1. EEM332 Lecture Slides1 EEM332 Design of Experiments En. Mohd Nazri Mahmud MPhil (Cambridge, UK) BEng (Essex, UK) nazriee@eng.usm.my Room 2.14 Ext. 6059

2. EEM332 Lecture Slides2 Agenda ANOVA with Excel and Minitab exercises

3. EEM332 Lecture Slides3 Example 3-1page62 Graphical examination of the data using scatter plots In Excel choose XY scatter plot In Minitab, choose >Graph>Plot>Specify X and Y variable The scatter diagram indicates increasing etch rate with power

4. EEM332 Lecture Slides4 Example 3-1page62 Graphical examination of the data using boxplots In Minitab, choose >Graph>Boxplots The boxplot indicates increasing etch rate with power

5. EEM332 Lecture Slides5 Example 3-1page62 Graphical 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 equations

6. EEM332 Lecture Slides6 Example 3-1page62 Graphical examination of the data using Regression Model useful to see the Response and intermediate factors Quadratic Model – choose Polynomial order 2

7. EEM332 Lecture Slides7 Example 3-1page62 Graphical 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 is Etch Rate = 138 + 2.53 RF Power Predictor Coef SE Coef T P Constant 137.62 41.21 3.34 0.004 RF Power 2.5270 0.2154 11.73 0.000 S = 21.54 R-Sq = 88.4% R-Sq(adj) = 87.8%

8. EEM332 Lecture Slides8 Example 3-1page62 ANOVA In Minitab, choose >Stat>ANOVA>One-way Can 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 P RF Power 3 66871 22290 66.80 0.000 Error 16 5339 334 Total 19 72210 > Between treatment mean square >> within-treatment(error) mean square  F-value 66.8 > F 0.05,3,16 (3.24)  P-value is very small

9. EEM332 Lecture Slides9 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 13129300028652890 23200330029753150 32800290029853050 42600270026002765 Perform ANOVA using Minitab to test the hypotheses that mixing techniques affect the tensile strength

10. EEM332 Lecture Slides10 Analysis of variance - Exercise Q 2 A manufacturer of television sets is interested in the effect of tube conductivity of four different types of coating for color picture tubes. The following conductivity data are obtained. Coating Type Conductivity 1143141150146 2152149137143 3134136132127 4129127132129 Perform ANOVA using Minitab to test the hypotheses that coating types affect the conductivity.

11. EEM332 Lecture Slides11 Analysis of variance - Exercises Q 3 Four different designs for a digital circuits are being studied in order to compare the amount of noise present. The following data have been obtained. Circuit designs Noise observed 1192019308 28061735680 34726253550 49546837897 Perform ANOVA using Minitab to test the hypotheses whether the noise are the same for all the four designs or not.