Using an example from a recent study of the finite element method (FEM) solutions of the natural frequencies of single-crystal silicon cantilevers in atomic force microscopy (AFM), we present the results of an analysis using two powerful tools of engineering statistics, namely, (a) stochastic FEM, and (b) design of experiments. The analysis of the FEM results using ABAQUS, ANSYS, and LS-DYNA anisotropic elastic element types yields conclusions that engineers can use to justify decisions with quantitative measure of uncertainties. For PVP engineers, we show with an example that this methodology is equally applicable to their decision making process and the appropriate risk assessment.

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