Module 20C - IE 361 Module 20 Design and Analysis of...

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IE 361 Module 20 Design and Analysis of Experiments: Part 1 (One-Way Studies and Analyses) Reading: Section 6.1, Statistical Quality Assurance Methods for Engineers Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 20 1 / 16
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Design and Analysis of Experiments After one brings a process to physical stability and quanti°es what it is capable of doing, it±s reasonable to consider fundamental changes to its con°guration/how it is run. Intelligent/e¢ cient data collection and analysis aimed at °nding fundamental process improvements is the subject of the °nal set of modules of this course. The topic is the "design and analysis of experiments," with the goal of eventually addressing complex situations where there are many "process knobs" (factors), each with multiple settings (levels) and thus many many potential ways that things could be done, and the object is to °nd good combinations of levels of important factors. Vardeman and Morris (Iowa State University) IE 361 Module 20 2 / 16
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The Big Problem The °gure below illustrates the problem addressed in these last four modules. The noisy process output y is a/ected by variables x 1 , x 2 , x 3 and potentially other variables (both recognized and unrecognized). The question is how to set up the "control panel" (the settings of the "knobs" or values of some variables x 1 , x 2 , x 3 ) to collect data and e¢ ciently learn how to optimize the process to get desired values of y . Figure: A Process With Many Inputs x or Factors A/ecting a Response y Vardeman and Morris (Iowa State University) IE 361 Module 20 3 / 16
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Samples from r Di/erent Experimental Conditions We begin with a most basic experimental scenario, where one has data consisting of observed responses, y , for some number, r , di/erent processes conditions. We± ll write y ij = the j th response in sample i (made under the i th set of process conditions) where sample sizes are n 1 , n 2 , . . . , n r . Vardeman and Morris (Iowa State University) IE 361 Module 20 4 / 16
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Samples from r Di/erent Experimental Conditions Example 20-1 A classic data set from Devore±s Probability and Statistics for Engineering and the Sciences concerns the current required to achieve a target brightness on a type of television tube. All combinations of 2 types of
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