EEM332 Lecture Slides 1

EEM332Design of Experiments

En. Mohd Nazri Mahmud

MPhil (Cambridge, UK)

BEng (Essex, UK)

nazriee@eng.usm.my

Room 2.14

Ext. 6059

EEM332 Lecture Slides 2

Agenda

ANOVA with Excel and Minitab exercises

EEM332 Lecture Slides 3

Example 3-1page62Graphical examination of the data using scatter plots

In Excel choose XY scatter plotIn Minitab , choose >Graph>Plot>Specify X and Y variable

y

220210200190180170160

720

620

520

RF Power

Etc

h R

ate

The scatter diagram indicates increasing etch rate with power

EEM332 Lecture Slides 4

Example 3-1page62Graphical examination of the data using boxplots

In Minitab , choose >Graph>Boxplots

y

The boxplot indicates increasing etch rate with power

220200180160

720

620

520

RF Power

Etc

h R

ate

EEM332 Lecture Slides 5

Example 3-1page62Graphical examination of the data using Regression Model (page 86)useful to see the response at intermediate factor levels

Linear Model

In Excel >Insert>Chart>XYScatter and add trendline and show equationsChart Title

y = 2.527x + 137.62

R2 = 0.8843

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650

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750

150 160 170 180 190 200 210 220 230

Etch Rate

Linear (Etch Rate)

EEM332 Lecture Slides 6

Example 3-1page62Graphical examination of the data using Regression Model useful to see the Response and intermediate factors

Quadratic Model – choose Polynomial order 2

Chart Title

y = 0.0284x2 - 8.2555x + 1147.8

R2 = 0.92

500

550

600

650

700

750

150 170 190 210 230 250

Etch Rate

Poly. (Etch Rate)

EEM332 Lecture Slides 7

Example 3-1page62Graphical examination of the data using Regression Model

In Minitab , choose >Stat>Regression

The boxplot indicates increasing etch rate with power

Regression Analysis: Etch Rate versus RF Power

The regression equation isEtch Rate = 138 + 2.53 RF Power

Predictor Coef SE Coef T PConstant 137.62 41.21 3.34 0.004RF Power 2.5270 0.2154 11.73 0.000

S = 21.54 R-Sq = 88.4% R-Sq(adj) = 87.8%

EEM332 Lecture Slides 8

Example 3-1page62ANOVA

In Minitab , choose >Stat>ANOVA>One-wayCan also tick Boxplot and Boxplot to select

One-way ANOVA: Etch Rate versus RF Power

Analysis of Variance for Etch Rat

Source DF SS MS F PRF Power 3 66871 22290 66.80 0.000Error 16 5339 334Total 19 72210

> Between treatment mean square >> within-treatment(error) mean squareF-value 66.8 > F 0.05,3,16 (3.24)P-value is very small

EEM332 Lecture Slides 9

Analysis of variance – Exercises using Minitab

Question 1

The tensile strength of portland cement is being studied.Four different mixing techniques can be used economically.A completely randomised experiment was conducted and the following data collected.

Mixing Technique

Tensile Strength

1 3129 3000 2865 2890

2 3200 3300 2975 3150

3 2800 2900 2985 3050

4 2600 2700 2600 2765

Perform ANOVA using Minitab to test the hypotheses that mixing techniques affectthe tensile strength

EEM332 Lecture Slides 10

Analysis of variance - ExerciseQ 2

A manufacturer of television sets is interested in the effect of tube conductivityof four different types of coating for color picture tubes. The following conductivity dataare obtained.

Coating Type

Conductivity

1 143 141 150 146

2 152 149 137 143

3 134 136 132 127

4 129 127 132 129

Perform ANOVA using Minitab to test the hypotheses that coating types affectthe conductivity.

EEM332 Lecture Slides 11

Analysis of variance - ExercisesQ 3

Four different designs for a digital circuits are being studied in order to comparethe amount of noise present. The following data have been obtained.

Circuit designs

Noise observed

1 19 20 19 30 8

2 80 61 73 56 80

3 47 26 25 35 50

4 95 46 83 78 97

Perform ANOVA using Minitab to test the hypotheses whether the noise are the samefor all the four designs or not.