Abstract
The GUM Supplement 1 presented the adaptive Monte Carlo (AMC) method. A basic implementation of an AMC procedure involves carrying out an increasing number of Monte Carlo trials until four parameters have stabilized in a statistical sense. Although the AMC method has been successfully used for uncertainty evaluations, the amount of stored data was seen as significant, and even after achieving stability, it can be lost with the increase in the number of trials. To overcome these problems, two modifications to the AMC method were proposed, implemented and validated. The first is related to data storage, while the second consists of applying an alternative criterion to assess convergence. After modifications, the AMC was named the modified adaptive Monte Carlo (MAMC) method and was applied when estimating the uncertainty of measurements carried out with a micrometer. The MAMC effectiveness was validated through the comparison of the uncertainty values and those from the application of the GUM and AMC methods. Under the evaluated experimental conditions, the MAMC showed greater repeatability when compared to AMC, regarding the number of trials to be carried out. This factor contributes toward the higher reliability of this method. The amount of data to be stored and manipulated through the application of the MAMC method was decreased significantly. This fact may increase the adoption of the AMC method.
Similar content being viewed by others
References
BIPM, IEC, IDCC, et al (2008) JCGM 100:2008 Evaluation of measurement data—guide to the expression of uncertainty in measurement
Kruth J-P, Van Gestel N, Bleys P, Welkenhuyzen F (2009) Uncertainty determination for CMMs by Monte Carlo simulation integrating feature form deviations. CIRP Ann 58:463–466. https://doi.org/10.1016/j.cirp.2009.03.028
Désenfant M, Priel M (2017) Reference and additional methods for measurement uncertainty evaluation. Measurement 95:339–344. https://doi.org/10.1016/j.measurement.2016.10.022
Wen X, Zhao Y, Wang D, Pan J (2013) Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error. Precis Eng 37:856–864. https://doi.org/10.1016/j.precisioneng.2013.05.002
Weckenmann A, Knauer M, Killmaier T (2001) Uncertainty of coordinate measurements on sheet-metal parts in the automotive industry. J Mater Process Technol 115:9–13. https://doi.org/10.1016/S0924-0136(01)00758-0
ISO—International Organization for Standardization (2017) ISO/IEC 17025:2017 General requirements for the competence of testing and calibration laboratories
Schwenke H, Siebert BRL, Wäldele F, Kunzmann H (2000) Assessment of uncertainties in dimensional metrology by Monte Carlo simulation: proposal of a modular and visual software. CIRP Ann 49:395–398. https://doi.org/10.1016/S0007-8506(07)62973-4
BIPM, IEC, IFCC, et al (2008) JCGM 101:2008 Evaluation of measurement data—supplement 1 to the “guide to the expression of uncertainty in measurement”—propagation of distributions using a Monte Carlo method 90
Yang C, Kumar M (2019) An adaptive Monte Carlo method for uncertainty forecasting in perturbed two-body dynamics. Acta Astronaut 155:369–378. https://doi.org/10.1016/j.actaastro.2018.05.053
Piratelli-Filho A, DI Giacomo B (2003) Uncertainty evaluation in small angle calibration using ISO GUM approach and Monte Carlo Method. In: XVII IMEKO world congress metrology in the 3rd MILLenium. Dubrovnik, Croatia
Andolfatto L, Mayer JRR, Lavernhe S (2011) Adaptive Monte Carlo applied to uncertainty estimation in five axis machine tool link errors identification with thermal disturbance. Int J Mach Tools Manuf 51:618–627. https://doi.org/10.1016/j.ijmachtools.2011.03.006
Matus M (2012) Uncertainty of the variation in length of gauge blocks by mechanical comparison: a worked example. Meas Sci Technol 23:1–6. https://doi.org/10.1088/0957-0233/23/9/094003
Arantes LJ, Fernandes KA, Schramm CR et al (2017) The roughness characterization in cylinders obtained by conventional and flexible honing processes. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-017-0544-2
Mahmoud GM, Hegazy RS (2017) Comparison of GUM and Monte Carlo methods for the uncertainty estimation in hardness measurements. Int J Metrol Qual Eng 8:14. https://doi.org/10.1051/ijmqe/2017014
Widmaier T, Hemming B, Juhanko J et al (2017) Application of Monte Carlo simulation for estimation of uncertainty of four-point roundness measurements of rolls. Precis Eng 48:181–190. https://doi.org/10.1016/j.precisioneng.2016.12.001
Rezende Júnior MV, Leal JES, Pires RR et al (2019) Traceability for measurements carried out on incremental step loading equipment. J Braz Soc Mech Sci Eng 41:316. https://doi.org/10.1007/s40430-019-1817-5
Balsamo A, Di Ciommo M, Mugno R et al (1999) Evaluation of CMM uncertainty through Monte Carlo simulations. Ann CIPR 48:425–428
Ramu P, Yagüe JA, Hocken RJ, Miller J (2011) Development of a parametric model and virtual machine to estimate task specific measurement uncertainty for a five-axis multi-sensor coordinate measuring machine. Precis Eng 35:431–439. https://doi.org/10.1016/j.precisioneng.2011.01.003
Acero R, Santolaria J, Pueo M, Abad J (2016) Uncertainty estimation of an indexed metrology platform for the verification of portable coordinate measuring instruments. Measurement 82:202–220. https://doi.org/10.1016/j.measurement.2015.12.024
Bali NP (2005) Golden real analysis. Firewall Media, New Delhi, Boston
ASTM (2019) ASTM E29-13: standard practice for using significant digits in test data to determine conformance with specifications. ASTM Interational i, pp 1–5. https://doi.org/10.1520/E0029-13R19.2
ISO—International Organization for Standardization (2013) ISO 7870-2: control charts—part 2: Shewhart control charts
Leal J (2016) Uma abordagem alternativa para avaliação da convergência do método de Monte Carlo adaptativo do GUM S1. Universidade Federal de Uberlândia, Uberlândia
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: José Roberto de França Arruda.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Leal, J.E.S., da Silva, J.A. & Arencibia, R.V. Contributions to the adaptive Monte Carlo method. J Braz. Soc. Mech. Sci. Eng. 42, 462 (2020). https://doi.org/10.1007/s40430-020-02548-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-020-02548-3