, Volume 34, Issue 3, pp 299–304 | Cite as

Monte Carlo Simulation in Uncertainty Evaluation: Strategy, Implications and Future Prospects

  • N. GargEmail author
  • S. Yadav
  • D. K. Aswal
Feature Article


Monte Carlo simulation (MCS) is an approach based on the propagation of the full probability distributions. It was introduced by the Joint Committee for Guides in Metrology (JCGM) in the supplement I-JCGM 101:2008. It is used to resolve the problem of calculating measurement uncertainties of complex measurands through simulation of random variables. Further, supplement II on “Extension to any number of output quantities” was published in 2011 and supplement III on “Modelling” is under publication. These supplements cover broader range of measurement issues which are not handled using law of propagation of uncertainty (LPU) alone and provide an alternative method to the conventional LPU approach. The MCS method plays a vital role in cases, where the linearization of the model does not provide enough depiction, or the probability density function of the output quantity deviates considerably from the Gaussian distribution. The SWOT analysis describes the strengths, weaknesses, opportunities and threats associated with the use of MCS in the measurement uncertainty evaluation and is addressed in this paper. The paper also summarizes the implications and prospects associated with the use of MCS in uncertainty evaluation for wide usage in solving problems in physical, biological and engineering sciences.


Measurement uncertainty Law of propagation of uncertainty (LPU) Monte Carlo simulation (MCS) 



  1. [1]
    M. G. Cox and B. R. L. Siebert, The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty, Metrologia, 43 (2006) S178–S188.ADSGoogle Scholar
  2. [2]
    Joint Committee for Guides in Metrology, 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.Google Scholar
  3. [3]
    Guide to the Expression of Uncertainty in Measurement (GUM), International Organization for Standardization (1995).Google Scholar
  4. [4]
    Joint Committee for Guides in Metrology, JCGM 102:2011, Evaluation of measurement data—Supplement 2 to the “Guide to the expression of uncertainty in measurement”—Extension to any number of output quantities.Google Scholar
  5. [5]
    Joint Committee for Guides in Metrology, JCGM 103, Evaluation of measurement data—Supplement 3 to the “Guide to the expression of uncertainty in measurement”—Modelling (Under preparation), Accessed 28 Aug 2019.
  6. [6]
    I. Farrance and R. Frenkel, Uncertainty in measurement: a review of Monte Carlo simulation using microsoft excel for the calculation of uncertainties through functional relationships, including uncertainties in empirically derived constants, Clin. Biochem. Rev., 35 (2014) 37–61.Google Scholar
  7. [7]
    C. E. Papadopoulos and H. Yeung, Uncertainty estimation and Monte Carlo simulation method, Flow Meas. Instrum., 12 (2001) 291–298.Google Scholar
  8. [8]
    P. M. Harris and M. G. Cox, On a Monte Carlo method for measurement uncertainty evaluation and its implementation, Metrologia, 51 (2014) S176–S182.ADSGoogle Scholar
  9. [9]
    G. Wübbeler, P. M. Harris, M. G. Cox and C. Elster, A two-stage procedure for determining the number of trials in the application of a Monte Carlo method for uncertainty evaluation, Metrologia, 47 (2010) 317–24.ADSGoogle Scholar
  10. [10]
    G. M. Mahmoud and R. S. Hegazy, Comparison of GUM and Monte Carlo methods for the uncertainty evaluation in hardness measurements, Int. J. Metrol. Qual. Eng., 8 (2017) 14.Google Scholar
  11. [11]
    A. B. Forbes, Approaches to evaluating measurement uncertainty, Int. J. Metrol. Qual. Eng., 3 (2012) 71–77.Google Scholar
  12. [12]
    S. Sediva and M. Havlikova, Comparison of GUM and Monte Carlo method for evaluation measurement uncertainty of indirect measurements, Proceedings of the 14th international carpathian control conference (ICCC), 26–29 May 2013, Rytro, Poland.Google Scholar
  13. [13]
    M. Á. Herrador, A. G. Asuero and A. G. González, Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo method: an overview, Chemom. Intell. Lab. Syst., 79 (2005) 115–122.Google Scholar
  14. [14]
    D. N. Joanes and C. A. Gill, Comparing measures of sample skewness and kurtosis, Statistician, 47 (1998) 183–189.Google Scholar
  15. [15]
    D. P. Doane and L. E. Seward, Measuring skewness: a forgotten statistic, J. Stat. Educ., 19 (2011) 1–18.Google Scholar
  16. [16]
    C. Stein, A two-sample test for a linear hypothesis whose power is independent of the variance, Ann. Math. Stat., 16 (1945) 243–58.MathSciNetzbMATHGoogle Scholar
  17. [17]
    Crystal Ball software, Oracle Crystal ball spreadsheet, Accessed 28 Aug 2019.
  18. [18]
    @Risk and Decisions Tool suite, Palisade, Accessed 28 Aug 2019.
  19. [19]
    Analytica, Lumina, Accessed 28 Aug 2019.
  20. [20]
    The Evaluator, Newton Metrology, Inc., Accessed 28 Aug 2019.
  21. [21]
    L. Klaus and S. Eichstädt, Monte-Carlo-based uncertainty propagation with hierarchical models: a case study in dynamic torque, Metrologia, 55 (2018) S70–SS85.ADSGoogle Scholar
  22. [22]
    K. Rost, K. Wendt and F. Härtig, Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation, Precis. Eng., 44 (2016) 220–230.Google Scholar
  23. [23]
    A. S. Tistomo, D. Larassati, A. Achmadi, Purwowibowo and G. Zaid, Estimation of uncertainty in the calibration of industrial platinum resistance thermometers (IPRT) using Monte Carlo method, MAPAN-J. Metrol. Soc India, 32 (2017) 273–278.Google Scholar
  24. [24]
    J. Yang, G. Li, B. Wu, J. Gong, J. Wang and M. Zhang, Efficient methods for evaluating task-specific uncertainty in laser-tracking measurement, MAPAN-J. Metrol. Soc India, 30 (2015) 105–117.Google Scholar
  25. [25]
    Y. U. Ko and M. S. Chung, Monte Carlo simulation of charging effects in linewidth metrology (II): on insulator substrate, Scanning, 20 (1998) 549–555.Google Scholar
  26. [26]
    S. Iakovidis, C. Apostolidis and T. Samaras, Application of the Monte Carlo method for the estimation of uncertainty in radiofrequency field spot measurements, Meas. Sci. Rev., 15(2015) 72–76.ADSGoogle Scholar
  27. [27]
    T. Poikonen, P. Blattner, P. Kärhä and E. Ikonen, Uncertainty analysis of photometer directional response index f 2 using Monte Carlo simulation, Metrologia, 49 (2012) 727–736.ADSGoogle Scholar
  28. [28]
    V. Schaller, G. Wahnström, A. S. Velasco, P. Enoksson and C. Johansson, Monte Carlo simulation of magnetic multi-core nanoparticles, J. Magn. Magn. Mater., 321 (2009) 1400–1403.ADSGoogle Scholar
  29. [29]
    W. Helin, L. Zuli and Y. Kailun, Monte Carlo simulation of thin-film growth on a surface with a triangular lattice, Vacuum, 52 (1999) 435–440.ADSGoogle Scholar
  30. [30]
    C. C. Chuang, Y. T. Lee, C. M. Chen, Y. S. Hsieh, T. C. Liu and C. W. Sun, Patient-oriented simulation based on Monte Carlo algorithm by using MRI data, BioMed. Eng. OnLine, 11 (2012) 21.Google Scholar
  31. [31]
    G. E. Evans and B. Jones, The application of Monte Carlo simulation in finance, economics and operations management, World congress on computer science and information engineering, 31st March–2nd April 2009, Los Angeles, CA, USA.Google Scholar
  32. [32]
    P. Furness, Applications of Monte Carlo simulation in marketing analytics, J. Direct Data Dig. Mark. Pract., 13 (2011) 132–147.Google Scholar
  33. [33]
    Y. H. Kwak and L. Ingall, Exploring Monte Carlo simulation applications for project management, Risk Manag., 9 (2007) 44–57.Google Scholar
  34. [34]
    P. Brandimarte, Handbook in Monte Carlo simulation: applications in financial engineering, risk management, and economics, Wiley, New York, (2014).zbMATHGoogle Scholar
  35. [35]
    D. G. Wang, Q. Q. Dong, J. Du, S. Yang, Y. J. Zhang, G. S. Na, S. G. Ferguson, Z. Wang and T. Zheng, Using Monte Carlo simulation to assess variability and uncertainty of tobacco consumption in a city by sewage epidemiology, BMJ Open, 6 (2016) e010583.Google Scholar
  36. [36]
    K. A. Fichthorn and W. H. Weinberg, Theoretical foundations of dynamical Monte Carlo simulations, J. Chem. Phys., 95 (1991) 1090–1096.ADSGoogle Scholar
  37. [37]
    V. Sizyuk and A. Hassanein, Efficient Monte Carlo simulation of heat conduction problems for integrated multi-physics applications, Numer. Heat Transf. Part B Fundam., 66 (2014) 381–396.ADSGoogle Scholar
  38. [38]
    A. Kolinski, L. Jaroszewski, P. Rotkiewicz, J. Skolnick, An efficient Monte Carlo model of protein chains. Modeling the short-range correlations between side group centers of mass. J. Phys. Chem. B, 102 (1998) 4628–4637.Google Scholar
  39. [39]
    A. Sutresno, F. Haryanto, S. Viridi and I. Arif, Investigation Monte Carlo simulation for 3 compartment model as biology system in urinary, Adv. Sci. Eng. Med., 7 (2015) 888–891.Google Scholar
  40. [40]
    Y. Zhao, H. Hou and Y. Zhao, Monte-Carlo simulation of grain growth in vapor–liquid–solid phase sintered materials, J. Comput. Theor. Nanosci., 4 (2011) 2311–2315.Google Scholar
  41. [41]
    A. Srivastava, K. P. Singh and S. B. Degweker, Monte Carlo methods for reactor kinetic simulations, Nucl. Sci. Eng., 189 (2018) 152–170.Google Scholar
  42. [42]
    N. Lanconelli, The importance of Monte Carlo simulations in modeling detectors for Nuclear Medicine, Math. Comput. Simul., 80 (2010) 2109–2114.MathSciNetzbMATHGoogle Scholar
  43. [43]
    A. G. Osborne and M. R. Deinert, Comparison of neutron diffusion and Monte Carlo simulations of a fission wave, Ann. Nucl. Energy, 62 (2013) 269–273.Google Scholar
  44. [44]
    S. Duffy and D. W. Schaffner, Monte Carlo simulation of the risk of contamination of apples with Escherichia coli O157:H7, Int. J. Food Microbiol., 78 (2002) 245–255.Google Scholar
  45. [45]
    M. Dekker and R. Verkerk, Dealing with variability in food production chains: a tool to enhance the sensitivity of epidemiological studies on phytochemicals, Eur. J. Nutr., 42 (2003) 67–72.Google Scholar
  46. [46]
    C. F. M. Carobbi, The GUM Supplement 1 and the Uncertainty Evaluations of EMC Measurements, 2010, Accessed 28 Aug 2019.
  47. [47]
    P. R. G. Couto, J. C. Damasceno and S. P. de Oliveira, Monte Carlo simulations applied to uncertainty in measurement, Chapter 2, Theory and applications of Monte Carlo simulations, 27–51, (2013). Scholar
  48. [48]
    A. Lepek, A computer program for a general case evaluation of the expanded uncertainty, Accredit. Qual. Assur., 8 (2003) 296–299.Google Scholar
  49. [49]
    M. Á. Herrador and A. G. González, Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo Simulation, Talanta, 64 (2004) 415–422.Google Scholar
  50. [50]
    I. T. Dimov, Monte Carlo method for applied scientist, World Scientific Publishing Co., Singapore, 67–132, (2008).Google Scholar
  51. [51]
    K. Shahanaghi and P. Nakhjiri, A new optimized uncertainty evaluation applied to the Monte-Carlo simulation in platinum resistance thermometer calibration, Measurement, 43 (2010) 901–911.Google Scholar
  52. [52]
    H. J. von Martens, Evaluation of uncertainty in measurements: problems and tools, Opt. Lasers Eng., 38 (2002) 185–206.ADSGoogle Scholar
  53. [53]
    I. Lira and W. Wöger, Comparison between the conventional and Bayesian approaches to evaluate measurement uncertainty, Metrologia, 43 (2006) S249–S259.ADSGoogle Scholar

Copyright information

© Metrology Society of India 2019

Authors and Affiliations

  1. 1.CSIR-National Physical LaboratoryNew DelhiIndia

Personalised recommendations