Design Of Experiments

November 28, 2009

DOE is a systematic statistical tool. It allows a set of experiments used to determine the relationship between different factors affecting a process and the output of the process. A set of tests are designed that change input variables in a planned manner. This will typically include a group of variable that are known to affect the system. Effects on the output are systematically recorded and analyzed. This is used when a systematic change of one variable at a time could become complex combinatorial exercise or finding correlations could become difficult. The method is attributed to Sir Ronald Fisher from 1920’s and 30’s.

A set of ten to twenty experiments are arranged. All the factors that appear to be relevant are varied and outputs noted for these variations. The analysis would bring out optimal conditions such as what factors influence the results significantly. The factors that are not significant also get identified. The analysis also brings out if any interactions are happening betweens some factors and if synergies exist amongst input variables. Compared to the one change at a time experimental methods these experiments allow judgment of significance of a group of variables acting in combination or acting alone.

With one change at a time testing the experimenter may stop the experiment after finding a variable with significant influence on the output and may yet miss the influence of another factor that may alter the effect of the first. While the experimenter determines the direction these tests are to take, the DOE experiments are planned for all possible dependencies. The experiments must then prescribe what data will be required to asses those interactions. Information gathering is also maximized as, by design, these experiments set the, exact length and size, data needs of the experiments.

For one variable at a time kind of experiment to succeed a complete analytical model is essential and in most real life situations these do not exist or are too time and funds consuming to develop. Instead, empirical knowledge gathered based on sound statistical basis is far more optimal. It is the optimality problem that calls for the DOE technique to be used often. Thus conducting as minimum a number of experiments as possible is often targeted. DOE uses a very small set of experiments that reduces costs.

The Process

Choosing a small set of experiments is often called building a design. One needs to start with defining an objective to the trial thereby allowing better understanding of important variables and for finding the optimum. The variable that are to be changed, the design variables, and the levels and ranges of variation are to be defined. The variable that measure the output or the response variables are defined and the required precision set. The final step in the process is to choose a standard design that fits the case. The objectives, number of variables both design and response, and the precision will have an influence on this choice. The standard designs are well known classes of experiment designs from theory.

One example of a situation where design of experiment would be necessary is when automotive designers would be attempting to find the combination of suspensions and tires that provides optimal riding comfort. Most desirable riding characteristics yet at reasonable cost would be such a solution.

For each of input variables, levels that represent the range of value for the study is defined. An experimental plan tells the experimenter the settings of input variable. The analysis looks for differences between responses for different groups of input changes. The differences are then identified to be due to single effect or interaction (of more than one input) effect. The number and type of these tests to be carried out should be specified during the planning of quality. You would need to specify the impact on the cost of quality too.

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