Skip to main content
SpringerLink
Log in

Evaluation of Uncertainty in the Effective Area and Distortion Coefficients of Air Piston Gauge Using Monte Carlo Method

  • Original Paper
  • Published:
MAPAN Aims and scope Submit manuscript

Abstract

The fixed number of trials in the Monte Carlo method (FMCM) has been employed for the evaluation of effective area along with their associated uncertainties and distortion coefficients of piston–cylinder (p–c) assembly of the air piston gauge with varying pressures ranging from 6.5 to 360 kPa. The FMCM uncertainty values are compared with the conventional method, i.e., the law of propagation of uncertainty in the experimental range 20–120 kPa using our primary pressure standard, i.e., ultrasonic interferometer manometer. It is observed that the relative uncertainty of the effective area using FMCM (~ 9.5 ppm) is lesser than that of the experimental value (~ 9.7 ppm) using the same parameters responsible for uncertainty measurement which leads to the quality enhancement in the measurement of pressure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. M. Désenfant, M. Priel, Road map for measurement uncertainty evaluation, Meas. J. Int. Meas. Confed. 39 (2006) 841–848. https://doi.org/10.1016/j.measurement.2006.04.008.

    Article  Google Scholar 

  2. Guide to the Expression of Uncertainty in Measurement, ISO/IEC Guid. 98 (1992):1993.

    Google Scholar 

  3. D. da Jornada, Uso de Planilhas Eletrônicas para Implementação do Método de Monte Carlo para Estimativa de Incerteza de Medição, Encontro Qual. Laboratórios. (2005).

    Google Scholar 

  4. P.M. Harris, M.G. Cox, On a Monte Carlo method for measurement uncertainty evaluation and its implementation, Metrologia. 51 (2014) S176–S182. https://doi.org/10.1088/0026-1394/51/4/s176.

    Article  ADS  Google Scholar 

  5. Krouwer JS, Critique of the Guide to the expression of uncertainty in measurement method of estimating and reporting uncertainty in diagnostic assays. PubMed NCBI, Clin Chem. 49 (2003) 1818–21. https://www.ncbi.nlm.nih.gov/pubmed/14578312.

    Article  Google Scholar 

  6. A. Kallner, L. Khorovskaya, T. Pettersson, A method to estimate the uncertainty of measurements in a conglomerate of instruments/laboratories, Scand. J. Clin. Lab. Invest. 65 (2005) 551–558. https://doi.org/10.1080/00365510500206567.

    Article  Google Scholar 

  7. M. Panteghini, Application of traceability concepts to analytical quality control may reconcile total error with uncertainty of measurement, Clin. Chem. Lab. Med. 48 (2010) 7–10. https://doi.org/10.1515/cclm.2010.020.

    Article  Google Scholar 

  8. B. Magnusson, H. Ossowicki, O. Rienitz, E. Theodorsson, Routine internal- and external-quality control data in clinical laboratories for estimating measurement and diagnostic uncertainty using GUM principles, Scand. J. Clin. Lab. Invest. 72 (2012) 212–220. https://doi.org/10.3109/00365513.2011.649015.

    Article  Google Scholar 

  9. Evaluation of Measurement Data—Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement”—Propagation of Distributions Using a Monte Carlo Method (2008).

  10. J.O. Westgard, R.N. Carey, S. Wold, Criteria for judging precision and accuracy in method development and evaluation, Clin. Chem. 20 (1974) 825–833. http://www.ncbi.nlm.nih.gov/pubmed/4835236 (accessed April 25, 2019).

  11. J.S. Krouwer, Estimating total analytical error and its sources. Techniques to improve method evaluation, Arch. Pathol. Lab. Med. 116 (1992) 726–731. http://www.ncbi.nlm.nih.gov/pubmed/1497445 (accessed April 25, 2019).

  12. J.S. Krouwer, Setting performance goals and evaluating total analytical error for diagnostic assays, Clin. Chem. 48 (2002) 919–927. http://www.ncbi.nlm.nih.gov/pubmed/12029009 (accessed April 25, 2019).

  13. V.M. Chinchilli, W.G. Miller, Evaluating test methods by estimating total error, Clin. Chem. 40 (1994) 464–471. http://www.ncbi.nlm.nih.gov/pubmed/8131284 (accessed April 25, 2019).

  14. U.S. Ellison Secretary, R. Bettencourt da Silva, E.P. Poland Fodor, R. Kaarls, E.B. Germany Magnusson, I.P. Robouch, E. St Gallen, S.A. van der Veen, M.W. Walsh Eurachem IRE Wegscheider, P. Yolci Omeroglu, E. Representatives, EURACHEM/CITAC Guide Quantifying Uncertainty in Analytical Measurement Composition of the Working Group* EURACHEM, 2012. https://www.eurachem.org/images/stories/Guides/pdf/QUAM2012_P1.pdf (accessed April 25, 2019).

  15. R. Frenkel, Statistical background to the ISO guide to the expression of uncertainty in measurement, 3rd ed., National Measurement Institute, Lindfield N.S.W., 2011. https://www.worldcat.org/title/statistical-background-to-the-iso-guide-to-the-expression-of-uncertainty-in-measurement/oclc/824564464 (accessed April 25, 2019).

  16. M.G. Cox, B.R.L. Siebert, The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty, Metrologia. 43 (2006) S178–S188. https://doi.org/10.1088/0026-1394/43/4/s03.

    Article  ADS  Google Scholar 

  17. M. Cox, P. Harris, B.R.-L. Siebert, Evaluation of measurement uncertainty based on the propagation of distributions using Monte Carlo simulation, Meas. Tech. 46 (2003) 824–833. https://doi.org/10.1023/b:mete.0000008439.82231.ad.

    Article  Google Scholar 

  18. G. Chew, T. Walczyk, A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software, Anal. Bioanal. Chem. 402 (2012) 2463–2469. https://doi.org/10.1007/s00216-011-5698-4.

    Article  Google Scholar 

  19. J. Singh, L.A. Kumaraswamidhas, A. Vijay, A. Kumar, N.D. Sharma, Estimation of uncertainty of effective area of a pneumatic pressure reference standard using Monte Carlo method, Indian J. Pure Appl. Phys. 54 (2016) 755–764.

    Google Scholar 

  20. J. Singh, L.A. Kumaraswamidhas, N.D. Sharma, A comparative investigation of pressure distortion coefficient of a pneumatic piston gauge and its associated uncertainty using varied approaches, Accredit. Qual. Assur. 24 (2019) 105–112. https://doi.org/10.1007/s00769-018-1355-3.

    Article  Google Scholar 

  21. A.S. Tistomo, D. Larassati, A. Achmadi, Purwowibowo, G. Zaid, Estimation of uncertainty in the calibration of industrial platinum resistance thermometers (IPRT) using Monte Carlo Method, MAPAN. 32 (2017) 273–278. https://doi.org/10.1007/s12647-017-0222-8.

    Article  Google Scholar 

  22. C.R. Tillyer, Error estimation in the quantification of alkaline phosphatase isoenzymes by selective inhibition methods, Clin. Chem. 34 (1988) 2490–2493. http://clinchem.aaccjnls.org/content/34/12/2490.short (accessed April 25, 2019).

  23. R. Wood, A simulation study of the Westgard multi-rule quality-control system for clinical laboratories, Clin. Chem. 36 (1990) 462–5. http://www.ncbi.nlm.nih.gov/pubmed/2311213 (accessed April 25, 2019).

  24. D. Theodorou, L. Meligotsidou, S. Karavoltsos, A. Burnetas, M. Dassenakis, M. Scoullos, Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS, Talanta. 83 (2011) 1568–1574. https://doi.org/10.1016/j.talanta.2010.11.059.

    Article  Google Scholar 

  25. V. Ramnath, Comparison of the GUM and Monte Carlo measurement uncertainty techniques with application to effective area determination in pressure standards, Int. J. Metrol. Qual. Eng. 1 (2010) 51–57. https://doi.org/10.1051/ijmqe/2010013.

    Article  Google Scholar 

  26. E.W. Holmes, S.E. Kahn, P.A. Molnar, E.W. Bermes, Verification of reference ranges by using a Monte Carlo sampling technique, Clin. Chem. 40 (1994) 2216–2222. http://clinchem.aaccjnls.org/content/40/12/2216.short (accessed April 25, 2019).

  27. T. Kouri, V. Kairisto, A. Virtanen, E. Uusipaikka, A. Rajamäki, H. Finneman, K. Juva, T. Koivula, V. Näntö, Reference intervals developed from data for hospitalized patients: computerized method based on combination of laboratory and diagnostic data, Clin. Chem. 40 (1994) 2209–2215. http://www.ncbi.nlm.nih.gov/pubmed/7988006 (accessed April 25, 2019).

  28. A. Dobney, H. Klinkenberg, F. Souren, W. Van Borm, Uncertainty calculations for amount of chemical substance measurements performed by means of isotope dilution mass spectrometry as part of the PERM project, Anal. Chim. Acta. 420 (2000) 89–94. https://doi.org/10.1016/s0003-2670(00)00971-5.

    Article  Google Scholar 

  29. T. Røraas, P.H. Petersen, S. Sandberg, Confidence intervals and power calculations for within-person biological variation: effect of analytical imprecision, number of replicates, number of samples, and number of individuals, Clin. Chem. 58 (2012) 1306–13. https://doi.org/10.1373/clinchem.2012.187781.

    Article  Google Scholar 

  30. R.F. Martin, General deming regression for estimating systematic bias and its confidence interval in method-comparison studies, Clin. Chem. 46 (2000) 100–104.

    Google Scholar 

  31. J.C. Boyd, D.E. Bruns, Quality specifications for glucose meters: assessment by simulation modeling of errors in insulin dose, Clin. Chem. 47 (2001) 209–214.

    Google Scholar 

  32. J. Middleton, Effect of analytical error on the assessment of cardiac risk by the high-sensitivity C-reactive protein and lipid screening model, Clin. Chem. 48 (2002) 1955–1962.

    Google Scholar 

  33. J. Middleton, J.E. Vaks, Evaluation of assigned-value uncertainty for complex calibrator value assignment processes: a prealbumin example, Clin. Chem. 53 (2007) 735–741. https://doi.org/10.1373/clinchem.2006.081174.

    Article  Google Scholar 

  34. S.Y. Woo, T.H. Yang, H.W. Song, Calibration of a built-in vacuum sensor in a gas pressure balance down to 1 Pa using RPG (Reverse-Operated Piston Gauge), Mapan J. Metrol. Soc. India. (2018). https://doi.org/10.1007/s12647-017-0234-4.

    Article  Google Scholar 

  35. R. Kumar, M.S. Azam, S.K. Ghosh, S. Yadav, 70 years of elastohydrodynamic lubrication (EHL): a review on experimental techniques for film thickness and pressure measurement, MAPAN. 33 (2018) 481–491. https://doi.org/10.1007/s12647-018-0277-1.

    Article  Google Scholar 

  36. A. Kumar, V.N. Thakur, A. Zafer, N.D. Sharma, S. Yadav, D.K. Aswal, Contributions of national standards on the growth of barometric pressure and vacuum industries, MAPAN. 34 (2019) 13–17. https://doi.org/10.1007/s12647-018-0293-1.

    Article  Google Scholar 

  37. S. Yadav, A. Zafer, A. Kumar, N.D. Sharma, D.K. Aswal, Role of national pressure and vacuum metrology in Indian industrial growth and their global metrological equivalence, MAPAN. 33 (2018) 347–359. https://doi.org/10.1007/s12647-018-0270-8.

    Article  Google Scholar 

  38. A. Kumar Vikas, N. Thakur, R. Sharma, H. Kumar, Omprakash, D. A. Vijaykumar, S. Yadav, On long-term stability of an air piston gauge maintained at National Physical Laboratory, India, Measurement. (2019).

  39. National Accreditation Board for Testing and Calibration Laboratories (NABL) Document - 141, Department of Science and Technology, Government of India, New Delhi, 2000.

  40. G. 1995 JCGM 100:2008, Evaluation of measurement data-Guide to the expression of uncertainty in measurement, 2008. www.bipm.org (accessed April 25, 2019).

  41. A. Kumar, V.N. Thakur, R. Sharma, H. Kumar, Omprakash, S. Yadav, Uncertainty evaluation and phase variation of ultrasonic interferometer manometer: a primary pressure and vacuum standard, Vacuum. 165 (2019) 232–238. https://doi.org/10.1016/j.vacuum.2019.04.023.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank dimensional metrology technical staff for the experimental support and CSIR-NPL for the partial financial support. Authors also want to thank Dr. D. K. Aswal (Director, CSIR-NPL) and Dr. Ranjana Mehrotra (Head, Physico-Mechanical Metrology Division, CSIR-NPL) for the constant encouragement. Mr. Vikas thanks UGC for the Ph.D. fellowship and AcSIR, CSIR-NPL for pursuing Ph.D. program.

Author information

Authors and Affiliations

  1. CSIR-National Physical Laboratory (CSIR-NPL), Dr. K. S. Krishnan Road, Delhi, 110012, India

    Vikas N. Thakur, Sanjay Yadav & Ashok Kumar

  2. Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K. S. Krishnan Road, Delhi, 110012, India

    Vikas N. Thakur, Sanjay Yadav & Ashok Kumar

Authors
  1. Vikas N. Thakur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjay Yadav
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ashok Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashok Kumar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thakur, V.N., Yadav, S. & Kumar, A. Evaluation of Uncertainty in the Effective Area and Distortion Coefficients of Air Piston Gauge Using Monte Carlo Method. MAPAN 34, 371–377 (2019). https://doi.org/10.1007/s12647-019-00336-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12647-019-00336-6

Keywords

Search

Navigation