Model and Denotations
As in regression analysis, DoE is concerned with modelling the dependence of a random target variable Y in dependence of a number of controllable deterministic variables x 1, …, x k (called factors). The major goal of DoE is to find configurations for x = (x 1, …, x k ) out of a given region V ⊂ R k which lead to “optimal” results for the target variable under consideration. The different configurations x (1), …, x (n) for the factors are summarized in a statistical design d n = (x (1), …, x (n)) ∈ V n of sizen. The optimality criterion is usually defined through some objective function, e.g., the information or entropy associated with an experiment, the variance of some predictor \(\hat{Y }({x}^{{_\ast}})\) for an unobserved configuration x ∗ = x 1 ∗, …, x k ∗ etc. The main areas of concern in DoE are:
- (a)
statistical design in regression analysis and analysis of variance
- (b)
factorial designs
- (c)
identification and elimination of disturbing influences (blocking)
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Pilz, J. (2011). Statistical Design of Experiments (DOE). In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_538
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