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Measurement Uncertainty Evaluation in Vickers Hardness Scale Using Law of Propagation of Uncertainty and Monte Carlo Simulation

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Abstract

The Monte Carlo simulation (MCS) method for uncertainty evaluation of measurement results has gained popularity as an alternative to the method based on law of propagation of uncertainty (LPU) ever since the recommendation by JCGM through supplement JCGM 101:2008. In this paper, efforts have been made to compute the uncertainty in measurement of hardness in the Vickers hardness scale using MCS and LPU method. Three different hardness blocks of different hardness scales, namely HV1, HV10 and HV30, have been calibrated following the standard procedure in the primary Vickers hardness machine established in CSIR-National Physical Laboratory. The mean hardness values and the associated measurement uncertainty of the hardness blocks are computed using LPU and MCS methods. A comparison of the results obtained through LPU and MCS methods has been carried out. It is observed that there is a good agreement between findings from both the methods adopted, hence confirming that MCS method can be employed in the various fields of hardness metrology for evaluation of measurement uncertainty.

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References

  1. H.W. Coleman and W.G. Steele, Experimentation, validation, and uncertainty analysis for engineers, John Wiley & Sons, New York, (2018).

    Book  Google Scholar 

  2. E. Savio, L. De Chiffre, S. Carmignato and J. Meinertz, Economic benefits of metrology in manufacturing, CIRP Ann., 65 (2016) 495–498.

    Article  Google Scholar 

  3. J.C. Damasceno and P.R. Couto, Methods for evaluation of measurement uncertainty (2018). https://doi.org/10.5772/intechopen.74873.

    Google Scholar 

  4. P. Harris and M. Cox, On a Monte Carlo method for measurement uncertainty evaluation and its implementation, Metrologia, 51 (2014) S176.

    Article  ADS  Google Scholar 

  5. A.G. Gonzalez, M.A. Herrador and A.G. Asuero, Uncertainty evaluation from Monte-Carlo simulations by using Crystal-Ball software, Accredit. Qual. Assur., 10 (2005) 149–154.

    Article  Google Scholar 

  6. H. Kumar, G. Moona, P. Arora, A. Haleem, J. Singh, R. Kumar and A. Kumar, Monte carlo method for evaluation of uncertainty of measurement in brinell hardness scale, Indian J. Pure Appl. Phys. (IJPAP), 55 (2017) 445–453.

    Article  ADS  Google Scholar 

  7. 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.

    Google Scholar 

  8. A. Lepek, A computer program for a general case evaluation of the expanded uncertainty, Accredit. Qual. Assur., 8 (2003) 296–299.

    Article  Google Scholar 

  9. Y. JCGM, Evaluation of measurement data—supplement 1 to the guide to the expression of uncertainty in measurement-propagation of distributions using a Monte Carlo method, Organisation for Standardization (Geneva, Switzerland), 2008.

  10. 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.

    Article  Google Scholar 

  11. M.S.B. Fernández, V.O. López and R.S. López, On the uncertainty evaluation for repeated measurements, MAPAN J. Metrol. Soc. India, 29 (2014) 19–28.

    Article  Google Scholar 

  12. K. Herrmann, Hardness testing: principles and applications, ASM International, Geauga County (2011).

    Google Scholar 

  13. ISO 6507-1: 2005, Metallic materials—Vickers hardness test, ed, 2005.

  14. M.P. Olaniya, P Kandpal, A Acharya, A.S. Gupta, A. Arora, D. Suresh and T.S. Ganesh, Timing traceability and the link between ISRO-NPLI, MAPAN J. Metrol. Soc. India, 33 (2018) 369–375

    Article  Google Scholar 

  15. S. Yadav, A. Zafer, A. Kumar, N.D. Sharma and D.K. Aswal, Role of national pressure and vacuum metrology in Indian industrial growth and their global metrological equivalence, MAPAN J. Metrol. Soc. India, 33 (2018) 347–359.

    Article  Google Scholar 

  16. G. Moona, M. Jewariya and R. Sharma, Relevance of dimensional metrology in manufacturing industries, MAPAN J. Metrol. Soc. India, 34 (2019) 97–104.

    Article  Google Scholar 

  17. U. Pant, H. Meena and D.D. Shivagan, Development and realization of iron–carbon eutectic fixed point at NPLI, MAPAN J. Metrol. Soc. India, 33 (2018) 201–208.

    Article  Google Scholar 

  18. S.S. Titus and S.K. Jain, Metrological characterization of the Vickers hardness primary standard machine established at CSIR-NPL, J. Inst. Eng. (India) Ser. C, 99 (2018) 315–321.

    Article  Google Scholar 

  19. G.M. Mahmoud and R.S. Hegazy, Comparison of GUM and Monte Carlo methods for the uncertainty estimation in hardness measurements, Int. J. Metrol. Qual. Eng., 8 (2017) 14. https://doi.org/10.1051/ijmqe/2017014.

    Article  Google Scholar 

  20. S. Raychaudhuri, Introduction to Monte Carlo simulation: Proceedings of the 2008 winter simulation conference Oracle Crystal Ball Global Business Unit 390 Interlocken Crescent, ed: Suite, 2008.

  21. M. Cox, P. Harris and B.-L. Siebert, Evaluation of measurement uncertainty based on the propagation of distributions using Monte Carlo simulation, Meas. Tech., 46 (2013) 824–833.

    Article  Google Scholar 

  22. C.E. Papadopoulos and H. Yeung, Uncertainty estimation and Monte Carlo simulation method, Flow Measur. Instrum., 12 (2001) 291–298.

    Article  Google Scholar 

  23. M.G. Cox and B.R. Siebert, The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty, Metrologia, 43 (2006) S178.

    Article  ADS  Google Scholar 

  24. 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.

    Article  Google Scholar 

  25. R. Palenčár, P. Sopkuliak, J. Palenčár, S. Ďuriš, E. Suroviak and M. Halaj, Application of Monte Carlo method for evaluation of uncertainties of ITS-90 by standard platinum resistance thermometer, Measur. Sci. Rev., 17 (2017) 108–116.

    Article  ADS  Google Scholar 

  26. A.S. Tistomo, D. Larassati, A. Achmadi 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.

    Article  Google Scholar 

  27. J. Singh, L. Kumaraswamidhas, K. Kaushik, N. Bura and N.D. Sharma, Uncertainty analysis of distortion coefficient of piston gauge using monte carlo method, MAPAN J. Metrol. Soc. India (2019) 1–7. https://doi.org/10.1007/s12647-019-00305-z.

  28. H. Schwenke, B. Siebert, F. Wäldele and H. Kunzmann, Assessment of uncertainties in dimensional metrology by Monte Carlo simulation: proposal of a modular and visual software, CIRP Ann., 49 (2000) 395–398.

    Article  Google Scholar 

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Acknowledgements

The authors are highly grateful the Director, CSIR-NPL, for his support, encouragement and providing infrastructural facilities for carrying out this work. We are also thankful to the Head, Physico-Mechanical Division, CSIR-NPL, for the support and encouragement.

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Correspondence to Indu Elizabeth.

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Elizabeth, I., Kumar, R., Garg, N. et al. Measurement Uncertainty Evaluation in Vickers Hardness Scale Using Law of Propagation of Uncertainty and Monte Carlo Simulation. MAPAN 34, 317–323 (2019). https://doi.org/10.1007/s12647-019-00341-9

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