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Integral Operators and Delay Differential Equations



David E. Gilsinn, Florian A. Potra


We begin this expository essay by reviewing with examples what a typical engineer already knows about statistics. We then consider a central question in engineering decision making, i.e., given a computer simulation of high-consequence systems, how do we verify and validate (V & V) and what are the margins of errors of all the important predicted results? To answer this question, we assert that we need three basic tools that already exist in statistical and metrological sciences: (A) Error Analysis. (B) Experimental Design. (C) Uncertainty Analysis. Those three tools, to be known as A B C of statistics, were developed through a powerful linkage between the statistical and metrological sciences. By extending the key concepts of this linkage from physical experiments to numerical simulations, we propose a new approach to answering the V & V question. The key concepts are: (1) Uncertainty as defined in ISO Guide to the Expression of Uncertainty in Measurement (1993). (2) Design of experiments prior to data collection in a randomized or orthogonal scheme to evaluate interactions among model variables. (3) Standard reference benchmarks for calibration, and inter-laboratory studies for weighted consensus mean. To illustrate the need for and to discuss the plausibility of this metrology-based approach, two example problems are presented: (a) Twelve simulations of the deformation of a linearly elastic simple cantilever beam with end point load, and (b) the calculation of a mean time to failure for a uniformly-loaded, 100-column, and single-floor steel grillage on fire.
Journal of Integral Equations and Applications


Gilsinn, D. and Potra, F. (2006), Integral Operators and Delay Differential Equations, Journal of Integral Equations and Applications, [online], (Accessed July 14, 2024)


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Created October 1, 2006, Updated February 19, 2017