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Unformatted text preview: IE 361 Module 22 Design and Analysis of Experiments: Part 3 (pWay Studies and Analyses With 2Level Factors) Reading: Section 6.3, 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 22 1 / 28 Complete pFactor Studies (2Level Factors) We wish now to think about experimentation and subsequent analysis for systems that have many ( p ) factors potentially a/ecting a response, y . We begin with fullcomplete pway factorial studies (where all combinations of some levels of these factors are represented in the data set) and concentrate on 2 & 2 & & 2 or 2 p studies (ones where each of the p factors has only 2 levels). There are two reasons for mostly specializing to 2level factors. The &rst is that there is some special notation and structure that make their analysis most transparent, and the second is that as a practical matter, one can rarely a/ord pfactor factorial experimentation with many (more than 2) levels of the factors. Vardeman and Morris (Iowa State University) IE 361 Module 22 2 28 pFactor Notation Example 221 As our motivating example, we will use data from a 2 3 chemical process pilot plant study taken from Statistics for Experimenters by Box, Hunter, and Hunter. The response of interest was a yield variable ( y in units of g ). Factors and levels were as in the following table. Factor "Low" ( & ) and "High" ( + ) Levels ATemperature 160 C vs 180 C BConcentration 20 % vs 40 % CCatalyst #1 vs #2 Note that it is typical in 2 p studies to make an arbitrary designation of one level of each factor a &rst or "low" level and the other level the second or "high" level. Vardeman and Morris (Iowa State University) IE 361 Module 22 3 / 28 pFactor Notation Example 221 continued In the pilot plant study, there were m = 2 runs of the pilot plant made at each combination of levels of these 3 factors. We& ll let y ijk = the sample mean yield at level i of A, level j of B , and level k of C and s ijk = the sample standard deviation of yield at level i of A, level j of B , and level k of C The catalyst data and some summary statistics are then given in the table on panel 5 along with some additional notation for this 2 3 factorial context. (The " ijk " notation above is very helpful when one needs to indicate various averages of the sample means. For example, y i .. is the average of all sample means for level i of Factor A, y . jk is the average of all sample means for level j of Factor B and level k of Factor C, etc.) Vardeman and Morris (Iowa State University) IE 361 Module 22 4 / 28 pFactor Notation (2Level Factors) Example 221 continued A B C 2 p name i j k y &s y ijk s 2 ijk & & & (1) 1 1 1 59,61 60 2 + & & a 2 1 1 74,70 72 8 & + & b 1 2 1 50,58 54 32 + + & ab 2 2 1 69,67 68 2 & & + c 1 1 2 50,54 52 8 + & + ac 2 1 2 81,85 83 8 & + + bc 1 2 2 46,44 45 2 + + + abc 2 2 2 79,81 80 2 While the "...
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 Fall '09

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