Does Up Arman

7/22/2019 Does Up Arman

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Design of ExperimentsDoE)

Pendahuluan (Konsep Definisi)

Exp with a Single Factor: ANOVA (Ch: 3)

Randomized Bloks (Ch: 4)

Latin Square (Ch: 4)

Factorial Design (Ch:5)

Two level Fractional Factorial Design (Ch:8)

Taguchi approach


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PENDAHULUAN

1. Menentukan penyebab penyebab variasi dalamresponse

2. Untuk menentukan kondisi yang optimal(maksimum atau minimum) sehingga optimasiresponse dapat dicapai

3. Membandingkan response menurut setiap level

pada faktor faktor yang dikontrol4. Mengembangkan model untuk prediksi

responses

Mengapa Eksperimen


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24-Dec-13 (c) 2001, Ron S. Kenett, Ph.D. 3

A Serious Problem...

I want mycar to go

fastlikethat one!


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What Factors Affect the Speed?

Key Factor is: ___________________

Yes

Air Holes

No

Slow

Fast

Shape


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Key Factor is: _______________________________

Yes

Air Holes

No

Slow

FastSlow

Shape

Effect of Air Holes


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DOE Balanced Effects

Key Factor is: _______________________________

Yes

Air Holes

No

Slow

FastSlow

Shape

Slow


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KONSEP DEFINISI


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Definisi1. Treatmentsdifferent

combinations of conditions that we

wish to test2. Treatment Levelsthe relative

intensities at which a treatment will

be set during the experiment

3. Factor (Treatment factor)one of

the controlled conditions of the

experiment (these combine to form

the treatments)

4. Experimental Unitsubject on

which a treatment will be applied

and from which a response will be

elicitedalso called measurementor response units

5. Responsesoutcomes that will be

elicited from experimental units

after treatments have been applied

Perlakuanberbagai kombinasi

kosndisi dan situasi yang berbeda

yang akan kita uji Level Perlakuanintensitas relatif

dimana satu perlakuan akan disetel

selama percobaan

Faktor (Faktor perlakuan)salah satu

kondisi terkontrol dari percobaan(kombinasi ini untuk membentuk

perlakuan)

Unit percobaansubyek pada yang

mana satu perlakuan akan diterapkan

dan dari yang mana satu tanggapan

akan timbuljuga pengukuran

dipanggil atau unit tanggapan

Tanggapihasil yang akan timbul dari

unit percobaan setelah perlakuan

telah diterapkan


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6. Design of Experiments (DOE)alsoreferred to as Experimental Design,this is the study of planningefficient and systematic collection

of responses from experimentalunits

7. Experimental Designrule forassigning treatment levels toexperimental units

8. Analysis of Variance (ANOVA)principal statistical means for

evaluating potential sources ofvariation in the responses

9. Replicationobserving individualresponses of multiple experimentalunits under identical experimentalconditions

10. Repeated Measurements

observing multiple responses of asingle experimental unit underidentical experimental conditions

Perancangan Percobaan (KIJANGBETINA)juga dikenal sebagai DesainPercobaan, ini adalah pembahasandari efisien perencanaan dan koleksi

sistematis dari tanggapan dari unitpercobaan

Desain percobaanketentuan untuktaraf perlakuan penugasan ke unitpercobaan

Analisa varians (ANOVA)datastatistik terpenting memaksudkan

untuk mengevaluasi sumberpotensial dari variasi pada tanggapan

Replikatanggapan individupengamatan dari unit percobaanperkalian pada kondisi percobaanserupa

Mengulangi Pengukurantanggapanperkalian pengamatan dari unitpercobaan tunggal pada kondisipercobaan serupa


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11. Blockingpartition theexperimental units into groups (orblocks) that are homogeneous insome sense

12. Covariateadditional responsescollected from the experimentalunits, usually to be used aspredictors (and so are sometimescalled predictive responses)theseare not part of a designedexperiment (why?)

13. Randomizationnonsystematicassignment of experimental unitsto treatments

14. Blindinghiding whichexperimental units have beenassigned to treatments from theanalyst

15. Confoundingdesign situation inwhich the effect of one factor ortreatment can not be distinguishedfrom another factor or treatment -this is the experimental equivalentof perfect multicolinearity (why?)

Menghalangisekat unit percobaan ke

dalam group (atau halangi) yang

homogen di beberapa rasa

Covariate tanggapanadditional

terkumpul dari unit percobaan,biasanya dipergunakan seperti peramal

(dan demikian sering menjadi

tanggapan bersifat prediksi yang

dipanggil)ini bukan bagian dari satu

percobaan didisain (kenapa?)

Pengacakantugas nonsystematic

dengan unit percobaan ke perlakuan

Membutakansembunyi yang mana

unit percobaan telah ditugaskan ke

perlakuan dari ahli analisa

Mengacaukankeadaan desaindarimana akibat dari faktor sesuatu

atau perlakuan tidak dapat dicirikan

faktor lain atau perlakuan ini adalah

padanan percobaan dengan

multicolinearity sempurna (kenapa?)


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Experimentation

Manipulation of the

values (or levels) of one

or more (independent)

variables or treatmentsand observation of the

corresponding change

in the values of one or

more (dependent)variables or responses

Manipulasi dari nilai

(atau tingkat) dari satu

atau lebih (bebas tak

terikat) variabel atauperlakuan dan observasi

dari perubahan sesuai

pada nilai dari satu atau

lebih (bergantung)variabel atau tanggapan


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Basic Principles

1. Replicationobservingindividual responses ofmultiple experimentalunits under identicalexperimental conditions

2. Randomizationnonsystematic assignment ofexperimental units totreatments

3. Blockingpartition the

experimental units intogroups (or blocks) that arehomogeneous in somesense

Replikatanggapanindividu pengamatan dariunit percobaan perkalianpada kondisi percobaanserupa

Pengacakanbukan tugassistematis dengan unitpercobaan ke perlakuan

Menghalangisekat unitpercobaan ke dalam group

(atau blok ) yang homogendi beberapa rasa


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Chap 3. Exp with a Single Factor:ANOVA

1. Simple design: Experimen dengan satu

faktor misalnya siswa di kelas A dg

kurikulum KTSP vs kelas B dg MBS dalam

UAN.

2. Faktor dapat dilakukan lebih dari dua level.

3. Analisis dilakukan dg Anova sederhana.


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Cotton weight

Percentage

Observasi (replikasi) T Rerata

1 2 3 4 5

15 7 7 15 11 9 49 9.820 12 17 12 18 18 77 15.4

25 14 18 18 19 19 88 17.6

30 19 25 22 19 23 108 21.635 7 10 11 15 11 54 10.8

Sumber: Table 2.1 hal 62

Strength


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/nGn

TSSTr/nGxSST

SST1-lnT

MSESSE2-nE

MSTr/MSEMSTrSSTr1Tr

FMSSSdfSV

2

j

J22

ANOVA


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Mixing Technique Tensile Strenght (lb/n2)

12

3

4

31293200

2800

2600

30003300

2900

2700

28652975

2985

2600

28903150

3050

2765

3-1. The tensile strength of Portland cement is being studied. Four different mxing

techniques can be used economically. The following data have been collected:

Test the hypothesis that mixing techniques affect the strength of the comnet. Use

= 0,05.

Temperature Density

100

125

150

175

21.8

21.7

21.9

21.9

21.9

21.4

21.8

21.7

21.7

21.5

21.8

21.8

21.6

21.4

21.6

21.4

21.7

21.5

3-4. And in experiment was run to determine whether four specific firing temperaturesaffect the density of a certain type of brick. The experiment led to the following data:

Does the firing temperature affect the density of the brick? Use = 0,05.


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Coating Type Conductivity

12

3

4

143152

134

129

141149

136

127

150137

132

132

146143

127

129

3-6. A manufacturer of television sets is interested in the effect on tube conductivity

data are obtained:

Is there a difference in conductivity due to coating type? Use = 0,05.

Estimate

Rodding Level Compressive Strenght

10

15

20

25

1530

1610

1560

1500

1530

1650

1730

1490

1440

1500

1530

1510

3-8. An article in theACI Material Journal(Vol. 84, 1947, pp. 213-216) describe

several experiments investigating the rodding of concrete to remove entrapped air. A 3-

inch X 6-inch cylinder was used, and the number of times this rod was used is the

design variable. The resulting compressive strength of the concrete specimen is the

reponse. The data are shown in the following table:

Is there any difference in compressive strength due the rodding level? Use = 0,05.


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Bab 4 Randomized Block, Latin Sq,and Related Designs1. RCBD (Randomized Complete Block Design)

2. Latin Square Design3. Graeco Latin Square Design

4. BIBD (Balanced Incomplete Block Design)


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1. RCBD (Randomized Complete Block

Design)


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2. The Latin Square Design


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Chemical

Bolt

1 2 3 4 5

1

2

3

4

73

73

75

73

68

67

68

71

74

75

78

75

71

72

73

75

67

70

68

69

4-1. A chemist wishes to test the effect of four chemical

agents on the strength of a particular type of cloth.

Because there might be variability from one bolt toanother, the chemist decides to use a randomized block

design, with the bolts of cloth considered as blocks. She

selects five bolt and applies all four chemicals ain

random order to each bolt. The resulting tensile strength

follow. Analyze the data from this experiment (use =0.05) and draw appropriate conclusions.


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Solution

Days

1 2 3 41

2

3

13

16

5

22

24

4

18

17

1

39

44

22

4-2. Three different washing solutions are being compared

to study their effectiveness in retarding bacteria growth in 5-

gallon milk containers. The analysis is done in a laboratory,and only three trials can be run on any day. Because days

could represent a potential source of variability, the

experimenter decides to use a randomized block design.

Observations are taken for four days, and the data areshown here. Analyze the data from this experiments (use

= 0.05) and draw conclusions.


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Nozzle

Design

Jet Efflux Velocity (m/s)

11.73 14.73 16.59 20.43 23.46 28.74

1

2

3

4

5

0.78

0.85

0.93

1.14

0.97

0.80

0.85

0.92

0.97

0.86

0.81

0.92

0.95

0.98

0.78

0.75

0.86

0.89

0.88

0.76

0.77

0.81

0.89

0.86

0.76

0.78

0.83

0.83

0.83

0.75

4-5. An article in the Fire Safety Journal (TheEffect

of Nozzle Design on the Stability and Performance of

Turbulent Water Jets, Vol. 4. August 1981) describes an

experiment in which a shape factor was determined forseveral different nozzle design at six levels of jet efflux

velocity. Interest focused on potential differences

between nozzle design, with velocity considered as a

nuisance variable. the data are shown below:


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Stirring

Rate (rpm)

Furnace

1 2 3 4

5

10

1520

8

14

1417

4

5

69

5

6

93

4

9

26

4-7. Any alumunium master alloy manufacturer produces grain refiners in

ingot form. The comperating produces the product in four furnaces is known to

have its own unique operating characteristics, soa any experiment run in the

foundry thay involves more than one furnace will consider furnaces as anuisance variable. The process engineers suspect that stiring rate affects the

grain size of the product. Each furnace can be run at four different atirring

rates. A randomized block design is run for a particular refiner, and the

resulting grain size data is show below:

1. Graph the residuals from thisexperiment on a normal probability

plot. Interpret this plot.

2. Is there any evidence that stirring

rate affects grain seze?

3. Plot the residuals versus furnace

and stirring rate. Does this plot

convey any useful information?4. What should the process engineers

recommend concerning the choice

of stirring rate and furnace for this

particular grain refiner if small grain

significant test.


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Distanc

e (ft)

Subject

1 2 3 4 5

46

8

19

107

5

6

66

3

4

66

3

4

61

2

2

66

5

3

4-13. An industrial engineer is conducting an experiment

on eye focus time. he is interested in the effect of the

distance of the object from the eye on the focus time.

Four different distances are of interest. He has fivesubjects available for the experiment. Because there may

be differences among individuals, he decides to conduct

the experiment in arandomized block design. The data

obtained follow. Analyze the data from this experiment(use = 0.05) and draw appropriate conclusions


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ANOVA Latin Sq Design

Source DF Seq SS Adj SS Adj MS F P

RM 4 68 68 17.000 1.590 0.239

Operator 4 150 150 37.500 3.520 0.040

Latin 4 330 330 82.500 7.730 0.003

Error 12 128 128 10.670

Total 24 676


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Batch

Day

1 2 3 4 5

12

3

4

5

A= 8

C = 11

B = 4

D= 6

E= 4

B= 7

E = 2

A = 9

C= 8

D= 2

D= 1

A = 7

C = 10

E= 6

B= 3

C= 7

D = 3

E = 1

B= 6

A= 8

E= 3

B = 8

D = 5

A= 10

C= 4

4-14. The effect of five different ingredients (A, B, C, D, E)

on the reaction time of a chemical process is being studied.

Each batch of new material is only large enough to permit

five runs to be made. Furthermore, each run requiresapproximately 1 hours, so only five runs can be made in

one day. The experimenter decided to run the experiment

as a Latin square so that day and batch effects may be

systematically controlled. She obtains the data that follow.

Analyze the data from this experiment (use = 0.05) and

draw conclusions.


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Order of

Assembly

Operator

1 2 3 4

1

2

3

4

C= 10

B = 7

A = 5

D= 10

D= 14

C = 18

B = 10

A= 10

A= 7

D = 11

C = 11

B= 12

B= 8

A = 8

D = 9

C= 14

4-15. An industrial engineer is investigating the effect of

four assembly methods (A, B, C, D,) on the assembly

time for a color television component. Four operators are

selected for the study. Furthermore, the engineer knows

that each assembly method produces such fatigue that

the time required for the last assembly may be greater

than the time required for the first, regardless of the

method. That is, a trend develops in the requiredassembly time. To account for this source of variability,

the engineer uses the Latin square design shown below.

Analyze the data from this experiment (use = 0.05) and

drw appropriate conclusions.


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Graeco Latin Square Design

Montgomery tabel 4.9 and Tabel 4.20

Operator

RM 1 2 3 4 5 T1 24 20 19 24 24 111

2 17 24 30 27 36 134

3 18 38 26 27 21 130

Operator 4 26 31 26 23 22 128

RM 1 2 3 4 5 5 22 30 20 29 31 132

1 A=24 B=20 C=19 D=24 E=24 T 107 143 121 130 134 6352 B=17 A=24 D=30 E=27 A=36

3 C=18 B=38 A=26 A=27 B=21

4 D=26 C=31 B=26B=23 C=22 Graeco

5 E=22 D=30C=20 C=29 D=31 Latin 1 2 3 4 5 T

1 24 30 26 27 36 143

2 21 17 20 20 23 1013 29 22 18 24 19 112

4 30 24 18 26 38 149

5 31 26 18 24 22 130

T 135 119 18 121 138 635

3. The Graeco-Latin Sq Design


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ANOVA Graeco-Latin Sq Design

Source DF Seq SS Adj SS Adj MS F P

RM 4 68 68 17.00 2.06 0.178

Operator 4 150 150 37.50 4.55 0.033

Latin 4 330 330 82.50 10.00 0.003

Greek 4 62 62 15.50 1.88 0.208

Error 8 66 66 8.25

Total 24 676


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Batches

Acid concentrations

1 2 3 4 5

1

2

34

5

A= 26

B= 18

C= 20D= 15

E = 10

B= 18

C = 21

D= 12E = 15

A= 24

C = 14

D= 18

E =16A= 22

B= 17

D= 16

E = 11

A= 25B= 14

C= 17

E = 13

A = 21

B= 13C= 17

D= 14

4-22. The yield of a chemical process was measured

using five batches of raw material, five acid

concentrations, ive satnding times (A, D, C, D, E), andfive catalyst concentrations (,,,,). The Graceo-

Latin square that follow was used. Analyze the data from

this experiment (use = 0.05) and draw conclusions


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Order of

Assembly

Operator

1 2 3 4

1

2

3

4

C= 11

B = 8

A = 9

D = 9

B = 10

C =12

D = 11

A =8

D= 14

A= 10

B= 7

C= 18

A= 8

D= 12

C= 15

B= 6

4-23. Suppose that in Problem 4-15 the engineer

suspects that the workplaces used by the faour

operators may represent an additional source ofvariation. A fourth factor, workplace (,,,,)may

be introduced and another experiment conducted,

yielding the Graceo-Latin square that follows,

Analyze the data from this experiment (use =

0.05) and draw conclusiona.


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4. The BIBD

Table 4.22 Montgomery

CataliystRaw Material

Ti1 2 3 4

1 73 74 71 2182 75 67 72 214

3 73 75 68 216

4 75 72 75 222

Tj 221 224 207 218 870


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Perhitungan Anova BIBDsama dengan

BCBD


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ANOVA BIBD


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Additive Car

1 2 3 4 5

1

23

4

5

1412

13

11

17

1411

12

14

1311

10

13

1312

12

12

109

8

4-27. An engineer is studying the mileage of

performance characteristics of five types of gasoline

additives. In the road test he wishes to use cars asblocks; however, because of a time constraint, he

must use an incomplete block design. He runs the

balanced design with the five blocks that follow.

Analyze the data from this experiments (use = 0.05)and draw conclusions.


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4-29. Seven different hardwood concentrations are

being studied to determine their effect on the strength

of the paper produced. However, the pilot plant can

only produce three runs each day. As days may differ,

the analyst uses the balanced incomplete block

design that follows. Analyze the data from this

experiment (use = 0.05) and draw conclusions.

Hardwood

Concentration

(%)

Days

1 2 3 4 5 6 7

2 114 120 117

4 126 120 1196 137 117 134

8 141 129 149

10 145 150 143

12 120 118 123

14 136 130 127


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Bab 5 Factorial Design

5.1 Basic Definition

5.2 The Advantages

5.3 The Two Factor Factorial Design

5.4 The General Factorial Design

5.5 Fitting Response Curve and Surfaces


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5.1 Basic Definition and Principles

a. Main Effect: the change in response

produced by the change in the level of the

factor.

b. Interaction: diffrenece in response between

the levels of one factor is not the same at all

levels of the other factors.

c. The three dimensional graph is called aresponse surface plot.


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A B X Y

-1 -1 20 20

1 -1 40 50

-1 1 30 401 1 52 12

Ada interaksi pada

eksperiment A.Tetapi ada interaksi

pada eksperimen B


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5.2 The Advantages

1. efficient,

2. check the interaction,

3. the effects of a factor to be estimatedat several levels of the other factors.


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5.3 The Two Factor Factorial Design

An example

Statistical Analysis of the fixed Effects Model

Model Adequasy Checking

Estimating the Model Parameters

Choice of Sample Size

The Assumption of No Interaction in a two

factor model One Observation per cell


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Table 5-1 Life (in hours) Data for Battery Design Example

Material Temperature

Type 15 70 125

1 130 155 34 40 20 70

74 180 80 75 82 58

2 150 188 136 122 25 70

159 126 106 115 58 45

3 138 110 174 120 96 104168 160 150 139 82 60


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No MT Temp x No MT Temp x No MT Temp x

1 1 1 130 13 2 1 150 25 3 1 138

2 1 1 155 14 2 1 188 26 3 1 110

3 1 2 34 15 2 2 136 27 3 2 174

4 1 2 40 16 2 2 122 28 3 2 120

5 1 3 20 17 2 3 25 29 3 3 96

6 1 3 70 18 2 3 70 30 3 3 104

7 1 1 74 19 2 1 159 31 3 1 168

8 1 1 180 20 2 1 126 32 3 1 160

9 1 2 80 21 2 2 106 33 3 2 150

10 1 2 75 22 2 2 115 34 3 2 139

11 1 3 82 23 2 3 58 35 3 3 82

12 1 3 58 24 2 3 45 36 3 3 60

Desain Data untuk MINITAB


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Two-way ANOVA: x versus MT, Temp

Source DF SS MS F P

MT 2 10684.0 5341.9 7.91 0.002

Temp 2 39119.0 19559.0 28.97 -

Interaction 4 9613.8 2403.4 3.56 0.019

Error 27 18231.0 675.2

Total 35 77647.0

S = 25.98 R-Sq = 76.52% R-Sq(adj) = 69.56%

Analisis of Variance


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5.3.7 One Observation per Cell

Temp FPressure

25 30 35 40 45

100 5 4 6 3 5125 3 1 4 2 3

150 1 1 3 1 2

Table 5.10 Impuriry


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Hasil Analisis of Variance

Two-way ANOVA: Impurity versus Temp, Press

Source DF SS MS F P

Temp 2 23.33 11.67 46.67 0.00

Press 4 11.60 2.90 11.60 0.00Error 8 2.00 0.25

Total 14 36.93

S = 0.5 R-Sq = 94.58% R-Sq(adj) = 90.52%


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5.4 The General Factorial Design

1. Kelanjutan dari two factor factorial design.

Faktor A dengan a levels, faktor B dengan b

levels, faktor C dengan c levels, dst.

2. Misal nya faktor ABC dengan levels a=3, b=2,

dan c=2 tentang response x=fill height

deviation.


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Table 5.13 Fill Height Deviation

Pressure (B) 25 psi 30 psi

Line Spee (C ) 200 250 200 250

Carbonation (A)

10-3 -1 -1 1

-1 0 0 1

120 2 2 6

1 1 3 5

145 7 7 10

4 6 9 11


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Data dalam format MINITAB atau SPSS

No A B C X No A B C X

1 10 25 200 -3 13 12 25 200 1

2 10 25 250 -1 14 12 25 250 1

3 10 30 200 -1 15 12 30 200 3

4 10 30 250 1 16 12 30 250 5

5 10 25 200 -1 17 14 25 200 5

6 10 25 250 0 18 14 25 250 7

7 10 30 200 0 19 14 30 200 7

8 10 30 250 1 20 14 30 250 10

9 12 25 200 0 21 14 25 200 4

10 12 25 250 2 22 14 25 250 611 12 30 200 2 23 14 30 200 9

12 12 30 250 6 24 14 30 250 11


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Analysis of Variance

5 5 Fitting Response Curve and


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5.5 Fitting Response Curve andSurfaces

i. Fitting response curve

ii. Fitting response surface

iii. Usinf regression

iv. To predict


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Table 5.16 Tool Life

Angle

cutting speed

in/min

degree 125 150 175

15

-2 -3 2

-1 0 3

20

0 1 4

2 3 6

25-1 5 00 6 -1

No A B X No A B X

1 15 125 -2 10 20 125 2

2 15 150 -3 11 20 150 3

3 15 175 2 12 20 175 6

4 15 125 -1 13 25 125 -1

5 15 150 0 14 25 150 5

6 15 175 3 15 25 175 0

7 20 125 0 16 25 125 08 20 150 1 17 25 150 6

9 20 175 4 18 25 175 -1


58/66

5.6 Blocking in a Factorial Design

Untuk lebih efisien dan mengoptimalkan

pelaksanaan eksperimen terkadang diperlukan

blocking, hal ini untuk menghindari noise yang

menggangu proses eksperimen.

Blocking didasarkan atas keseragaman dari

response yang akan muncul.


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Table 5-19 Intensity Level at Target Detection

operator block 1 2 3 4

filter type 1 2 1 2 1 2 1 2

Ground cutter low 90 86 96 84 100 92 92 81

medium 102 87 106 90 105 97 6 80

hught 114 93 112 91 108 95 98 83

T b l 5 21 R d D t ti E i t


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Day

Operator

1 2 3 4 5 6

1 A B C D F E

90 106 108 81 90 88

2 C A B F E D

114 96 105 83 86 84

3 B E F A D C102 90 95 92 85 104

4 E D A B C F

87 84 100 96 110 91

5 F C D E A B93 112 92 80 90 98

6 D F E C B A

86 91 97 98 100 92

Tabel 5.21 Radar Detection Experiment


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5-4. An article in Industrial Quality Control(1956, pp. 5-

8) describes an experiment to investigate the effect of

the type of glass and the type of phosphor on the

brightness of an television tube. The response variableis the current necessary (in microamps) to obtain a

specified brightness level. The data are as follow:

i.Is there any indication that either factor influences

brightness? Use = 0.05.ii.Do the two factors iteract? Use = 0.05.

iii.Analyze the residuals from this experiment


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5-1 The yield of chemical process is being studied. The

two most important variables are thought to be the

pressure and the temperature. Three levels of each factor

are selected, and a factorial experiment with two

replicates is performed. The yield data follow:

i.Analyze the data and draw conclusions. Use = 0.05.

ii.Prepare appropriate residual plots and comment on the

models adequancy.iii.Under what conditions would you operate this process?

5 17 Th lit t l d t t f f b i fi i hi


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5-17. The quality control department of a fabric finishing

plant is studying the effect of several factors on the dyeing

of cotton-sunthetic cloth used to manufacture mens shirt.

Three operators, three cycle times, and two temperatureswere selected, and three small specimens of cloth were

dyed under each set of conditions. The finished cloth was

compared and drw cpnclusions. Comment on the models

adequacy.

UTS


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UTS

MK: Design and Analysis of Experiment

1.Dalam rancangan percobaan di kenal konsep:Simple design, RCBD, Latin Square, dan BIBD.Deskripsikan apa yang di maksud dengan

empat desain/ rancangan tersebut.2. Contoh: Anda diminta mengerjakan secara

manual analisis rancangan percobaansederhana (simple anova) dengandata pada

soal: 3.6 (Petunjuk lihat mk statistik atau dgexel maupun spss).


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3. Saudara diminta

membuat

rancanganpengolahan SPSS

dari tampilan

rancangan dalam

soal Montgomery

no: 3.17 3.30

4.2 4.5 5.7 4.15

4.22 4.27 4.29Hint: lihat contoh

disamping.

Does Up Arman

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