Advertisement

Assessing process capability index using sampling plan in the presence of measurement system errors

  • Adel Brik
  • Mohamed Goddi
  • Jamel Dhahri
  • Nabil Ben FredjEmail author
ORIGINAL ARTICLE

Abstract

Measurement system errors impact the collected data used to evaluate the process capability. The work developed in this paper aims at integrating these errors in the calculation of the threshold value of Cpused for making the decision about the process capability \( \left({C}_{p0}^{\ast}\right) \) and to propose a procedure that corrects the parameters of the sampling plan used to estimate this capability index. An expression of \( {C}_{p0}^{\ast } \)that depends on the gauge repeatability and reproducibility (GR&R), errors type I and type II, the capability index corresponding to the rejectable quality level (CpRQL), and to the acceptable quality level (CpAQL) was developed. The effects of these parameters and their relative interactions on the difference between capability index calculations with and without integrating the measurement system error (ΔCpthreshold) and the corresponding difference in the parts per million of defects ppm (Δppm) were assessed using a response surface design. It was found that the integration of the measurement system error is essential particularly when the difference between CpAQL and CpRQL is small. Concerning the correction of the sampling plan parameters, a procedure was developed to integrate the measurement system error evaluated by the GR&R. This procedure guarantees a common decision concerning the process capability whatever the state of the measurement system is, and this decision would, therefore, depend on the sample quality only.

Keywords

Process capability index Cp Measurement system error GR&R Threshold value of Cp Sampling plan parameters 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    De-Felipe D, Benedito E (2017) Monitoring high complex production processes using process capability indices. Int J Adv Manuf Technol 93(1–4):1257–1267CrossRefGoogle Scholar
  2. 2.
    Anis MZ (2008) Basic process capability indices: an expository review. Int Stat Rev 76(3):347–367CrossRefGoogle Scholar
  3. 3.
    Kane VE (1986) Process capability indices. J Qual Technol 18(1):41–52CrossRefGoogle Scholar
  4. 4.
    Anis MZ, Md T (2016) On some subtle misconceptions about process capability indices. Int J Adv Manuf Technol 87(9–12):3019–3029CrossRefGoogle Scholar
  5. 5.
    De-Felipe D, Benedito E (2017) A review of univariate and multivariate process capability indices. Int J Adv Manuf Technol 92(5–8):1687–1705CrossRefGoogle Scholar
  6. 6.
    Nikzad E, Amiri A, Abbasi B (2017) Residuals based process capability indices for two-stage processes. J Ind Eng Int 13(2):239–247CrossRefGoogle Scholar
  7. 7.
    Rakhmawati DY, Wu C-W, Yang C-L (2016) Performance evaluation of processes with asymmetric tolerances in the presence of gauge measurement errors. Comm Stat -Theo Meth 45(10):3011–3026MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Seifi S, Nezhad MSF (2017) Variable sampling plan for resubmitted lots based on process capability index and Bayesian approach. Int J Adv Manuf Technol 88(9–12):2547–2555CrossRefGoogle Scholar
  9. 9.
    Aslam M, Wu C-W, Azam M, Jun C-H (2013) Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. App Math Mod 37(3):667–675CrossRefzbMATHGoogle Scholar
  10. 10.
    Liu S-W, Lin S-W, Wu C-W (2014) A resubmitted sampling scheme by variables inspection for controlling lot fraction nonconforming. Int J Prod Res 52(12):3744–3754CrossRefGoogle Scholar
  11. 11.
    Pearn WL, Wu C-W (2006) Variables sampling plans with PPM fraction of defectives and process loss consideration. J Op Res Society 57(4):450–459CrossRefzbMATHGoogle Scholar
  12. 12.
    Pearn WL, Wu C-W (2007) An effective decision making method for product acceptance. Omega 35(1):12–21CrossRefGoogle Scholar
  13. 13.
    Wu C-W (2012) An efficient inspection scheme for variables based on Taguchi capability index. Eur J Oper Res 223(1):116–122CrossRefzbMATHGoogle Scholar
  14. 14.
    Mahshid R, Mansourvar Z, Hansen HN (2018) Tolerance analysis in manufacturing using process capability ratio with measurement uncertainty. Precision Eng 52:201–210CrossRefGoogle Scholar
  15. 15.
    Wu C-W (2011) Using a novel approach to assess process performance in the presence of measurement errors. J Stat Comp Sim 81(3):301–314MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Baral AK, Anis MZ (2015) Assessment of Cpm in the presence of measurement errors. J Stat Theo Appl 14(1):13–27CrossRefGoogle Scholar
  17. 17.
    Wang F-K (2016) Process yield analysis for nonlinear profiles in the presence of gauge measurement errors. Qual Rel Eng Int 32(7):2435–2442CrossRefGoogle Scholar
  18. 18.
    Ben Amara S, Dhahri J, Ben Fredj N (2017) Process true capability evaluation with the consideration of measurement system variability and expected quality loss. Qual Rel Eng Int 33(5):937–944CrossRefGoogle Scholar
  19. 19.
    AIAG Work Group (2010) Measurement systems analysis: reference manual, 4th edn. Automotive Industry Action Group, Detroit, MI, USAGoogle Scholar
  20. 20.
    Dalalah D, Hani DB (2016) On the actual and observed process capability indices: a signal-to-noise ratio model. Measurement 81:241–250CrossRefGoogle Scholar
  21. 21.
    Selmi S, Ben Amara S, Ben Fred N, Kobi A, Ben Salah I (2018) Process capability indices and X¯, R control chart limit adjustments by taking into account measurement system errors. Int J Adv Manuf Technol 95(5–8):1919–1930CrossRefGoogle Scholar
  22. 22.
    Maleki MR, Amiri A, Castagliola P (2017) Measurement errors in statistical process monitoring: a literature review. Comp Indus Eng 103:316–329CrossRefGoogle Scholar
  23. 23.
    Burr IR (1976) Statistical quality control methods. Marcel Dekker, New YorkzbMATHGoogle Scholar
  24. 24.
    Montgomery DC (2009) Introduction to statistical quality control: a modern introduction, 6th edn. John Wiley & Sons, New YorkzbMATHGoogle Scholar
  25. 25.
    Myers RH, Montgomery DC, Anderson-Cook CM (2016) Response surface methodology, product and process optimization using experimental design, 4th edn. John Wiley & Sons, New YorkzbMATHGoogle Scholar
  26. 26.
    Dean A, Voss D, Draguljić D (2017) Design and analysis of experiments, 2nd edition, Springer International Publishing AG BaselCrossRefzbMATHGoogle Scholar
  27. 27.
    Fang KT, Li R, Sudjianto A (2006) Design and modeling for computer experiments. Taylor & Francis Group, DidcotzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Adel Brik
    • 1
    • 2
  • Mohamed Goddi
    • 1
  • Jamel Dhahri
    • 1
  • Nabil Ben Fredj
    • 1
    Email author
  1. 1.Laboratoire de Mécanique, Matériaux et Procédés (LR99ES05), ENSITUniversité de TunisTunisTunisia
  2. 2.Ecole Supérieure Privée d’Ingénierie et de Technologie, ESPRITArianaTunisia

Personalised recommendations