# What is Design of Experiments?

01/01/1999

E xperimental Designs are used to identify or screen important factors affecting a process, and to develop empirical models of those processes. Design of Experiment (DoE) techniques enable teams to learn about process behavior by running a series of experiments, where a maximum amount of information will be learned, in a minimum number of runs. Tradeoffs as to amount of information gained for number of runs, are known before running the experiments.

For example, a designed experiment has three factors; each set at two levels - typically the maximum and minimum settings for each of the factors. A Designed Experiment with three factors each at two levels, is called a 23factorial experiment (or Taguchi L 8 experiment), and requires eight runs, as follows:

 Run number Factor A Factor B Factor C 1 Low Low Low 2 High Low Low 3 Low High Low 4 High High Low 5 Low Low High 6 High Low High 7 Low High High 8 High High High

Each row represents an experimental run - a set of conditions for the three factors. After the above eight runs have been completed, and measured response recorded for each run, an empirical model can be built to predict process behavior based on the settings of these factors. Fractional factorial experiments efficiently learn about several factors affecting a process - for instance a 28-4fractional factorial experiment requires 16 runs, and allows up to 8 factors to be varied at the same time (in a particular or designed way).

After a Designed Experiment
Following a designed experiment, a model can be made to visualize and predict a response as a function of the factors varied. At the left is a graph predicting corrosion variation as a function of Mg and Mn. Here, this is an interaction effect - the effect of Mn depends on the level of Mg. A Designed Experiment allows the measurement of effects of factors and interactions. Often prediction of process behavior is not intuitively obvious, due to the presence of interactions.

Another outcome of Designed Experiments is the screening of the number of important factors from the 'trivial many' to the 'vital few' factors which are critical to efficient process running and product quality. Once the critical factors have been identified, these may be monitored using SPC (statistical process control) charts, which allow the operator to distinguish between 'common cause' and 'special cause' variation.

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