Skip to main content
SpringerLink
Log in

Influence of probability distribution in measurement uncertainty of plane-strain fracture toughness test

  • Practitioner's Report
  • Published:
Accreditation and Quality Assurance Aims and scope Submit manuscript

Abstract

The evaluation of measurement uncertainty by testing laboratories has a direct impact on the interpretation of the results. In several cases, it is recommended to determine the measurement uncertainty by the Monte Carlo method (MCM), which considers the propagation of distributions rather than the propagation of uncertainty. Measurement uncertainty of plane-strain fracture toughness KIC test was evaluated through the MCM and an examination of the influence of the probability distribution on the uncertainty values was performed through analysis of variance (ANOVA). In addition, results were compared to those obtained by the Guide to the Expression of Uncertainty in Measurement (GUM). Results demonstrate the importance of using the Monte Carlo method for the evaluation of measurement uncertainty and confirm that the probability distribution of input data has a significant influence on the expanded uncertainty values obtained for the plane-strain fracture toughness test.

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

References

  1. ISO/IEC 17025 (2017) General requirements for the competence of testing and calibration laboratories

  2. Oliveira SP, Rocha AC, Filho JT, Couto PRG (2009) Uncertainty of measurement by Monte-Carlo simulation and metrological reliability in the evaluation of electric variables of PEMFC and SOFC fuel cells. Meas J Int Meas Confed 42:1497–1501. https://doi.org/10.1016/j.measurement.2009.08.005

    Article  Google Scholar 

  3. Chen A, Chen C (2016) Comparison of GUM and Monte Carlo methods for evaluating measurement uncertainty of perspiration measurement systems. Meas J Int Meas Confed 87:27–37. https://doi.org/10.1016/j.measurement.2016.03.007

    Article  Google Scholar 

  4. Fabricio DAK, da Hack P, Caten ten CS (2016) Estimation of the measurement uncertainty in the anisotropy test. Meas J Int Meas Confed 93:303–309. https://doi.org/10.1016/j.measurement.2016.07.027

    Article  Google Scholar 

  5. Kuhinek D (2011) Measurement uncertainty in testing of uniaxial compressive strength and deformability of rock samples. Meas Sci Rev 11:112–117

    Google Scholar 

  6. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2008) Evaluation of measurement data: Guide to the expression of uncertainty in measurement (GUM 1995 with minor corrections)

  7. Herrador MA, González AG (2004) Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation. Talanta 64:415–422. https://doi.org/10.1016/j.talanta.2004.03.011

    Article  CAS  Google Scholar 

  8. Cox MG, Dainton MP, Harris PM (2002) Software support for metrology best practice guide no. 6. uncertainty and statistical modelling. Meas Good Pract Guid. https://doi.org/10.1001/jama.285.10.1373

  9. Lepek A (2003) A computer program for a general case evaluation of the expanded uncertainty. Accredit Qual Assur 8:296–299. https://doi.org/10.1007/s00769-003-0649-1

    Article  CAS  Google Scholar 

  10. BIPM, Iec, IFCC, Ilac, ISO, Iupac, IUPAP, OIML (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. Eval JCGM 101(2):90

    Google Scholar 

  11. Wen XL, Zhao YB, Wang DX, 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

    Article  Google Scholar 

  12. Motra HB, Hildebrand J, Wuttke F (2016) The Monte Carlo method for evaluating measurement uncertainty: application for determining the properties of materials. Probab Eng Mech 45:220–228. https://doi.org/10.1016/j.probengmech.2016.04.005

    Article  Google Scholar 

  13. Shahanaghi K, Nakhjiri P (2010) A new optimized uncertainty evaluation applied to the Monte-Carlo simulation in platinum resistance thermometer calibration. Meas J Int Meas Confed 43:901–911. https://doi.org/10.1016/j.measurement.2010.03.008

    Article  Google Scholar 

  14. Herrador MÁ, Asuero AG, González AG (2005) Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo method: an overview. Chemom Intell Lab Syst 79:115–122. https://doi.org/10.1016/j.chemolab.2005.04.010

    Article  CAS  Google Scholar 

  15. Martins MAF, Requião R, Kalid RA (2011) Generalized expressions of second and third order for the evaluation of standard measurement uncertainty. Meas J Int Meas Confed 44:1526–1530. https://doi.org/10.1016/j.measurement.2011.06.008

    Article  Google Scholar 

  16. Zhu T, Liu X, Connelly PR, Zhong J (2008) An optimized wild bootstrap method for evaluation of measurement uncertainties of DTI-derived parameters in human brain. Neuroimage 40:1144–1156. https://doi.org/10.1016/j.neuroimage.2008.01.016

    Article  PubMed  Google Scholar 

  17. Hiller J, Reindl LM (2012) A computer simulation platform for the estimation of measurement uncertainties in dimensional X-ray computed tomography. Measurement 45:2166–2182. https://doi.org/10.1016/j.measurement.2012.05.030

    Article  Google Scholar 

  18. Rost K, Wendt K, Härtig F (2015) Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation. Precis Eng 44:220–230. https://doi.org/10.1016/j.precisioneng.2016.01.001

    Article  Google Scholar 

  19. Garcia E, Hausotte T, Amthor A (2013) Bayes filter for dynamic coordinate measurements—accuracy improvment, data fusion and measurement uncertainty evaluation. Meas J Int Meas Confed 46:3737–3744. https://doi.org/10.1016/j.measurement.2013.04.001

    Article  Google Scholar 

  20. Leyi G, Wei Z, Jing Z, Songling H (2011) Mechanics analysis and simulation of material Brinell hardness measurement. Measurement 44:2129–2137. https://doi.org/10.1016/j.measurement.2011.07.024

    Article  Google Scholar 

  21. Vujisić M, Stanković K, Osmokrović P (2011) A statistical analysis of measurement results obtained from nonlinear physical laws. Appl Math Model 35:3128–3135. https://doi.org/10.1016/j.apm.2010.12.017

    Article  Google Scholar 

  22. Stanković K, Vujisić M, Kovačević D, Osmokrović P (2011) Statistical analysis of the characteristics of some basic mass-produced passive electrical circuits used in measurements. Measurement 44:1713–1722. https://doi.org/10.1016/j.measurement.2011.07.007

    Article  Google Scholar 

  23. Kovačević A, Brkić D, Osmokrović P (2011) Evaluation of measurement uncertainty using mixed distribution for conducted emission measurements. Measurement 44:692–701. https://doi.org/10.1016/j.measurement.2010.12.006

    Article  Google Scholar 

  24. Heasler PG, Burr T, Reid B et al (2006) Estimation procedures and error analysis for inferring the total plutonium (Pu) produced by a graphite-moderated reactor. Reliab Eng Syst Saf 91:1406–1413. https://doi.org/10.1016/j.ress.2005.11.036

    Article  Google Scholar 

  25. Lam JC, Chan K, Yip Y et al (2010) Accurate determination of lead in Chinese herbs using isotope dilution inductively coupled plasma mass spectrometry (ID-ICP-MS). Food Chem 121:552–560. https://doi.org/10.1016/j.foodchem.2009.12.046

    Article  CAS  Google Scholar 

  26. Theodorou D, Zannikou Y, Zannikos F (2015) Components of measurement uncertainty from a measurement model with two stages involving two output quantities. Chemom Intell Lab Syst 146:305–312. https://doi.org/10.1016/j.chemolab.2015.05.025

    Article  CAS  Google Scholar 

  27. Mondéjar ME, Segovia JJ, Chamorro CR (2011) Improvement of the measurement uncertainty of a high accuracy single sinker densimeter via setup modifications based on a state point uncertainty analysis. Measurement 44:1768–1780. https://doi.org/10.1016/j.measurement.2011.07.012

    Article  Google Scholar 

  28. Marton D, Starý M, Menšík P (2014) Water management solution of reservoir storage function under condition of measurement uncertainties in hydrological input data. Procedia Eng 70:1094–1101. https://doi.org/10.1016/j.proeng.2014.02.121

    Article  Google Scholar 

  29. Locci N, Muscas C, Ghiani E (2002) Evaluation of uncertainty in measurements based on digitized data. 32:265–272

    Google Scholar 

  30. Anderson TL (2005) Fracture mechanics: fundamentals and applications, 3rd edn. CRC, New York

    Book  Google Scholar 

  31. ASTM (2013) E399–12e3 Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K1C of Metallic Material. ASTM Int. https://doi.org/10.1520/E0399-12E03.2

    Article  Google Scholar 

  32. Gonçalves DRR, Peixoto RAF (2015) Beneficiamento de escórias na aciaria: Um estudo da viabilidade econômica da utilização dos produtos na siderurgia e na construção civil. Rev ABM Metal Mater e Mineração 71:506–510

    Google Scholar 

  33. Albano F de M (2016) Desenvolvimento de melhorias no processo de provisão de ensaios de proficiência por comparação interlaboratorial. Universidade Federal do Rio Grande do Sul

  34. Angrisani L, Lo Moriello RS, D’Apuzzo M (2006) New proposal for uncertainty evaluation in indirect measurements. IEEE Trans Instrum Meas 55:1059–1064. https://doi.org/10.1109/TIM.2006.876540

    Article  Google Scholar 

  35. Ghiani E, Locci N, Muscas C (2004) Auto-evaluation of the uncertainty in virtual instruments. IEEE Trans Instrum Meas 53:672–677. https://doi.org/10.1109/TIM.2004.827080

    Article  Google Scholar 

  36. Lampasi DA, Di Nicola F, Podesta L (2006) Generalized lambda distribution for the expression of measurement uncertainty. IEEE Trans Instrum Meas 55:1281–1287. https://doi.org/10.1109/TIM.2006.876408

    Article  Google Scholar 

  37. Randa J (2009) Uncertainty analysis for noise-parameter measurements at NIST. IEEE Trans Instrum Meas 58:1146–1151. https://doi.org/10.1109/TIM.2008.2007044

    Article  Google Scholar 

  38. Tokarska M (2014) Evaluation of measurement uncertainty of fabric surface resistance implied by the Van der Pauw equation. IEEE Trans Instrum Meas 63:1593–1599. https://doi.org/10.1109/TIM.2013.2289695

    Article  Google Scholar 

  39. 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

    Article  Google Scholar 

  40. European Committee for Standardization (2011) EN 13674-1—Railway applications—Track-Rail—Part 1: Vignole railway rails 46 kg/m and above

  41. Ribeiro JL, Ten Caten CS (2011) Série Monográfica Qualidade: Projeto de Experimentos. Porto Alegre

  42. Zangl H, Hoermaier K (2017) Educational aspects of uncertainty calculation with software tools. Meas J Int Meas Confed 101:257–264. https://doi.org/10.1016/j.measurement.2015.11.005

    Article  Google Scholar 

  43. Krechmer K (2016) Relational measurements and uncertainty. Meas J Int Meas Confed 93:36–40. https://doi.org/10.1016/j.measurement.2016.06.058

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the support of CNPq (National Council for Scientific and Technological Development—Brazil), grant number 140141/2017-0, and CAPES (Coordination for the Improvement of Higher Education Personnel—Brazil).

Author information

Authors and Affiliations

  1. Federal Institute of Santa Catarina, 3450-D Nereu Ramos Avenue, Chapecó, SC, 89813-000, Brazil

    Daniel Antonio Kapper Fabricio

  2. Department of Industrial Engineering and Transportation, Federal University of Rio Grande do Sul, 99 Osvaldo Aranha Avenue, 5th floor, Porto Alegre, RS, 90035-190, Brazil

    Carla Schwengber ten Caten

  3. Federal Institute of Rio Grande do Sul, 750 São Vicente Avenue, Farroupilha, RS, 95180-000, Brazil

    Lisiane Trevisan

  4. Physical Metallurgy Laboratory, Federal University of Rio Grande do Sul, 99 Osvaldo Aranha Avenue, Room 610, Porto Alegre, RS, 90035-190, Brazil

    Afonso Reguly

Authors
  1. Daniel Antonio Kapper Fabricio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carla Schwengber ten Caten
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lisiane Trevisan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Afonso Reguly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Antonio Kapper Fabricio.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fabricio, D.A.K., Caten, C.S., Trevisan, L. et al. Influence of probability distribution in measurement uncertainty of plane-strain fracture toughness test. Accred Qual Assur 23, 231–242 (2018). https://doi.org/10.1007/s00769-018-1326-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00769-018-1326-8

Keywords

Search

Navigation