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# lect1 - IE 410 Design of Experiments Notes for Lecture 1 I...

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IE 410: Design of Experiments Notes for Lecture 1, 8/25/03 I. Class Logistics The first part of the class will be devoted to discussing the logistics of the class as shown on the syllabus and course schedule.

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II. Introduction to Design of Experiments Why Experiment? To gain information . Why design the experiment? To gain the most information with the least effort. To collect information from which valid conclusions may be drawn.
What is the best way to design an experiment? It depends, thus the need for this class.

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A. What is an experiment (from a mathematical / statistical perspective)? Purpose: 1. To determine if various factors effect some response (Y) 2. To build models relating the response to the factors .
Examples to clarify: Example 1. Response Variable Y = yield from a chemical process. (Perhaps measured in percent conversion of the raw materials to final product) Factors studied: Factor A: Temperature at which process is run Factor B: Amount of catalyst used in the process

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The response variable (Y) is also called the DEPENDENT variable because its value is assumed to depend on the values of the factors. Similarly, factors are also sometimes called independent variables . Factors are also commonly known as "treatments ", a term which comes from agriculture where design of experiments was first developed.
Definitions : Factor or Treatment LEVELS : The values assigned to the factors for the various runs of the experiment: Amount of Catalyst (Lbs.) | 200 300 -----|-------------------------- 20 | 84% 92% Temp | 87% 91% (C) | 30 | 75% 87% | 79% 88% | 45 | 97% 96% | 23% 93% Thus in this experiment Factor A (temperature) is at

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three levels, 20, 30, and 45 degrees. Factor B is at two levels, 200 and 300 lbs. OBSERVATIONS of the response variable Y are listed in the table. Note that for each combination of treatment levels, we have 2 observations on the response Y.
Natural Questions Is 2 enough? Is 1 sufficient? Do we really need observations for each combination of treatment levels? Must we have the same number of observations for each treatment level combination? Why 3 and 2 levels respectively? Does either of the factors affect the response? These are questions you will be able to answer by the end of the course.

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Example 2.
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lect1 - IE 410 Design of Experiments Notes for Lecture 1 I...

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