Modification of the Audze-Eglājs criterion to achieve a uniform distribution of sampling points

Audze-Eglźjs criterion for DoE provides nonuniformly distributed experimental points.Simple improvement of AE criterion that ensures uniform distribution is presented.The improvement lies in considering periodicity of the design space.Extensive calculations verifying biased and improved uniform sampling are included. Display Omitted The Audze-Eglźjs (AE) criterion was developed to achieve aźuniform distribution of experimental points in aźhypercube. However, the paper shows that the AE criterion provides strongly nonuniform designs due to the effect of the boundaries of the hypercube. We propose aźsimple remedy that lies in the assumption of periodic boundary conditions. The biased behavior of the original AE criterion and excellent performance of the modified criterion are demonstrated using simple numerical examples focused on (i) the uniformity of sampling density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate the statistical parameters of functions of random variables. An engineering example of reliability calculation is presented, too.

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