2. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-082 (136) Experimental Strategies  Trial & Error –Introduce one or more changes at a time and to evaluate the effect on the system  One factor at a time –Manipulate one factor at a time looking for the best value of each factor  Factorial experiments, DOE –Change all the factors in the same time looking for their effects – including also their interactions – on the response

3. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-083 (136) Experiments, Trial & error Based on: - Feeling - Knowledge - Experience Variable X1 Variable X2 X: points to be tested X X X X X X X Results:  accidential  missing structure  missing plan  do not improve our understanding of the process 100 90 70

4. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-084 (136) Experiments, one factor at a time Method Variable X1 Variable X2 XXXXOXXXXX X: Vary X1 first, X2 constant O: determine the best output X: Vary X2, keep X1 constant : The optimum output for Y X X X X X X X 100 90 70

5. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-085 (136) Experiments, one factor at a time Pros and cons  ADVANTAGES –Very simple to understand and to apply  DISADVANTAGES –It uses lines to explore a space (bi-dimensional, in the previous example) –You loose any opportunity to discover interactions between factors –It is less efficient compared to factorial experiment: we have to do more trials

6. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-086 (136) Experiments, the 6  Approach Factorial Experiments Variable X1 Y = f ( X1, X2,…Xn ) X XX X Method: Repeated measurements at the corner points Determine  and  Adding centerpoints to determine linear or non linear relationship Empirical modell Y = a + bX 1 + cX 2 + dX 1 X 2 +  Determine the optimum value for Y Optimum of Y Variable X2 100 90 70 Is max always the best?

7. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-087 (136) Factorial Experiments Pros and cons  ADVANTAGES –It is the more efficient (less trials) way to evaluate effects –It is possible to evaluate interactions between factors –It gives you less risk in taking decisions  DISADVANTAGE: –“Work” with statistics...

8. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-088 (136) Performing an experiment 1.Define the goals – what are the questions to be answered?  If the goal is to test whether certain input settings have a certain effect: Formulate a hypothesis to test  If the goal is to find optimal input settings: Formulate the goal function(s) for the outputs 2.Plan the experiment 3.Perform and observe 4.Analyze results 5.Draw conclusions – hypothesis accepted/rejected? In focus here

9. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-089 (136) Design of Experiments Product or Process Y’s Response They are the output of our experiments Noise Factors They are all the incontrollable variables of those variables that are difficult (too expensive) to control, but that can affect the response variation X’s Controllable factors They are the variables manipulated during the experiment to evaluate their effects on the response

10. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0810 (136) Define the goals  Verify if a relationship cause-effect does exist –Relationship cause-effect between all potential causes of variation (Xs) and the system response (Y).  Find the vital few causes of variation (X’s) –Those that have a major effect on the response. (vital few vs. trivial many –parameter design)  Define the target value for each parameter (X’s) –Define the target value for each parameter in order to optimise the response: Maximized, minimized or centred on target value DOE terminology Y=f(x) Product or Process X’s Y X’s = factors Y = response Y=f(x) equation between input (X’s) and output (Y): empirical model

11. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0811 (136) Aspects of experiment planning  System knowledge  Relevant input variables  Measurement of output variables  Continuous vs attribute data  Sample size  Statistical significance and power  Cost – budget  Allocation and reservation of resources – personnel and equipment

12. DOE example Lawn

13. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0813 (136) DOE example Lawn  Find out how sun and rain contributes to the growth of a lawn Sun Water W*S Y 1 +1 2 3 +1 4+1 Water:+1 = 1.1l/m 2 *week -1 = 0.1 l/m 2 *week Sun:+1 = 50 h/week -1 = 0 h/week

14. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0814 (136) DOE example Lawn Results Sun Water W*S Y (cm) 1 +11.5 2+1 4.5 3+14.5 4+1 13.5 4.513.5 1.5 4.5 The effect of a factor on a response variable is the change in the response when the factor goes from its low level to its high level. E(S)=(4.5+13.5)/2-(1.5+4.5)/2=9-3=6 E(W)=(4.5+13.5)/2-(1.5+4.5)/2=9-3=6 E(S*W)=(1.5+13.5)/2-(4.5+4.5)/2=3 Effect663 Sun Water - + + -

15. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0815 (136) DOE example Lawn Graphical display Sun Water W*S Y (cm) 1 +11.5 2+1 4.5 3+14.5 4+1 13.5 4.513.5 1.5 4.5 Effect663 Sun Water - + + - Sun -+ E(S)=(4.5+13.5)/2-(1.5+4.5)/2=9-3=6 E(W)=(4.5+13.5)/2-(1.5+4.5)/2=9-3=6 Water -+ 3 9 E(S)=6 3 9 E(W)=6

16. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0816 (136) DOE example Lawn Graphical display Sun Water W*S Y (cm) 1 +11.5 2+1 4.5 3+14.5 4+1 13.5 4.513.5 1.5 4.5 Effect663 Sun Water - + + - Sun - + E(S*W)=(1.5+13.5)/2-(4.5+4.5)/2=7.5-4.5=3 W - 1.5 13.5 E(W*S)=3 W + 4.5

17. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0817 (136) DOE example Lawn Graphical display S - + W - W + S - + W - W + S - + W - W + S - + W - W + S - + W - W + S - + W - W + NONE WEAK STRONG WEAK

18. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0818 (136) DOE example Lawn Empirical Model Sun Water W*S Y (cm) 1 +11.5 2+1 4.5 3+14.5 4+1 13.5 4.513.5 1.5 4.5 Sun Water - + + - From the experiment you can get the empirical model showing the relationship between factors and output. Calculate your coefficients. Effect663 Coefficient331.5

19. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0819 (136) DOE example Lawn Empirical Model Sun Water W*S Y (cm) 1 +11.5 2+1 4.5 3+14.5 4+1 13.5 4.513.5 1.5 4.5 Sun Water - + + - You would like to cut your lawn once a week so you would like it to grow 6 cm/week. How much sun and water shall you have? Effect663 Coefficient331.5

20. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0820 (136) Statistical significance Just one run per variable setting gives an uncertain result  Normality test of the effects  Replicates - perform multiple runs per variable setting to obtain data for mean value and standard deviation calculations  ANOVA – ANalysis Of Variance

21. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0821 (136) Catapult Exercise Where: T = launch angle v = initial speed g = acceleration due to gravity = 32 ft/s x = horizontal distance from origin of projectile y = vertical distance from origin of projectile Basic Projectile Equation For Reference Only 2 22 )(cos2 )tan(x Tv g xTy            

22. Top right corner for field-mark, customer or partner logotypes. See Best practice for example. Slide title 40 pt Slide subtitle 24 pt Text 24 pt Bullets level 2-5 20 pt MSI-08:000252 Uen Rev PA3Ericsson Confidential08. Analyze2008-05-0822 (136) What to do with in the catapult exercise?  Practise shooting with centre points  What reduces variation?  Randomise your runs  Make your experiment  Give your results to the teachers  Calculate your empirical model at your mean values  Make graphs  Verify your model through test  Calculate your set-up against the goal you get from teachers. Where are the standard deviation lowest?  Competition!!!!