Straightness and flatness evaluation using data envelopment analysis

In today's world of precision engineering, robustness and accuracy in the evaluation of the form tolerances are considered as competitive advantages for manufacturing enterprises. Amongst various methods for accurate and robust evaluation, which have been studied, nonlinear optimization methods based on operational research have proved to be successful as far as they can ensure unique and global convergence in practical applications. However, it is well known that ensuring the convergence is the most difficult thing to deal with for a nonlinear optimization technique because the performance is in general highly sensitive to parameter setting. Therefore, this paper introduces a robust linear programming formulation-based algorithm in which the performance is not dependent on the quality of parameters. Interestingly, in this algorithm, the data envelopment analysis technique is used to form a convex hull that decides the minimum enclosed zone in a robust manner. From the computational experiments, it is shown that the proposed algorithm can be a promising alternative to the traditional nonlinear optimization method for straightness and flatness evaluation.

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