The work described is the result of a study extending over the past few years by a chemist and a statistician. Development has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but we believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.

On the Experimental Attainment of Optimum Conditions

A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function of inputs that, when evaluated, produces outputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observed elementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or ad...

Factorial sampling plans for preliminary computational experiments

A class of incomplete three level factorial designs useful for estimating the coefficients in a second degree graduating polynomial are described. The designs either meet, or approximately meet, the criterion of rotatability and for the most part can be orthogonally blocked. A fully worked example is included.

https://www.jstor.org/stable/pdfplus/1266454.pdf

Some New Three Level Designs for the Study of Quantitative Variables

The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of today’s engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper, we review several of these techniques, including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning and kriging. We survey their existing application in engineering design, and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations, and how common pitfalls can be avoided.

/pdf/metamodels-for-computer-based-engineering-design-survey-and-382x1fki1s.pdf

J. P. Burman

Papers

The design of optimum multifactorial experiments