Statistical evaluation of minimum zone method in coordinate metrology

Abstract

Minimum zone method, minimum circumscribing method and maximum inscribing method are used for calculation of form deviations and determination of datum system in ISO and JIS standards. However, there are no researches for statistical evaluations of results from these methods. This is mainly because the results from these methods are determined by positions of only few contact points. The novel statistical evaluation method for minimum zone method has been proposed in this article. The average and the distribution of the maximum order of measured points are calculated from the probability density function and the cumulative distribution function of measured points. From the distribution of maximum order of the measured points, the range of maximum value and minimum value of measured points are calculated. For the straight lines, the limits and the distribution of the slope of the line are also calculated using these methods. The series of simulations for minimum zone method of straight lines show that the methods in this paper are useful to estimate the results of minimum zone method.