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ME 388 – Applied Instrumentation Laboratory Design of Experiments (DOE)

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Reference (If you can find it) R.D Moen, T.W. Nolan, L.P. Provost, Improving Quality Through Planned Experimentation, McGraw-Hill, 1991 D.C. Montgomery, Design and Analysis of Experiments, 5 th Edition, Wiley, 2001

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Six Sigma (black belt) System for constant improvement Use of statistical tools for process analysis, problem solving and improvement Six Sigma statement by GE: …The central idea behind Six Sigma is that if you can measure how many "defects" you have in a process, you can systematically figure out how to eliminate them and get as close to "zero defects" as possible…

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Definition A powerful “statistics-based” experimental methodology that is used to efficiently determine how multiple independent variables affect dependent variables of a system or process.

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A properly executed DOE will… Provide the most information With the fewest amount of tests Compared to a sequential “string-of- pearls” type approach

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DOE’s are used for 1.Screening experiments 2.To determine Interactions between independent variables 3.Optimization

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Motivation Knowledge Optimization Improvement

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Steps to use DOE Have some technical knowledge of process or system (assumed here) Have some statistics background (assumed here) Design experiment (and run) Analyze data

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Terminology Factor = independent variable Level = a given value or setting for an independent variable (for example, a 2- level experiment involves testing a high and low value for each independent variable)

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2 level, 2 factor design (2 2 ) F2F2 - F 1 + - +

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2 level, 3 factor design (2 3 ) F2F2 - F 3 + - F 1 + - +

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2 level, 4 factor design (2 4 ) F4F4 F2F2 - F 3 + - F 1 + -- + +- +

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Fractional Factorial Designs Reduce number of test At the expense of complete data Rely on reasonable judgments and technical knowledge –Assume triple, quadruple and greater interactions are not significant

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2 7-3 design

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2 7-4 design

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Analysis Develop extended test/design matrix “Effects” are assessed for each variable and combination of variables Effects plots can also be generated

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