Save Time With Fractional Factorial DOEsBy Shree Padnis
Design of Experiments (DOE) is a key tool in the Six Sigma methodology. DOEs help improve processes in a quantum fashion, and is an approach for effectively and efficiently exploring the cause and effect relationship between numerous process variables (Xs) and the output or process performance variable (Y).
Design of Experiments help in the following ways:
- The DOE helps in identifying the vital few sources of variation.
- DOEs quantify the effects of the important Xs including their interactions.
- Performing Designs of Experiments produces an equation that quantifies the relationship between the process Xs and the process output Y, thus enabling the transition to the Y=f(x) philosophy of Six Sigma.
There are many types of DOEs which can be applied to a particular problem based on various planning factors and the outcome desired at the end of the analysis. This article will try and explain the analysis strategy that a Black Belt can undertake for Resolution III and IV Design of Experiments.
Though a full factorial design is the most desirable design wherein one could gather information on all the main effects, two way interactions, three way interactions and other higher order interactions are very unpractical to run due to the prohibitive size of the experiments. For a design of seven factors at two levels one would have to complete 128 runs.
Fractional factorial designs are good alternatives to a full factorial design, especially in the initial screening stage of a project. The same seven factors could be tested in either 8 runs or 16 runs or 32 runs with the loss of certain information.
- Resolution III DOE: A design where main factor effects are confounded with two factor and higher order interactions.
- Resolution IV DOE: A design where main effects are confounded with three factor and higher order interactions and all two factor interactions are confounded with two factor interactions and higher order interactions.
- Resolution V DOE: A design where main effects are confounded with four factor and higher order interactions and two factor interactions are confounded with three factor interactions and higher order interactions.
Resolution III and Resolution IV are very commonly used designs in the screening of various factors during the Analyze and Improve phases of Six Sigma.
The problem, which one faces in utilizing these resolution designs, lies in the confounding structure of the designs, however three fundamental principles of factorial effects can be effectively utilized for the analysis of these designs.
Hierarchical Ordering Principle
- Lower order effects are more likely to be important than higher order effects.
- Effects of the same order are equally likely to be important.
This principle suggests that when resources are scarce, priority should be given to the estimation of lower order effects. Its application is particularly effective when the number of factorial effects is large. It is an empirical principle whose validity has been confirmed in many real experiments
Effect Sparsity Principle
- The numbers of relatively important effects in a factorial experiment are small.
This principle may also be called the pareto principle in experimental design.Effect Heredity Principle
- In order for an interaction to be significant, at least one of its parent factors should be significant.
The third principle governs the relationship between an interaction and its parent factors. This principle is very useful in de-aliasing the confounding structure. To understand the analysis method for Resolution III and IV Design of Experiments we will undertake an example and show how the three principles can be effectively used.
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