DOE Steps Problem statement Choice of factors, levels, and ranges Choice of response variable(s) Choice of experimental design Performing the experiment Statistical analysis Conclusions and recommendations 14
Special Terminology : Design of Experiments 15 Response variable Measured output value Factors Input variables that can be changed Levels Specific values of factors (inputs) Continuous or discrete Replication Completely re-run experiment with same input levels Used to determine impact of measurement error Interaction Effect of one input factor depends on level of another input factor
Major Approaches to DOE 16 Factorial Design Taguchi Method
17 Factorial Design
Factorial Design : Full factorial design 18A full factorial design of experiments consists of the following:Vary one factor at a timePerform experiments for all levels of all factorsHence perform a large number of experiments that are needed!All interactions are captured.Consider a simple design for the following case:Let the number of factors = kLet the number of levels for the ithfactor = niThe total number of experiments (N) that need to be performed isKiinN1
DOE - Factorial Designs - 2 3 20 Trial A B C 1 Lo Lo Lo 2 Lo Lo Hi 3 Lo Hi Lo 4 Lo Hi Hi 5 Hi Lo Lo 6 Hi Lo Hi 7 Hi Hi Lo 8 Hi Hi Hi
DOE - Factorial Designs - 2 3 21 Trial A B C 1 -1 -1 -1 2 -1 -1 +1 3 -1 +1 -1 4 -1 +1 +1 5 +1 -1 -1 6 +1 -1 +1 7 +1 +1 -1 8 +1 +1 +1
Output Matrix 22 Let us represent the outcome of each experiment to be a quantity y. Thus y 1 will represent the outcome of experiment number 1 with all three factors having their “LOW ” values, y 2 will represent the outcome of the experiment number 2 with the factors A & B having the “Low” values and the factor C having the “High” value and so on. The outcome of the experiments may be represented as the following matrix:
Output Matrix 23
28 Fractional Factorial Designs
DOE - Fractional Factorial Designs 29 In a multivariable experiments, with k number of variables and l number of levels per variable demands l k number of measurements for complete understanding of the process or calibration. In statistics, fractional factorial designs are experimental designs consisting of a carefully chosen subset (fraction) of the experimental runs of a full factorial design.
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- Spring '19
- Magdy Khalaf
- Fractional factorial designs, EFQM Excellence Model