Robust Estimation of Optimal Sample Size for CMM Measurements with Statistical Tolerance Limits

Abstract

The paper proposes the kernel probability density function approach to estimate the distribution of measurements on a part which is measured in a coordinate measuring machine (CMM). The study is based on the experimental data derived from internal cylinder measurements. The distribution free model suggested by Wilks was used as a reference for the selection of the sample size. Three cross sections of a cylinder were measured regarding to this reference. The work defines the minimum required sample size for obtaining at least 0.95 proportion of radius variation for particular studied cylindrical part with 95% confidence level.

Optimization of Sample Size for Two-Point Diameter Verification in Coordinate Measurements

“…The reliability of the method strongly depends on the proper choice of the six-sigma range. The method reduces to some degree the tolerance interval size (acceptance interval), but it is compensated by the significant minimization of the sample size, more than in 4 times relative to [8] (for approximately 89% cases estimated with ( 5) and (7) with the assumption of the uniform distribution of the process, Fig. 4).…”

“…In a previous paper, the authors estimated the optimal sample size for detecting 95% of the radius variation range (roundness form deviation of cylinder crosssections) with 95% confidence level [8].…”

“…Research in the sample strategy field is generally focusing on the evaluation of geometrical form deviation (e.g. roundness, flatness) [5,7,8,11]. In this paper: we consider the case when the diameter tolerance band is assumed to be larger than the variation of the two-point diameter in one single part.…”

Investigating the Distribution of Flatness Measurements in Battery Manufacturing through Empirical Investigation and Statistical Theory

“…Hence, the theoretical distribution of flatness plays a crucial role in both design and manufacturing processes. Chelishcev et al [20] used a CMM to measure the rotating parts and used the probability density function method to predict the size distribution of the measured parts and demonstrated the applicability of a distribution-free model in predicting the sample size, minimum content, and confidence level for CMM-based Geometric Dimensioning and Tolerancing inspection without the need for prior measurements. Berrado et al [21] put forth a method that considers the measurement round-off and small sample sizes.…”