Design Of Experiment

1. Design Of Experiment Eng. Ibrahim Kuhail

2. Introduction • Two fundamental approaches to problem solving problems in the discovery of knowledge: • Theoretical (physical/mathematical modeling) • Experimental measurement (Most often a combination is used) DOE Lecture 1

3. Introduction(Cont.) Features of Alternative Methods • Theoretical Models • Simplifying assumptions needed • General results • Less facilities usually needed • Can start study immediately • Experimental approach • Study the “real world”-no simplifying assumptions needed • Results specific to apparatus studied • High accuracy measurements need complex instruments • Extensive lab facilities maybe needed • Time delays from building apparatus, debugging DOE Lecture 1

4. Experimental Problems • Two aspects to any experimental problem: • DOE • Statistical analysis. DOE Lecture 1

5. Design of Experiments • Design of Experiment (DoE): is a structured, organized method that is used to determine the relationship between the different factors (Xs) affecting a process and the output of that process (Y). • DOE is the process of planning the experiment so that appropriate data will be collected, resulting in valid and objective conclusions. DOE Lecture 1

6. Design of Experiments (Cont.) • This method was first developed in the 1920s and 1930, by Sir Ronald A. Fisher, the renowned mathematician and geneticist. • DOE is used for: • Characterizing Processes. • Optimizing Processes. • Product Design. DOE Lecture 1

7. Experiment • Test or series of tests where some changes are made to the input variables of a process or system. • Experimentation is very important in product design, manufacturing process, process improvements, and in developing a robust process. DOE Lecture 1

8. Robust Process • A robust process is the process that is affected minimally by external source of variability. • The sensitivity of this process is high. DOE Lecture 1

9. Objectives of Experiments • Determine which variables are most influential on the response Y. • Determine where to set the influential X’s, so that Y is almost near the nominal value. • Determine where to set the influential X’s, so that variability in Y is very small. • Determine where to set the influential X’s, so that the effect of the uncontrollable factors are minimized. DOE Lecture 1

10. Process (System) • A process or a System is the combination of machines, methods, people, and other resources that transforms some input into an output that has one or more observable responses. DOE Lecture 1

11. General model of a process (system) DOE Lecture 1

12. Black Box • Within the black box; the following techniques may take place: • Personal opinion. • Scientific theory. • Trial and Error. • Experimentation. DOE Lecture 1

13. Uncontrollable Factors • Uncontrollable Factors are factors that you can’t control them. You must minimize their effect on the response of the process. • Types of uncontrollable factors: • Input Factors. • Potential Input. • Key Input. DOE Lecture 1

14. Strategies of Experimentation • Best-Guess Approach. In this approach, the level of one factor is switched for the next test based on the current outcome of the current test. Disadvantages: • Time consuming without any guarantee of success. • No guarantee on finding best solution. DOE Lecture 1

15. Strategies of Experimentation (Cont.) • One Factor At A Time Approach: In this approach; a starting point for each factor is selected, then successively varying each factor over its range with the other factors held constant at the baseline. Disadvantages: • Time consuming. • It doesn’t take into account any possible interaction between the factors. DOE Lecture 1

16. Interaction: Is the failure of the factor to produce the same effect on the response at different levels of other factor. DOE Lecture 1

17. Strategies of Experimentation (Cont.) • Factorial Design: • Used when dealing with several factors. • Factors are varied together instead of one at a time. • Based on Fisher’s factorial concept DOE Lecture 1

18. Types of factorial experiments • 22 factorial design: • 4 tests each is a corner of a square. • It may be done by replicating the design twice. • It enables the experimenters to investigate the individual effect of each factor. • It uses the data efficiently. DOE Lecture 1

19. Types of factorial experiments (Cont.) • 23 factorial design: • There will be 8 tests, each is a corner of a cube. • 24 factorial design: • All the possible combinations of the levels of the factors are used. • Fractional Factorial Experiment: • Used when there are 5 or more factors. • it is a variation of the basic factorial design, in which only a subset of runs are made. DOE Lecture 1

20. Types of Factorial Experiments (Cont.) • If there are K-factors, each of two levels; then the factorial design will require 2k runs DOE Lecture 1

21. Basic Principles of Experimental Design • 3 Basic principle of DOE • Replication: repetition of the basic experiment • Obtain an estimation of exp. error. • Precise estimate of factor effect. But it is costly. • Randomization: the allocation of the experimental material and the order in which the individual runs of the experiment are randomly determined • By randomization; we averaging out the effect of extraneous factors that may be present. • Blocking: it is a technique used to improve the precision with which comparisons among the factors of interest are made. • Reduce or eliminate the variability of nuisance factors. DOE Lecture 1

22. Nuisance Factors • Nuisance Factor: Is a factor that may affect the experiment response, but in which we are not directly interested. They can be divided into: • Controllable nuisance factor: a factor whose levels may be set by the experimenter. • Uncontrollable nuisance factor: it is uncontrollable, but it can be measured. Covariance analysis is used to control its effect. DOE Lecture 1

23. Nuisance Factors (Cont.) • Noise factor: a factor that varies naturally and uncontrollably in the process and can be controlled for purposes of the experiment. • Each factor will have levels and a range • A block: Is a set of homogeneous experimental conditions. DOE Lecture 1