Design & Analysis of Experiments 8E 2012 Montgomery

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Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery The 3k Factorial Design Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Notation Factor levels are sometime denoted 1, 2, 3 Qualitative or categorical factors are low, medium, high Individual runs are defined by k digits combinations, such as 000 to denote the test combination in a three-variable design where all three factors are at the low level -1, 0, +1 is the orthogonal coding for quantitative factors Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Note that by convention, Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery 9.2 Confounding Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery An example of this method: Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery An Example Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Factors at Two and Four Levels Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Nonregular Fractional Factorial Designs Section 9.5, page 415 In regular designs, all of the elements of the alias matrix are either 0, +1 or -1. In nonregular designs, there will be nonzero elements of the alias matrix that are not either +1 or -1. This means that terms that are aliased are not “completely confounded” The Plackett-Burman designs of the previous chapter are nonregular designs Nonregular fractional factorials have some good applications in factor screening experiments Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Jones and Montgomery (2011) present 16-run two-level nonregular designs for 6 – 8 factors in 16 runs – they call these “no-confounding” designs These are reasonable alternatives to the regular resolution IV designs Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery The recommended designs do not have any complete confounding involving main effects and two-factor interactions or of two-factor interactions with each other Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Nonregular Designs in 9-14 Factors in 16 Runs Section 9.5.2 text These are alternatives to the regular resolution III fractions Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Other designs are shown in the text Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Use of an Optimal Design Tool An optimal design tool can be used to create a custom design for a specific situation This requires: Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Examples of Optimal Designs Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Alias Structure for the Design in Table 9.37 Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery

Design & Analysis of Experiments 8E 2012 Montgomery Chapter 9 Design & Analysis of Experiments 8E 2012 Montgomery