3. Design of Experiments (DOE) (Analysis of Variance – ANOVA) Hae-Jin Choi School of Mechanical Engineering, Chung-Ang University 1 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY What is Design of Experiments (DOE)? Experiments are used widely in the engineering n world Process characterization & optimization ¨ Evaluation of material properties ¨ Product design & development ¨ Component & system tolerance determination ¨ Design of Experiments (DOE) is; n Planning experiments or tests to save resources ¨ (time and money) Analyzing results of experiments or tests to ¨ characterize your system Advanced Design for Complex Systems 2 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY Example: Golfing How to improve my score in Golfing? n Practice!!! n Other than that? n Type of driver used (oversized or regular sized) ¨ Type of ball (2 piece or 3 piece) ¨ Walking or riding cart ¨ Drinking water or beer ¨ Etc… ¨ What combination of the factors is the best for me? Advanced Design for Complex Systems 3 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY General model of a process or system System: function, model, or n manufacturing process to Controllable factors transform input to output x1 x2 xp ¨ Golf game Input: provided materials or n energy into the process or system ¨ Physical energy to play golf Response Response (output): outcome of a Input System (Output) n process or performance of a (Process) y system ¨ Score Controllable factors: factors that ….. n experimenters can control ¨ Driver type, ball type, etc. z1 z2 zq Uncontrollable factors (noise n Uncontrollable factors factors): factors that experiments (Noise factors) cannot control ¨ Course layout, grass type, weather, etc. Advanced Design for Complex Systems 4 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY What needs to be analyzed? Determining which variables n Controllable factors are most influential on the x1 x2 xp response y Determining where to set the n controllable factors x so that y Response Input System (Output) is almost always near the (Process) y desired nominal value ….. z1 z2 zq Uncontrollable factors (Noise factors) Advanced Design for Complex Systems 5 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY Experiments with One Factor Plasma etching process: n Advanced Design for Complex Systems 6 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY Plasma etching process: An engineer is interested in investigating the relationship n between the RF power setting and the etch rate for this tool. The objective of an experiment like this is to model the relationship between etch rate and RF power, and to specify the power setting that will give a desired target etch rate. The response variable is etch rate. n She is interested in a particular gas (C2F6) and gap (0.80 cm), n and wants to test four levels of RF power: 160W, 180W, 200W, and 220W. She decided to test five wafers at each level of RF power. The experimenter chooses 4 levels of RF power 160W, 180W, n 200W, and 220W The experiment is replicated 5 times – runs made in random n order Advanced Design for Complex Systems 7 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY Plasma etching process: Advanced Design for Complex Systems 8 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY • Does changing the power change the mean etch rate? • We would like to have a systematic way to answer these questions Analysis of Variance (ANOVA) Advanced Design for Complex Systems 9 SCHOOLOFMECH. ENG. CHUNG-ANGUNIVERSITY The Analysis of Variance (ANOVA) In general, there will be a levels of the factor, or a treatments, n and n replicates of the experiment, run in random order…a completely randomized design (CRD) N = an total runs n We consider the fixed effects case…the random effects case n will be discussed later Objective is to test hypotheses about the equality of the a n treatment means Advanced Design for Complex Systems 10