Other meanings of Design
Statistics
Design of experiments (DOE) is a systematic methodology for planning experiments so that data collected can be analyzed to yield valid and objective conclusions. It involves specifying the experimental factors, levels, and treatments, as well as the number of replicates and the order of runs, to maximize information while minimizing resources. Originating in agriculture with the work of Ronald Fisher, DOE has become essential in engineering, industry, and science for process optimization and product development.
The three fundamental principles of DOE are randomization, replication, and blocking. Randomization ensures that treatments are assigned to experimental units without bias, replication provides an estimate of experimental error, and blocking reduces known sources of variability by grouping similar units. Common designs include completely randomized designs, randomized block designs, and factorial designs. Factorial designs, especially the 2^k series, allow the study of interactions between factors, which is a key advantage over one-factor-at-a-time approaches. Fractional factorial designs, such as Plackett-Burman and Box-Behnken designs, are used when the number of runs must be limited, often in screening experiments.
Ronald A. Fisher introduced the principles of DOE in the 1920s at Rothamsted Experimental Station, where he developed the analysis of variance and the concept of randomization. His 1935 book The Design of Experiments laid the foundation for the field. Later, George Box and K. B. Wilson introduced response surface methodology in the 1950s, which combines DOE with regression analysis to optimize processes. The work of Genichi Taguchi in the 1980s brought DOE to quality engineering, emphasizing robust design and the use of orthogonal arrays.
DOE is widely used in industrial engineering for product and process optimization, such as in the automotive and semiconductor industries. In agriculture, it remains central to field trials for comparing crop varieties and treatments. In clinical trials, randomized controlled trials are a form of DOE that ensures unbiased assessment of new treatments. In computer simulation, design of experiments is applied to tune parameters of complex models, often using space-filling designs like Latin hypercubes. In recent years, DOE has been integrated with machine learning for efficient hyperparameter tuning and active learning.
Beyond the classical designs, there are many niche and advanced topics. Optimal designs, such as D-optimal and A-optimal, are constructed algorithmically to maximize a specific criterion, useful when standard designs are not applicable. The concept of 'aliasing' in fractional designs means that effects are confounded, requiring careful interpretation. The design of experiments has also been applied in ecology for studying environmental impacts, and in archaeology for testing excavation strategies. A notable edge case is the 'lurking variable' problem, where an unobserved factor can invalidate conclusions if not controlled. The use of DOE in the development of new materials, such as in the design of experiments for additive manufacturing, is a growing area.
This article focuses on the statistical methodology of designing experiments, not on the broader concept of design in art or engineering.
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