Central European Journal of Operations Research

, Volume 25, Issue 4, pp 907–928 | Cite as

Treating measurement uncertainty in industrial conformity control

  • Zsolt T. Kosztyán
  • Csaba Hegedűs
  • Attila Katona
Original Paper

Abstract

Every conformity control method based on measurements is subject to uncertainty, which distorts the decision. In the traditional conformity control approaches, this uncertainty is an inherent part of the deviation of the observed characteristic; however, the distribution of the real product characteristic may differ from the distribution of measurement uncertainty, which obscures the real conformity or nonconformity. The specification and consideration of this uncertainty are particularly necessary if it is high and/or the consequences associated with the decision errors are severe. This paper studies the effects of the cost structure associated with the decision outcomes and the skewness and kurtosis of the measurement uncertainty distribution. The proposed method can specify when and how the measurement uncertainty should be taken into account to increase the expected profit associated with the decision.

Keywords

Optimization Quality control Uncertainty Risk of decision 

Notes

Acknowledgements

Funding was provided by Magyar Tudományos Akadémia (Bolyai Hungarian Post-Doctoral Fellowship).

References

  1. AIAG (2010) Measurement system analysis, 4th edn. ASQ AIAG—The Automotive Industries Action Group, Southfield, MIGoogle Scholar
  2. Albers W, Kallenberg W, Nurdiati S (2006) Data driven choice of control charts. J Stat Plan Inference 136(3):909–941CrossRefGoogle Scholar
  3. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2008a) Evaluation of measurement data—guide to the expression of uncertainty in measurement, JCGM 100:2008. Technical report, Joint Committee for Guides in MetrologyGoogle Scholar
  4. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2008b) Evaluation of measurement data—supplement 1 to the ”guide to the expression of uncertainty in measurement”—propagation of distributions using a monte carlo method. JCGM 101:2008. Technical report, Joint Committee for Guides in MetrologyGoogle Scholar
  5. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML (2012) Evaluation of measurement data—the role of measurement uncertainty in conformity assessment. JCGM 106:2012. Technical report, Joint Committee for Guides in MetrologyGoogle Scholar
  6. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML (1995) Guide to the expression of uncertainty in measurement. Technical report, International Organization for Standardization, GenevaGoogle Scholar
  7. D’Agostini G (2004) Asymmetric uncertainties: sources, treatment and potential dangers. arXiv preprint arXiv:physics/0403086
  8. Esseen CG (1956) A moment inequality with an application to the central limit theorem. Scand Actuar J 1956(2):160–170CrossRefGoogle Scholar
  9. Eurachem (2007) Use of uncertainty information in compliance assessment. Technical report, EurachemGoogle Scholar
  10. Forbes AB (2006) Measurement uncertainty and optimized conformance assessment. Measurement 39(9):808–814CrossRefGoogle Scholar
  11. Heping P, Xiangqian J (2009) Evaluation and management procedure of measurement uncertainty in new generation geometrical product specification (gps). Measurement 42(5):653–660CrossRefGoogle Scholar
  12. Herrador MA, González A (2004) Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation. Talanta 64(2):415–422CrossRefGoogle Scholar
  13. ILAC (1996) Guidelines on assessment and reporting of compliance with specification. ILAC-G8:1996. Technical report, International Laboratory Accreditation Cooperation, Silverwater, AustraliaGoogle Scholar
  14. ISO (1999) Sampling procedures for inspection by attributes—Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection (ISO 2859-1:1999). Technical Report, International Organization for Standardization, GenevaGoogle Scholar
  15. Jones FE, Schoonover RM (2002) Handbook of mass measurement. CRC Press, Boca RatonCrossRefGoogle Scholar
  16. Mielniczuk J (1986) Some asymptotic properties of kernel estimators of a density function in case of censored data. Ann Stat 14(2):766–773CrossRefGoogle Scholar
  17. Montgomery DC (2012) Statistical quality control, 7th edn. Wiley, New YorkGoogle Scholar
  18. Pavlovčič F, Nastran J, Nedeljković D (2009) Determining the 95 probability distributions. In: XIX IMEKO world congress fundamental and applied metrology. September 6–11, 2009, Lisbon, Portugal. IMEKO, pp 2338–2342Google Scholar
  19. Pendrill L (2014) Using measurement uncertainty in decision-making and conformity assessment. Metrologia 51(4):S206–S218CrossRefGoogle Scholar
  20. Pendrill LR (2008) Operating ’cost’ characteristics in sampling by variable and attribute. Accredit Qual Assur 13(11):619–631CrossRefGoogle Scholar
  21. Rabinovich SG (2006) Measurement errors and uncertainties, 3rd edn. Springer, New YorkGoogle Scholar
  22. Rényi A (1953) On the theory of order statistics. Acta Math Hungar 4(3–4):191–231CrossRefGoogle Scholar
  23. Rossi G (2014) Measurement-based decisions. In: Measurement and probability, Springer Series in Measurement Science and Technology. Springer, Netherlands, pp 237–251Google Scholar
  24. Rossi GB, Crenna F (2006) A probabilistic approach to measurement-based decisions. Measurement 39(2):101–119CrossRefGoogle Scholar
  25. Schilling EG, Neubauer DV (2009) Acceptance Sampling in Quality Control, 2nd edn. CRC Press, Boca RatonGoogle Scholar
  26. Shevtsova I (2011) On the absolute constants in the berry-esseen type inequalities for identically distributed summands. arXiv preprint arXiv:1111.6554
  27. Synek V (2006) Effect of insignificant bias and its uncertainty on the coverage probability of uncertainty intervals part 1. evaluation for a given value of the true bias. Talanta 70(5):1024–34CrossRefGoogle Scholar
  28. Synek V (2007) Effect of insignificant bias and its uncertainty on the coverage probability of uncertainty intervals part 2. evaluation for a found insignificant experimental bias. Talanta 71(3):1304–11CrossRefGoogle Scholar
  29. Vilbaste M, Slavin G, Saks O, Pihl V, Leito I (2010) Can coverage factor 2 be interpreted as an equivalent to 95% coverage level in uncertainty estimation? two case studies. Measurement 43(3):392–399CrossRefGoogle Scholar
  30. von Martens H-J (2002) Evaluation of uncertainty in measurements—problems and tools. Opt Lasers Eng 38(3):185–206CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Quantitative MethodsUniversity of PannoniaVeszprémHungary

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