DOE Steps Problem statement Choice of factors levels and ranges Choice of

Doe steps problem statement choice of factors levels

This preview shows page 14 - 30 out of 46 pages.

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
Image of page 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
Image of page 15
Major Approaches to DOE 16 Factorial Design Taguchi Method
Image of page 16
17 Factorial Design
Image of page 17
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
Image of page 18
.
Image of page 19
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
Image of page 20
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
Image of page 21
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:
Image of page 22
Output Matrix 23
Image of page 23
24 ANOVA
Image of page 24
ANOVA 25
Image of page 25
ANOVA 26
Image of page 26
ANOVA 27
Image of page 27
28 Fractional Factorial Designs
Image of page 28
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.
Image of page 29
Image of page 30

You've reached the end of your free preview.

Want to read all 46 pages?

  • Spring '19
  • Magdy Khalaf
  • Fractional factorial designs, EFQM Excellence Model

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture