ERT427 Design of Experiment Sem I 2014/2015

1. ERT427 Design of ExperimentSem I 2014/2015 By: Pn. Siti Jamilah Hanim Mohd Yusof

2. Chapter 1: Introduction Strategy of experimentation, typical applications of experimental designs, basic principles guidelines for designing experiment.

3. Strategy of experimentation • Experiment – to discover! • Definition: a test or series of tests in which purposeful changes are made to the input variables of a process or system to observe and identify the reasons for changes observed in the output response. • Engineering -important in new product design, manufacturing process development and process improvement. • Objective- to develop robust process, a process affected minimally by external sources of variability

4. EXAMPLE • A metallurgical engineer interested in studying the effect of two different hardening processes, oil quenching and saltwater quenching on aluminum alloy. • Objective: to determine which quenching solution produces the max hardness on alloy. • As we consider this experiment, a number of important questions come to mind. Such as??

5. In any experiment, methods of data collection has adversely affected the conclusion that can be drawn from the experiment. • E.g: comparison of solution must be done at constant heat.

6. Process – combination of machines, methods, people and other sources that transforms some input (often a material) into an output that has one or more observable response

7. Example Possible Objectives: Determining, • Which variables are most influential on output y • Where to set the influential x’s so that y is almost always near to desired value • Where to set the influential x’s so that variability in y is small • Where to set the x’s so that effects of uncontrollable variables, z’s are minimum

8. Strategy of experimentation: • The general approach to planning and conducting experiment; • BEST GUESS APPROACH - frequently used - often works well since the experimenters have a great deal of technical or theoretical knowlegde of the system and practical experience - However, 2 disadvantages • Required long time if initial guess is incorrect or inaccurate • No guarantee that the best solution has been found

9. 2) ONE-FACTOR-AT -A-TIME - extensively used - consist of selecting a starting point or baseline set of levels, for each factor, then successively varying each factor over its range with the other factors held constant at baseline level. Example: Some of the factors that might affect golf score are: • Type of driver used (oversized or regular sized) • Type of ball used (balata or 3 piece) • Mode of travel (walking or riding) • Type of beverage while playing (water or beer)

10. - series of graph are constructed - interpretation of graphs above? ? - Major disadvantage: fails to consider any interaction between factors, so it is less efficient if interaction existed. *What is interaction? the failure of one factor to produce the same effect on the response at different levels of another factor (Fig. 1-3) -

11. 3) FACTORIAL - correct approach to deal with several factors. - factors are varied together, instead of one at a time. - enable the experimenter to investigate the individual effects of each factor (or main effects) and identify any interaction. EXAMPLE Consider, a golf experiment with 2 factors of interest; a) type of driver b) type of ball

12. From Fig. 1-4, • both factors at two levels • All possible combinations are used • Geometrically, the 4 runs form the corner of the square. • 22 factorial design (2 factors, 2 levels ) Why 4 runs? If duplicates, how many runs?

13. From the experimental data shown in Fig. 1-5 below (run twice), we can calculate the effects. 1) Driver effect

14. 2) Ball effect 3) Ball- driver interaction effect From calculation, driver effect is larger than other effect and differ from zero. So??

15. Factorial design makes the most efficient use of experimental data. • Extention of factorial design: 23, 24….2k, with k=2,3,4…. • For 23 factorial design: • 8 combinations (represented by each corner of cube)

16. For 24 factorial design: • 16 combinations (runs) • So, more factors, more experiments. At some point it’ll become infeasible or impossible (if 10 factors?) • How to overcome? Fractional factorial experiment, a variation of the basic factorial design in which only a subset of runs are made. • One half fraction (8 from 16 runs)

17. Typical applications of experimental designs • Important tool in engineering world to improve performance of manufacturing process • Extensive application for development of new processes.

18. Experimental design also play a major role in engineering design activities where new product are developed and existing ones improved.

19. Basic principles • Statistical design of experiment- process of planning the experiment so that appropriate data that can be analyzed by statistical methods will be collected, resulting in valid and objective conclusions. • 2 aspects to any experimental problem: • Design of experiment • Statistical analysis of the data. • Three basic principles of experimental design are: Closely related!

21. Example: Randomization of runs from Design Expert software

22. Guidelines for designing experiment

23. 1) Recognition of and statement of problem • Important to solicit input from all concerned parties e.g engineering, manufacturing, marketing, management, customer etc. Team approach • Prepare a list of specific problems or questions to be addressed by experiment • Important to keep overall objective in mind. For example, is this a new process? Objective: Characterization or factor screening a mature or characterized process ? Objective: Optimization • Sequential approach using a series of smaller experiments is a better strategy.

24. 2) Choice of factors, level, and ranges • Potential design factors • factors that the experimenter wish to vary • Classification: • Design factors, - selected parameters for study • held constant factors - parameters held at specific level • allowed to vary factors - e.g experimental units or nonhomogenous material - rely on randomization to balance out effect

25. Nuisance factors • undesired factors, yet have large effects • Classification: 1)Controllable -level can be set by experimenter -use blocking technique 2) Uncontrollable - Uncontrolled parameter but can be measured - Analysis of covariance is used to compensate effect 3) Noise factors -parameter varies naturally, uncontrol - Find the setting of controllable design factors that minimize the variability transmitted from noise factors (sometimes called a process robustness study).

26. After design factors are selected, the range and specific level at which runs will be made are chosen. • Process knowledge, the combination of practical experience and theoretical understanding is required to do this. • For factor screening or process characterization, it is best to keep the number of factor levels low (two levels works very well) and region of interest (range) should be large.

27. 3) Selection of the response variable • Response variable – should provides useful info about process under study. • Usually, average or standard deviation (or both) of measured characteristics are used. • Gauge capability (or measurement error) is very important – average measurement value is considered in poor condition. • Should define the response variable and measurement methods before conducting the experiment.

28. 4) Choice of experimental design • Involves: • Consideration of sample size ( number of replicates) • Selection of the suitable run order for experimental trials. • Determination whether blocking or other randomization restrictions are involved • Several statistical software provide this phase of experimental design, using provided info on factors, level and ranges.

29. 5) Performing the experiment • Vital to monitor the process carefully • Coleman and Montgomery (1993) suggested running trial runs before conducting experiment – obtain info on consistency of experimental material, a check on measurement system, rough idea of error, a chance to practice experiment and revise step 1-4.

30. 6) Statistical analysis of the data • Provide objective results and conclusions of experiment • Many software packages (in step 4) also provide direct interface to statistical analysis. • involves simple graphical methods, hypothesis testing and confidence interval estimation, residual analysis and model adequacy checking. • Results may be presented in terms of empirical model, an equation derived from the data that express the relationship between response and important design factors.

31. 7) Conclusion and recommendations • From data analysis, practical conclusions can be drawn, followed by recommendation of action. • Graphical methods in presenting the results. • Follow up runs and confirmation testing –to validate the conclusion.

32. Always remember that experimentation is iterative. • A successful experiment requires knowledge of important factors, the range and level to use and proper units of measurement.

33. Thank you…