Research on Uncertainty Evaluation Methods of Straightness of Straight Edge Based on Monte Carlo Method
LI Yuan-feng1,MENG Ling-chuan1,HUANG Yao2,YANG Hao-tian3
1. Beijing Jiaotong University, Beijing 100044, China
2. National Institute of Metrology, Beijing 100029, China
3. University College London, London, WC1E 6BT, UK
Abstract：The straightness uncertainty of straight edge in least-square rule and in minimum-zone rule have been evaluated by Monte Carlo method (MCM). Comparing with the straightness uncertainty evaluated by guide to the expression of uncertainty in measurement (GUM), it's been found that the straightness uncertainty in least-square rule evaluated by MCM is 0.028 μm less than that by GUM and the straightness uncertainty in minimum-zone rule evaluated by MCM is 0.026 μm less than that by GUM. It has been confirmed that both the methods are valid for evaluating the straightness uncertainty of straight edge at a certain numerical tolerance of 0.05 μm. Kolmogorov-smirnov test, jarque-bera test, normal probability plot, skewness and kurtosis test were employed as the statistic testing methods. By employing specific statistic testing method on measurand, it's been found that the kurtosis deviation of measurand distribution from normal distribution is responsible for the uncertainty difference.
李元峰,孟令川,黄垚,杨皓天. 基于蒙特卡洛方法平尺测量直线度不确定度评估方法的研究[J]. 计量学报, 2023, 44(4): 540-548.
LI Yuan-feng,MENG Ling-chuan,HUANG Yao,YANG Hao-tian. Research on Uncertainty Evaluation Methods of Straightness of Straight Edge Based on Monte Carlo Method. Acta Metrologica Sinica, 2023, 44(4): 540-548.
Janssen H. Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence［J］. Reliability Engineering and System Safety, 2013(109): 123-132.
JCGM 101: 2008, Evaluation of measurement data-Supplement1 to the “Guide to the expression of uncertainty in measurement”-Propagation of distributions using a Monte Carlo method［S］. 2008.
［2］
JCGM 102: 2011, Evaluation of measurement data-Supplement2 to the “Guide to the expression of uncertainty in measurement”-Extension to any number of output quantities［S］. 2011.
Meng L C, Zhu Z X. Uncertainty Estimate on Effective Diameter of Thread Plug Gauge by Monte Carlo Simulation［J］. Acta Metrologica Sinica, 2017, 38(6): 98-103.
Liu Y Y, Yang J, Zhao X Y, et al. Comparative Analysis of Uncertainty Measurement Evaluation with GUM and MCM［J］. Acta Metrologica Sinica, 2018, 39(1): 135-139.
Song M S, Wang W. Assignment of Simulation Sample Capability M in Uncertainty Evaluation by Monte Carlo Method［J］. Acta Metrologica Sinica, 2010, 31(1): 91-96.
［19］
Couto P R G, Damasceno J C, Oliveira S P, et al.. Monte Carlo Simulations Applied to Uncertainty in Measurement［J］. Theory and Applications of Monte Carlo simulations, 2013: 27-51.
［20］
Lopes R H C. Kolmogorov-Smirnov Test［M］. Berlin Heidelberg: Springer Berlin Heidelberg, 2011.
［22］
Chambers J M, Cleveland W S, Kleiner B, et al. Graphical Methods For Data Analysis［J］. Journal of Sleep Research, 2012, 21(4): 484.
［7］
Vagenas G. Uncertainty analysis for stride-time-derived modelling of lower limb stiffness: applying Taylor series expansion for error propagation on Monte-Carlo simulated data［J］. Sports Biomechanics, 2021.
［16］
吴呼玲. 最小包容区域法评定直线度误差［J］. 林区教学, 2008(9), 124-125.
Chen G, Zhai Q J, Hu Z, et al. Straightness measurement system and experimental instrument of straight edge［J］. China Measurement & Testing Technology , 2014, 40(1): 105-108.
［21］
Thadewald T, Büning H. Jarque-Bera Test and its Competitors for Testing Normality—A Power Comparison. Journal of Applied Statistics, 2007, 34(1): 87-105
2023, Vol. 44 
