Estimation of form-error and determination of sample size in precision metrology
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Form-error measurement is mandatory for the quality assurance of manufactured parts and plays a critical role in precision engineering. There is now a significant literature on analytical methods of form-error measurement, which either use mathematical properties of the relevant objective function or develop a surrogate for the objective function that is more suitable in optimization. On the other hand, computational or numerical methods, which only require the numeric values of the objective function, are less studied in the literature on form-error metrology. This thesis introduces a computational algorithm, based on the theory of finite-differences derivative-descent, for measuring form of a variety of features, including straightness, flatness, circularity, sphericity, and cylindricity. One goal of this research was to critically evaluate the performance of the two computational methods, finite-differences and Nelder-Mead, with that of the least-squares method. Another goal was to determine the optimal sample size.