these runs are 1,a , b, c, ab ,ac

, bc and abc. The treatment combinations are written in such an order that factors

are introduced one by one with each new factor being combined with the

preceding terms and also in this order of writing the treatments is called

the standard order or Yates order. Table 2.4 is the example of 23 designs or called

3 factors.

Table 2.4 Experiments with Factor 23 Designs

Treatment NameFactor

A B C

(1) -1 -1 -1

A 1 -1 -1

B -1 1 -1

C 1 1 -1

AB -1 -1 1

AC 1 -1 1

BC -1 1 1

ABC 1 1 1

Response Surface Methodology or RSCM :

Response Surface methodology is a collection of mathematical and

statistical techniques that are useful for modeling and analysis of problem in

which a response of interest is influenced by several variables and the objective is

to optimize this response. If we denote the expected response by E (y) = f(x1,x2) =


h , then the surface represented by h = f(x1,x2) is called a response surface. For

example, suppose that a chemical engineer wishes to find the levels of

temperature (x1) and pressure (x2) that maximize the yield (y) of a process.

The processes function of yield:

y = f(x1,x2) + e (2-5)

The Steepest Ascent Method

The method of steepest ascent is a procedure for moving sequentially

along the path of steepest ascent, that is, in the direction of the maximum increase

in the response. If minimization is desired, then it call is technique the method of

steepest descent.

Experiments are conducted along the path of steepest ascent until no

further increase is response is observed. Then a new first-order model may be fit,

a new path of steepest ascent determined, and the procedure continued.

Eventually, the experimenter will arrive in the vicinity of the optimum. This is

usually indicated by lack of fit of a first-order model. At that time additional

experiments are conducted to obtain a more precise estimate of the optimum.

There are several steps of steepest ascent:

1. Choose a step size in one of the process variables, say Dxj. Usually, it

would select the variable it is know the most about, or it would select the

variable that has the largest absolute regression coefficient |bj|.

2. The step size in the other variables is

∆ x i=β̂ i

β̂ j

∆ x j

(2-6)

3. Convert the Dxi from coded variables to the natural variables.

Center Points to the 2k Design

A potential concern in the use of two-level factorial design is the

assumption of linearity in the factor effects and the perfect linearity is unnecessary

and the 2k system will work quite well even when the linearity assumption holds


only very approximately. There are two purposes why the center point runs

interspersed among the experimental setting runs for two purposes:

1. To provide a measure of process stability and inherent variability

2. To check for curvature.

Based on the idea of some replication in a factorial design, runs at the center

provide an estimate of error and allow the experimenter to distinguish between

two possible models:

First order model

Consider the following first-order model in k variables for fitting

y=β0+∑i=1

k

β i xi+∑i=1

k

∑j>i

k

βij xi x j+¿ ε ¿ (2-7)

There is a unique class of designs that minimize the variance of the

regression coefficients β1. These are the orthogonal first order designs. A first

order design is orthogonal if the off diagonal elements of the (X`X) matrix are all

zero. This implies that the cross products of the columns of the X matrix sum to

zero. The 2k factorial and fractions of the 2k series in which main effects are not

aliased with each other belongs to the class of orthogonal first order design and

assume the low and high level of the k factors are coded -1 and 1 levels to used in

design.

Figure 2.1 Surface Graph and Contour Map

Second order model


Series1Series8

Series15Series22Series29

Series36

Series43

Series50

-10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 140.0 150.0

1471013161922252831343740434649

The central composite design or CCD is used for fitting a second-order model.

The CCD consists of a 2kfactorial with nf runs, 2kaxial or star runs, and nc center

runs. Following figure shows the CCD for k = 2 and k = 3 factors.

y=β0+∑i=1

k

β i xi+∑i=1

k

∑j>i

k

βij xi x j+¿∑i=1

k

β ii x2

i+ε ¿ (2-8)

The CCD is developed through sequential experimentation. Suppose a 2k

is used to fit a first order model and suppose this model exhibits lack off it. Then

axial runs are added to allow the quadratic terms to be incorporated in to the

model. The CCD is a very efficient design for fitting the second order model.

There are two parameters in the design that must be specified:

The distance α of the axial runs from the design center

The number of center points nc.

Figure 2.2 CCD


CHAPTER III

DATA COLLECTION

3.1. Experiment Procedure

Some tools and ingredients are necessary to conduct the experiment Paper,

Scissors, Ruler, Pencil, and Operator are the main ingredient and tools to conduct

the experiment. Basically, paper, scissor, ruler, pencil are used to draw the

helicopter paper.

There are 16 combinations and 3 replications, so the total experiment is 48

experiments. There are three factors or variables that might be considered for

effecting the measure downward speed of the paper helicopter. Those factors are:

1) Paper Clip

Small Size

Large Size

2) Tail Lenght

Small Size = the tail lenght size is 10 cm

Large Size = the tail lenght size is 15 cm

3) Tail Widht

Small size = the tail widht size is 3 cm

Large size = the tail widht size is 4.5 cm

4) Body Lenght.

Small Size = the lenght size is 5 cm

Large Size = the lenght size is 7.5 cm

5) Controllable Factor

Type of Paper

Height of Experiment = 3 meters

Type of Paper Clip

Tool of Time Measurement

Among those variable, the experiment can be made into the 16

combinations with 3 replications, so the total paper helicopters are 48


experiments. Table 3.1 shows the paper helicopeter combination with single

replication. In order to make the monitoring process easier, the levels of each

factor are symbolized shown in Table 3.1.

Table 3.1paper helicopter Combination

Number of Experiment

Body Length Tail Widht Tail Lenght Paper Clip

1 -1 -1 -1 -12 -1 -1 -1 13 -1 -1 1 -14 -1 -1 1 15 -1 1 -1 -16 -1 1 -1 17 -1 1 1 -18 -1 1 1 19 1 -1 -1 -110 1 -1 -1 111 1 -1 1 -112 1 -1 1 113 1 1 -1 -114 1 1 -1 115 1 1 1 -116 1 1 1 1

Source: Self-constructed by experimenters

Table 3.2 Center Point

No 1 2 3 4 5 6 7 8 9 10 11 12Coded -1 1 -1 1 -1 1 -1 1 -1 1 -1 1

Center point3.26

3.28 3.1 3.42 3.07 3.42 3.28 3.64 3.42 2.88 3.28 3.28


3.2. Response Measurement

After did an experiments, the downward speed of paper helicopter was

measured and the result could be obtained by using stopwatch. The table below

shows the result of response measurement. For example experiment number 1, the

first replication shows the time response is 3.42 second, the second replication is 3.28

second and third response is 3.01 second. This can be explained because of


uncontrollable variables. The researcher assumed there are several uncontrollable

factors that caused this observation. One hypothesis is because of the air

distraction towards several paper helicopters.

Table 3.3 Response Measurement Result

NoBody

Length (BL)

Tail Width (TW)

Tail Length

(Ti)

Paper Clip

Responses

1 2 3

1 S S S S 3,6 3,55 3,422 S S S L 3,7 3,46 3,63 S S L S 3,73 3,78 3,64 S S L L 3,64 3,42 3,735 S L S S 3,51 3,28 3,016 S L S L 3,37 3,64 3,567 S L L S 3,69 3,62 3,918 S L L L 3,69 3,28 3,429 L S S S 3,42 3,64 3,2810 L S S L 3,69 3,37 3,7311 L S L S 3,73 3,78 3,8212 L S L L 3,51 3,6 3,4613 L L S S 3,42 3,28 3,4214 L L S L 3,24 3,24 3,3315 L L L S 3,96 3,42 3,5516 L L L L 3,64 3,1 3,55


It is clearly seen on the table above, the downward speed rate between

paper helicopter that used small body lenght, large tail width, small tail lenght and

small paper clip has higher result rather than the another paper helicopter.Thus, it

can be assumed that body length size, tail widht size, tail lenght size and size of

paper clip has an effect on the downward speed rate. This assumption can be

tested later in the hypothesis testing.

Those three factors will be analyzed by using several methods to

determine whether or not those factors have significant effect towards response

(downward speed rate), which are: ANOVA test, residual plot, interaction plot,

and regression model. ANOVA test is being used to determine the effect of

factors towards speed rate. Residual plot is used to determine the goodness of

model of the experiment. Interaction plot is used to determine whether or not the


factors have interaction with another factor. Later, regression model is used to

predict the future experiment with different input towards downward paper

helicopter speed rate.

3.3. Experiment Hypothesis

There are fifth models of hypothesis that is going to be tested, which are

Linear, two-way interaction, three way interaction, fourth way interaction and

interaction effect. The hypotheses are:

Linear:

1. H0A: There is no significant effect of Factor A (paper clip) to the response

(downward speed the paper helicopter).

H1A: There is a significant effect of Factor A (paper clip) to the response


2. H0B: There is no significant effect of Factor B (tail length) to the response


H1B: There is a significant effect of Factor B (tail length) to the response


3. H0C: There is no significant effect of Factor C (tail width) to the response


H1C: There is a significant effect of Factor C (tail width) to the response


4. H0D: There is no significant effect of Factor D (body length) to the

response (downward speed the paper helicopter).

H1D: There is a significant effect of Factor D (body length) to the response


Two-way Interaction(s):

5. H0AB: There is no interaction between Factor A (paper clip) and Factor B

(tail length).

H1AB: There is an interaction between Factor A (paper clip) and Factor B

(tail length).

6. H0AC: There is no interaction between Factor A (paper clip) and Factor C

(tail width).


H1AC: There is an interaction between Factor A (paper clip) and Factor C

(tail width).

7. H0AD: There is no interaction between Factor A (paper clip) and Factor D

(body length).

H1AD: There is an interaction between Factor A (paper clip) and Factor D

(body length).

8. H0BC: There is no interaction between Factor B (tail length) and Factor C

(tail width).

H1BC: There is an interaction between Factor B (tail length) and Factor C

(tail width).

9. H0BD: There is no interaction between Factor B (tail length) and Factor D

(body length).

H1BD: There is an interaction between Factor B (tail length) and Factor D

(body length).

10. H0CD: There is no interaction between Factor C (tail width) and Factor D

(body length).

H1CD: There is an interaction between Factor C (tail width) and Factor D

(body length).

Three-way Interaction:

11. H0ABC: There is no interaction between Factor A (paper clip), Factor B (tail

length), and Factor C (tail width).

H1ABC: There is an interaction between Factor A (paper clip), Factor B (tail

length), and Factor C (tail width).

12. H0ABD: There is no interaction between Factor A (paper clip), Factor B (tail

length), and Factor D (body length).

H1ABD: There is an interaction between Factor A (paper clip), Factor B (tail

length), and Factor D (body length).

13. H0ACD: There is no interaction between Factor A (paper clip), Factor C (tail

width), and Factor D (body length).

H1ACD: There is an interaction between Factor A (paper clip), Factor C (tail



14. H0BCD: There is no interaction between Factor B (tail length), Factor C (tail


H1BCD: There is an interaction between Factor B (tail length), Factor C (tail


Fourth-way Interaction:

15. H0ABCD: There is no interaction between Factor A (paper clip), Factor B

(tail length), Factor C (tail width) and Factor D (body length).

H1ABCD: There is an interaction between Factor A (paper clip), Factor B

(tail length), Factor C (tail width) and Factor D (body length).

Interaction effects:

16. H0AB: There is no interaction between Factor A (paper clip) and Factor B

(tail length) towards response (downward speed the paper helicopter).

H1AB: There is an interaction between Factor A (paper clip) and Factor B

(tail length) towards response (downward speed the paper helicopter).

17. H0AC: There is no interaction between Factor A (paper clip) and Factor C

(tail width) towards response (downward speed the paper helicopter).

H1AC: There is an interaction between Factor A (paper clip) and Factor C


18. H0AD: There is no interaction between Factor A (paper clip) and Factor D

(body length) towards response (downward speed the paper helicopter).

H1AD: There is an interaction between Factor A (paper clip) and Factor D


19. H0BC: There is no interaction between Factor B (tail length) and Factor C


H1BC: There is an interaction between Factor B (tail length) and Factor C


20. H0BD: There is no interaction between Factor B (tail length) and Factor D


H1BD: There is an interaction between Factor B (tail length) and Factor D



21. H0CD: There is no interaction between Factor C (tail width) and Factor D


H1CD: There is an interaction between Factor C (tail width) and Factor D


22. H0ABC: There is no interaction between Factor A (paper clip), Factor B (tail

length), and Factor C (tail width) towards response (downward speed the

paper helicopter).

H1ABC: There is an interaction between Factor A (paper clip), Factor B

(tail length), and Factor C (tail width) towards response (downward speed

the paper helicopter).

23. H0ABD: There is no interaction between Factor A (paper clip), Factor B (tail

length), and Factor D (body length) towards response (downward speed


H1ABD: There is an interaction between Factor A (paper clip), Factor B (tail

length), and Factor D (body length) towards response (downward speed


24. H0ACD: There is no interaction between Factor A (paper clip), Factor C (tail

width), and Factor D (body length) towards response (downward speed the

paper helicopter).

H1ACD: There is an interaction between Factor A (paper clip), Factor C (tail


paper helicopter).

25. H0BCD: There is no interaction between Factor B (tail length), Factor C (tail


paper helicopter).

H1BCD: There is an interaction between Factor B (tail length), Factor C (tail


paper helicopter).

26. H0ABCD: There is no interaction between Factor A (paper clip), Factor B

(tail length), Factor C (tail width) and Factor D (body length) towards



H1ABCD: There is an interaction between Factor A (paper clip), Factor B

(tail length), Factor C (tail width) and Factor D (body length) towards



CHAPTER IV

DATA ANALYSIS

4.1. Pre Test

Fourth Factors are being considered as the Independent Variables that will

be examined whether or not the factor influenced (or has significant effect) to the

response as the Dependent Variables (downward speed of paper helicopter).

Those fourth factors are: body length, tail width, tail length and paper clip; each of

it have same levels. The first factor, paper clip, is the “categorical” factor with two

levels which are large and small. The second factor, tail length, is the “numerical”

factor with two levels of factor which are (10 cm) small and (15cm) large. The

third factor, tail width, is the “numerical” factor with two levels of factor which

are (3 cm) small and (4.5 cm) large. The last factor, body length, is clearly the

“numerical” factor with two levels of factor which are 5 cm (small) and (7.5 cm)

large.

The symbol of minus (-) and plus (+) means a low and high level

respectively. It is perfectly indicates for level of downward speed of paper

helicopter factor can be assumed which one indicates the low or high level. For

factor with 2 levels, the level can be obtained by -1 and +1. In this case, the fourth

levels factors are 3 numerical and 1 categorical, so it can be assumed at any level.

This case indicates the 4 factors and same levels with 2 of Factorial Design or

simply called by 2k Level Factorial Design. Three Replications is being observed

in order to accurate the data experiment.

The run number test is shown from the total combination of the factorial

design. The total run number is 48 combinations (2 level * 2 level * 2 level * 2 level *

3 replication = 48 combinations). The run number is obtained by using Minitab

Software. The order of the run number is shown in Table 4.1.

Mung Bean Project | Design of ExperimentPage 26Industrial Engineering 2012 | President University

Table 4.1 Run Number

Std Order

Run Order

Center Pt

Paper Clip

Tail Length

Tail Width

Body Length

Response

1 1 1 -1 -1 -1 -1 3.602 2 1 1 -1 -1 -1 3.703 3 1 -1 1 -1 -1 3.734 4 1 1 1 -1 -1 3.645 5 1 -1 -1 1 -1 3.516 6 1 1 -1 1 -1 3.377 7 1 -1 1 1 -1 3.698 8 1 1 1 1 -1 3.699 9 1 -1 -1 -1 1 3.4210 10 1 1 -1 -1 1 3.6911 11 1 -1 1 -1 1 3.7312 12 1 1 1 -1 1 3.5113 13 1 -1 -1 1 1 3.4214 14 1 1 -1 1 1 3.2415 15 1 -1 1 1 1 3.9616 16 1 1 1 1 1 3.6417 17 1 -1 -1 -1 -1 3.5518 18 1 1 -1 -1 -1 3.4619 19 1 -1 1 -1 -1 3.7820 20 1 1 1 -1 -1 3.4221 21 1 -1 -1 1 -1 3.2822 22 1 1 -1 1 -1 3.6423 23 1 -1 1 1 -1 3.6224 24 1 1 1 1 -1 3.2825 25 1 -1 -1 -1 1 3.6426 26 1 1 -1 -1 1 3.3727 27 1 -1 1 -1 1 3.7828 28 1 1 1 -1 1 3.6029 29 1 -1 -1 1 1 3.2830 30 1 1 -1 1 1 3.2431 31 1 -1 1 1 1 3.4232 32 1 1 1 1 1 3.1033 33 1 -1 -1 -1 -1 3.4234 34 1 1 -1 -1 -1 3.6035 35 1 -1 1 -1 -1 3.6036 36 1 1 1 -1 -1 3.7337 37 1 -1 -1 1 -1 3.0138 38 1 1 -1 1 -1 3.5639 39 1 -1 1 1 -1 3.9140 40 1 1 1 1 -1 3.4241 41 1 -1 -1 -1 1 3.2842 42 1 1 -1 -1 1 3.7343 43 1 -1 1 -1 1 3.8244 44 1 1 1 -1 1 3.4645 45 1 -1 -1 1 1 3.4246 46 1 1 -1 1 1 3.3347 47 1 -1 1 1 1 3.5548 48 1 1 1 1 1 3.55

Source: Primary Data by Minitab 17


4.2. Estimating the Factor Effect

The first step of experimental design is to estimate the factor effect. The

factor effect could give the information of important design factor and interaction

as well as its signs and magnitudes. This step involves main effect plot and

interaction between factors supported by normal probability plot, half normal

probability plot, and Pareto charts of the standardize effect.

When performing a statistical analysis, one of the simplest graphical tools

is a Main Effects Plot. This plot shows the average outcome for each value

(response) of each variable (factor), combining the effects of the other variables as

if all variables were independent.

1-1

3.625

3.600

3.575

3.550

3.525

3.500

3.475

3.450

1-1 1-1 1-1

Paper Clip

Mea

n

Tail Length Tail Width Body Length

Main Effects Plot for ResponseData Means

Figure 4.1 Main Effect Plot for Response


Figure 4.1 shows the Main Effect Plot for the Response for each Factor.

First, the average (mean) of response for Factor A (Paper Clip) indicates the effect

of small (-1) level is the greater than the large level (+1). Second, the average

(mean) of response for Factor B (Tail Length) indicates the effect of 15 cm (+1)

level is extremely greater than 10 cm level (-1). Third, the average (mean) of

response for Factor C (Tail Width) indicates the effect of 3 cm (-1) level is the


greater than 4.5 cm (+1). Fourth, the average (mean) of response for factor D

(Body Length) indicates the effect of 5 cm (-1) level greater than 7.5 cm (+1)

level. By this graph, it can be concluded that the lower level of three factors has

greater mean rather than the higher level.

Interaction Plot

Another graphic statistical tool is called an Interaction Plot. This type of

chart illustrates the effects between variables which are not independent. If there

is any intersection between factors, means the factor has interaction with another

factor. Figure 4.2 shows the Interaction Plot for data means

1-1 1-1 1-13.75

3.60

3.45

3.75

3.60

3.45

3.75

3.60

3.45

Paper Clip

Tail Length

Tail Width

Body Length

-11

ClipPaper

-11

LengthTail

-11

WidthTail

Interaction Plot for ResponseData Means

Figure 4.2 Interaction Plot for Response


Based on Figure 4.2, it is shown that there is an interaction between Paper

Clip and Tail. Besides that, it is shown that there is no interaction between all of

it; paper clip-tail width, tail length-tail width, paper clip-body length, tail length-

body length, and tail width-body length.


Coded Coefficients

Term Effect Coef SE Coef T-Value P-ValueConstant 3.5290 0.0244 144.71 0.000Paper Clip -0.0604 -0.0302 0.0244 -1.24 0.024Tail Length 0.1612 0.0806 0.0244 3.31 0.002Tail Width -0.1304 -0.0652 0.0244 -2.67 0.012Body Length -0.0429 -0.0215 0.0244 -0.88 0.385Paper Clip*Tail Length -0.1521 -0.0760 0.0244 -3.12 0.004Paper Clip*Tail Width -0.0237 -0.0119 0.0244 -0.49 0.630Paper Clip*Body Length -0.0446 -0.0223 0.0244 -0.91 0.368Tail Length*Tail Width 0.0496 0.0248 0.0244 1.02 0.317Tail Length*Body Length 0.0104 0.0052 0.0244 0.21 0.832Tail Width*Body Length -0.0262 -0.0131 0.0244 -0.54 0.594Paper Clip*Tail Length*Tail Width

-0.0088 -0.0044 0.0244 -0.18 0.859Paper Clip*Tail Length*Body Length

0.0238 0.0119 0.0244 0.49 0.630Paper Clip*Tail Width*Body Length

-0.0296 -0.0148 0.0244 -0.61 0.548Tail Length*Tail Width*Body Length

-0.0063 -0.0031 0.0244 -0.13 0.899Paper Clip*Tail Length*Tail Width*Body Length

0.0821 0.0410 0.0244 1.68 0.102

Term VIFConstantPaper Clip 1.00Tail Length 1.00Tail Width 1.00Body Length 1.00Paper Clip*Tail Length 1.00Paper Clip*Tail Width 1.00Paper Clip*Body Length 1.00Tail Length*Tail Width 1.00Tail Length*Body Length 1.00Tail Width*Body Length 1.00Paper Clip*Tail Length*Tail Width 1.00Paper Clip*Tail Length*Body Length 1.00Paper Clip*Tail Width*Body Length 1.00Tail Length*Tail Width*Body Length 1.00Paper Clip*Tail Length*Tail Width*Body Length 1.00

Figure 4.3 Estimated Effects and Coefficients for Response (Full Model)


Graphical plot is necessary to estimate the factorial effect, however, it

cannot predict accurately. Then, numerical statistic analysis is being used to

analyze the factorial effect accurately based on numerical value that is obtained by

statistical software, Minitab 17. Based on Figure 4.3, there are three factors that

significantly affect the response, which are: Paper Clip, Tail Length, and Tail

Width. In addition, the interaction plot between Paper Clip and Tail Length is


significant. The p-value of those factors and interactions are lower than

significance levels (P-value ≤ α = 0.05).

Figure 4.4 showed the normal plot of the standardized effects on response.

Based on that plot, it is shown that the red point is significant with α =0.05, which

are: Factor B (Tail Width), Factor C (Tail Length), and Interaction AB (Paper

Clip and Tail Length). It shows the Factor B (Tail Width) has significant positive

effects on response because it is located at the right side of line. Otherwise, Factor

C and Interaction AB have significant negative effects on responses.

43210-1-2-3

99

95

90

80

70

60

5040

30

20

10

5

1

A Paper ClipB Tail LengthC Tail WidthD Body Length

Factor Name

Standardized Effect

Perc

ent

Not SignificantSignificant

Effect Type

AB

C

B

Normal Plot of the Standardized Effects(response is Response, α = 0.05)

Figure 4.4 Normal Plot of Standardized Effects on Response (Full Model)


Meanwhile, the half normal plot shows the absolute standardized effects to

compare their relative magnitudes. Since the point of factor B is the furthest to the

right means the effect is most highly significant to the response, followed by

Interaction AB and Factor C respectively.


3.53.02.52.01.51.00.50.0

98

95

90

85

80

70

60

50

40

3020100


Factor Name

Absolute Standardized Effect

Perc

ent

Not SignificantSignificant

Effect Type

AB

C

B

Half Normal Plot of the Standardized Effects(response is Response, α = 0.05)

Figure 4.5 Half Normal Plot of Standardized Effects on Response (Full Model)


Pareto Chart of the Standardized Effects helps to determine the

magnitudes as well as the significant of this effect. The effect that exceeds the red

line is statistically important or significant. It is shown that the Factor A,

Interaction AB, and Factor C are passing the reference line at the level of

significance of 5%.

Based on previous statistical software output, it is shown that there is the

difference result by numerical output and categorical output.


Term

BCD

ABC

BD

AC

ABD

CD

ACD

D

AD

BC

A

ABCD

C

AB

B

3.53.02.52.01.51.00.50.0


Factor Name

Standardized Effect

2.037

Pareto Chart of the Standardized Effects(response is Response, α = 0.05)

Figure 4.6 Pareto Chart of Standardized Effects on Response (Full Model)


Form Initial Model

The initial Full model including all terms in coded units by using the coefficients

presented in Figure 4.3 is:

4.4. ANOVA Test

The main effects plot and interaction plot do not provide a great deal of

information. Showing just the main effects and interaction of each factor level

without accounting for the levels of other factors is simplistic and could be

misleading. The ANOVA test is being used to determine the effect of the factors

and/or interaction towards the response in the numerical model.

Figure 4.4 shows the p-value of each factor and interaction between

factors that are obtained from Minitab. The rejection criterion for p-value shows if

the p-value < than α (α = 0.05) means to reject H0. Based on ANOVA test on

Figure 4.4, it can be concluded that tail widht and tail lenght that have an effect to

the response (downward speed of paper helicopter), the p-value of tail width is

0.003 and p-value of tail lenght is 0.015. Another factor which is body length and


paper clip have no significant effect to the response because the p-value is greater

than α, the p-value of body lenght is 0.409 and p-value of paper clip is 0.500. In

addition, there is no significant effect for interaction between factors (two-way

interaction, three-way interaction and four way intercactions) towards response.

Analysis of Variance

Source DF Adj SS AdjMS F-Value P-ValueModel 16 1.60673 0.100420 3.16 0.001 Linear 4 0.55295 0.138237 4.35 0.005 Paper Clip 1 0.01473 0.014727 0.46 0.500 Tail Length 1 0.31202 0.312019 9.81 0.003 Tail Width 1 0.20410 0.204102 6.42 0.015 Body Length 1 0.02210 0.022102 0.69 0.409 2-Way Interactions 6 0.34725 0.057874 1.82 0.118 Paper Clip*Tail Length 1 0.27755 0.277552 8.73 0.005 Paper Clip*Tail Width 1 0.00677 0.006769 0.21 0.647 Paper Clip*Body Length 1 0.02385 0.023852 0.75 0.391 Tail Length*Tail Width 1 0.02950 0.029502 0.93 0.341 Tail Length*Body Length 1 0.00130 0.001302 0.04 0.841 Tail Width*Body Length 1 0.00827 0.008269 0.26 0.613 3-Way Interactions 4 0.01866 0.004665 0.15 0.964 Paper Clip*Tail Length*Tail Width 1 0.00092 0.000919 0.03 0.866 Paper Clip*Tail Length*Body Length 1 0.00677 0.006769 0.21 0.647 Paper Clip*Tail Width*Body Length 1 0.01050 0.010502 0.33 0.569 Tail Length*Tail Width*Body Length 1 0.00047 0.000469 0.01 0.904 4-Way Interactions 1 0.08085 0.080852 2.54 0.118 Paper Clip*Tail Length*Tail Width*Body Length 1 0.08085 0.080852 2.54 0.118 Curvature 1 0.60702 0.607020 19.08 0.000Error 43 1.36777 0.031809 Lack-of-Fit 1 0.05075 0.050750 1.62 0.210 Pure Error 42 1.31702 0.031358Total 59 2.97449

Figure 4.3 P-value of ANOVA

4.5. Residual Plot and Model Adequacy

The normal probability plot is a graphical technique for assessing whether

or not a data set is approximately normally distributed (Chambers et al., 1983).

The data are plotted against a theoretical normal distribution in such a way that

the points should form an approximate straight line. Departures from this straight

line indicate departures from normality.


http://www.itl.nist.gov/div898/handbook/eda/section4/eda43.htm#Chambers

http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm

0.500.250.00-0.25-0.50

99.9

99

90

50

10

1

0.1

Residual

Perc

ent

3.73.63.53.43.3

0.4

0.2

0.0

-0.2

-0.4

Fitted Value

Res

idua

l

0.320.160.00-0.16-0.32

16

12

8

4

0

Residual

Freq

uenc

y

605550454035302520151051

0.4

0.2

0.0

-0.2

-0.4

Observation Order

Res

idua

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Response

Figure 4.4 Residual Plots for Response

Based on Figure 4.4, the points on this plot are distributed because it is the

straight line, which indicates that the model is normal distributed. The plot shows

that it is light-tailed distribution. Histogram Chart shows this model is also

normally distributed, it can be shown that the chart is bell shaped. Based on

normal probability plot and histogram, it can be concluded that the model is

normally distributed.

Figure 4.4 shows the Residual Plots for Response obtained by Minitab.

The residual plot (versus fits) shows the variance is an increase function of y

(response or growth rate). The residual plot (versus order) shows that is negative

autocorrelation.

4.6. Hypothesis Testing

Based on Effect Test, Interaction Plot, Residual Plot, and ANOVA test;

the hypothesis testing can be done based on those analyses. The following

Hypotheses Testing is shown on Table 4.5.

Table 4.4 Hypotheses Testing for Problem 6.20

Hypotheses H0 H1 DecisionLinear


Factor A There is no significant effect of Factor A (paper clip) to the response (downward speed rate of paper helicopter)

There is a significant effect of Factor A (paper clip) to the response (downward speed rate of paper helicopter)

Reject H0

Factor B There is no significant effect of Factor B (tail lenght) to the response (downward speed rate of paper helicopter)

There is a significant effect of Factor B (tail lenght) to the response (downward speed rate of paper helicopter)

Reject H0

Factor C There is no significant effect of Factor C (tail width ) to the response (downward speed rate of paper helicopter)

There is a significant effect of Factor C (tail width) to the response (downward speed rate of paper helicopter)

Do not Reject H0

Factor D There is no significant effect of Factor D (body length) to the response (downward speed rate of paper helicopter)

There is a significant effect of Factor D (body length) to the response (downward speed rate of paper helicopter)

Do not Reject H0

Two-way InteractionsFactor A & B There is no interaction between

Factor A (paper clip) and Factor B (tail lenght)

There is an interaction between Factor A (paper clip) and Factor B (tail lenght)

Do not Reject H0

Factor A & C There is no interaction between Factor A (paper clip) and Factor C (tail width)

There is an interaction between Factor A (paper clip) and Factor C (tail width)

Do not Reject H0

Factor A & D There is no interaction between Factor A (paper clip) and Factor D (body length)

There is an interaction between Factor A (paper clip) and Factor D (body length)

Do not Reject H0

Factor B & C There is no interaction between Factor B (tail lenght) and Factor C (tail width)

There is an interaction between Factor B (tail lenght) and Factor C (tail width)

Do not Reject H0

Factor B & D There is no interaction between Factor B (tail lenght) and Factor D (body length)

There is an interaction between Factor B (tail lenght) and Factor D (body length)

Do not Reject H0

Factor C & D There is no interaction between Factor C (tail width) and Factor D (body length)

There is an interaction between Factor C (tail width) and Factor D (body length)

Do not Reject H0

Three-way InteractionsFactor A-B-C There is no interaction between

Factor A (paper clip), Factor B (tail lenght), and Factor C (tail width)

There is an interaction between Factor A (paper clip), Factor B (tail lenght), and Factor C (tail width)

Do not Reject H0

Factor A-B-D There is no interaction between Factor A (paper clip), Factor B (tail lenght), and Factor D (body length)

There is an interaction between Factor A (paper clip), Factor B (tail lenght), and Factor D (body length)

Do not Reject H0

Factor A-C-D There is no interaction between Factor A (paper clip), Factor C (tail width), and Factor D (body length)

There is an interaction between Factor A (paper clip), Factor C (tail width), and Factor D (body length)

Do not Reject H0

Factor B-C-D There is no interaction between Factor B (tail lenght), Factor C (tail width), and Factor D (body length)

There is an interaction between Factor B (tail lenght), Factor C (tail width), and Factor D (body length)

Do not Reject H0


Four-way InteractionsFactor A-B-C-D

There is no interaction between Factor A (paper clip), Factor B (tail lenght), Factor C (tail width), and Factor D (body length)

There is an interaction between Factor A (paper clip), Factor B (tail lenght), Factor C (tail width), and Factor D (body length)

Do not Reject H0

The decision for reject or do not reject H0 is based on ANOVA test. The p-

value indicates the effect on the factor. If p-value is greater than α (α = 0.05), do

not reject H0, or vice versa. The p-value of Factor B is 0.03 and the p-value of

Factor C is 0.015 which are less than α (α = 0.05), which means those Factors are

significantly has effect on the response.

Based on Table 4.5, it can be concluded the Factor B (tail lenght) and Factor C

(tail width) has significant effect towards Response (downward speed rate of

paper helicopter) independently. There is no interaction between Factor B and

Factor C. Thus, the others H0 on hypothesis should not be rejected. Factor A

(paper clip) and Factor D (body length) are not significantly effect to the

Response (downward speed rate of paper helicopter).


4.7. Regression Model

Multiple regression analysis is a statistical technique to predict the

variance in the dependent variable by regressing the independent variable against

it. Multiple regression analysis used in situation where two or more independent

variables are hypothesized to affect one dependent variable. Based on ANOVA

test, the regression model can be obtained by one factor only, which is: Factor B

(Plant Food). Then the model equation used in this case can be explained as

follows:

Y = β0 + β2 X2 + e

Where:

Y = Growth Rate

β0 = Constant

β2 = X2 Regression coefficient

X2 = Factor B (Plant Food)

e = random error term/residuals

Regression EquationGrowth Rate = 3.561 - 2.089 Food_No + 2.089 Food_Yes

Figure 4.5 Regression Model from Minitab

According to the result of multiple regression analysis tests that has been

done by Minitab; the regression model is clearly shown in Figure 4.5. The general

equation of regression model is:

Y = 3.561 ± 2.089 X2 + e

From the regression linear above, the conclusions are as follow:

1. The equation has a Constant of 12.295 which means that if Factor B (Plant

Food) is assumed being zero, the response (growth rate) is 3.561.

2. The coefficient regression of Factor B (Plant Food) is 2.089 which means

every 100% improvement in variable of Factor B (Plant Food) will

increase (+) the response (Growth Rate) for 208.9% if the plant using

Plant Food, otherwise Factor B (Plant Food) will decrease (-) the response

(growth rate) for 208.9% if the plant is not using Plant Food.

From Regression Analysis, it can be conclude that the Plant Food has

significant effect to the Growth Rate of Mung Bean Plant. The Plant Food has

influenced about 208.9% towards Growth Rate.


CHAPTER V

CONCLUSION

The analyses of problems are obtained using Minitab Software. Mung

Bean sprout is being used as the experimental design. Frequency of watering,

Plant Food usage, and Volume of water are the factors that might be affecting the

response, which is Growth Rate. 18 combinations are being observed with 2

replications each. The total run number is 36 combinations. Main Effect Plot,

Interaction Plot, ANOVA test, and Residual Plot are being used to analyze the

experiment.

Based on Main Effect Plot, the average (mean) of response for Factor A

(Frequency) indicates the effect of Three a day Level is the greatest followed by

Twice and Once a day. Second, the average (mean) of response for Factor B

(Plant Food) indicates the effect of Yes Level is extremely greater than No Level.

Third, the average (mean) of response for Factor C (Volume) indicates the effect

of 2 squirts Level is the greatest followed by 3 squirts and 1 squirt.

Based on Interaction Plot, it is shown that there is no interaction between

Factor A (frequency) and Factor B (plant food). Also, there is an interaction

between Factor A (frequency) and Factor C (volume). Last, there is no interaction

between Factor B (plant food) and Factor C (volume).

Based on ANOVA Test, only Factor B (plant food) that has an effect to

the response (growth rate). Another factors, Factor A (frequency) and Factor C

(volume) has no significant effect to the response. In addition, there is no

significant effect for interaction between factors (two-way interaction and three-

way interaction) towards response.

Based on Residual Plot, the points on this plot are not distributed closed to

the straight line, which indicates that the model is not normal distributed. The plot

shows that it is light-tailed distribution. Histogram Chart shows this model is not

normally distributed, it can be shown that the chart is not bell shaped. The residual

plot (versus fits) shows the variance is an increase function of y (response or

growth rate). The residual plot (versus order) shows that is negative

autocorrelation.


REFERENCE

Haryadi. 2012. Perencanaan dan Analisis Experimen dengan Minitab.

Palangkaraya : Karya Ilmiah Pengabdian pada Masyarakat.

Montgomery, Douglas C. 2009. Design and Analysis of Experiments 7th

Edition. Asia : John Wiley and Sons Pte Ltd

Pan,Jianbiao . Minitab Tutorials for Design and Analysis of Experiments

pdf : Accessed from www.google.co.id. (21 January 2015)


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