Skip to main content

Advertisement

Springer Nature Link
Log in

Design of a New Attribute Control Chart Under Neutrosophic Statistics

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

In this manuscript, we will originally design a Shewhart attribute control chart under the neutrosophic statistical interval method. The neutrosophic measures to study the performance of the proposed chart are given. The neutrosophic control chart coefficients are determined through the neutrosophic algorithm. A simulation study is also added to show the efficiency of the proposed control chart under the neutrosophic statistical interval method over the attribute control chart under the classical statistics. The comparison of the proposed chart with the existing chart is also given in terms of neutrosophic average run length (NARL). Some tables of NARL are given and explained using the real data from the company.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Alipour, H., Noorossana, R.: Fuzzy multivariate exponentially weighted moving average control chart. Int. J. Adv. Manuf. Technol. 48(9–12), 1001–1007 (2010)

    Article  Google Scholar 

  2. Aslam, M.: A new sampling plan using neutrosophic process loss consideration. Symmetry 10(5), 132 (2018)

    Article  MathSciNet  Google Scholar 

  3. Aslam, M., Arif, O.A.: Testing of grouped product for the Weibull distribution using neutrosophic statistics. Symmetry 10(9), 403 (2018)

    Article  Google Scholar 

  4. Aslam, M., Raza, M.A.: Design of new sampling plans for multiple manufacturing lines under uncertainty. Int. J. Fuzzy Syst. (2018). https://doi.org/10.1007/s40815-018-0560-x

    Google Scholar 

  5. Bradshaw Jr., C.W.: A fuzzy set theoretic interpretation of economic control limits. Eur. J. Oper. Res. 13(4), 403–408 (1983)

    Article  Google Scholar 

  6. Chen, J., Ye, J., Du, S.: Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics. Symmetry 9(10), 208 (2017)

    Article  Google Scholar 

  7. Chen, J., Ye, J., Du, S., Yong, R.: Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers. Symmetry 9(7), 123 (2017)

    Article  Google Scholar 

  8. Duncan, A.: A Chi square chart for controlling a set of percentages. Ind. Qual. Control 7(11), 11–15 (1950)

    Google Scholar 

  9. Engin, O., Çelik, A., Kaya, İ.: A fuzzy approach to define sample size for attributes control chart in multistage processes: an application in engine valve manufacturing process. Appl. Soft Comput. 8(4), 1654–1663 (2008)

    Article  Google Scholar 

  10. Faraz, A., Shapiro, A.F.: An application of fuzzy random variables to control charts. Fuzzy Sets Syst. 161(20), 2684–2694 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ghobadi, S., Noghondarian, K., Noorossana, R., Mirhosseini, S.S.: Developing a fuzzy multivariate CUSUM control chart to monitor multinomial linguistic quality characteristics. Int. J. Adv. Manuf. Technol. 79(9–12), 1893–1903 (2015)

    Article  Google Scholar 

  12. Gildeh, B.S., Shafiee, N.: X-MR control chart for autocorrelated fuzzy data using D p, q-distance. Int. J. Adv. Manuf. Technol. 81(5–8), 1047–1054 (2015)

    Article  Google Scholar 

  13. Gülbay, M., Kahraman, C.: Development of fuzzy process control charts and fuzzy unnatural pattern analyses. Comput. Stat. Data Anal. 51(1), 434–451 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gülbay, M., Kahraman, C.: An alternative approach to fuzzy control charts: direct fuzzy approach. Inf. Sci. 177(6), 1463–1480 (2007)

    Article  MATH  Google Scholar 

  15. Gülbay, M., Kahraman, C., Ruan, D.: α-Cut fuzzy control charts for linguistic data. Int. J. Intell. Syst. 19(12), 1173–1195 (2004)

    Article  MATH  Google Scholar 

  16. Hou, S., Wang, H., Feng, S.: Attribute control chart construction based on fuzzy score number. Symmetry 8(12), 139 (2016)

    Article  MathSciNet  Google Scholar 

  17. Hsieh, K.-L., Tong, L.-I., Wang, M.-C.: The application of control chart for defects and defect clustering in IC manufacturing based on fuzzy theory. Expert Syst. Appl. 32(3), 765–776 (2007)

    Article  Google Scholar 

  18. Montgomery, D.C.: Introduction to statistical quality control. Wiley, Hoboken (2007)

    MATH  Google Scholar 

  19. Morabi, Z.S., Owlia, M.S., Bashiri, M., Doroudyan, M.H.: Multi-objective design of X control charts with fuzzy process parameters using the hybrid epsilon constraint PSO. Appl. Soft Comput. 30, 390–399 (2015)

    Article  Google Scholar 

  20. Şentürk, S.: Construction of fuzzy c control charts based on fuzzy rule method. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A-Uygulamalı Bilimler ve Mühendislik 18(3), 563–572 (2017)

    Google Scholar 

  21. Senturk, S., Erginel, N.: Development of fuzzy X− ~ −R ~ and X− ~ −S ~ control charts using α-cuts. Inf. Sci. 179(10), 1542–1551 (2009)

    Article  Google Scholar 

  22. Şentürk, S., Erginel, N., Kaya, İ., Kahraman, C.: Fuzzy exponentially weighted moving average control chart for univariate data with a real case application. Appl. Soft Comput. 22, 1–10 (2014)

    Article  Google Scholar 

  23. Shu, M.-H., Wu, H.-C.: Fuzzy X and R control charts: fuzzy dominance approach. Comput. Ind. Eng. 61(3), 676–685 (2011)

    Google Scholar 

  24. Smarandache, F.: Neutrosophic logic-generalization of the intuitionistic fuzzy logic. arXiv preprint arXiv: math/0303009 (2003)

  25. Smarandache, F.: Introduction to neutrosophic statistics. Infinite Study (2014). https://arxiv.org/pdf/1406.2000

  26. Sorooshian, S.: Fuzzy approach to statistical control charts. J. Appl. Math. 2013, 1–6 (2013)

    MathSciNet  Google Scholar 

  27. Taleb, H., Limam, M.: On fuzzy and probabilistic control charts. Int. J. Prod. Res. 40(12), 2849–2863 (2002)

    Article  Google Scholar 

  28. Wei, Y., Qiu, J., Karimi, H.R.: Fuzzy-affine-model-based memory filter design of nonlinear systems with time-varying delay. IEEE Trans. Fuzzy Syst. 99, 1 (2017)

    Google Scholar 

  29. Wei, Y., Qiu, J., Lam, H.-K.: A novel approach to reliable output feedback control of fuzzy-affine systems with time-delays and sensor faults. IEEE Trans. Fuzzy Syst. 25(6), 1808–1823 (2017)

    Article  Google Scholar 

  30. Williams, R.H., Zigli, R.M.: Ambiguity impedes quality in the service industries. Qual. Progress 20(7), 14–17 (1987)

    Google Scholar 

  31. Wu, Y., Karimi, H.R., Lu, R.: Sampled-data control of network systems in industrial manufacture. IEEE Trans. Industr. Electron. 1, 1 (2018)

    Google Scholar 

  32. Wu, Y., Lu, R.: Event-based control for network systems via integral quadratic constraints. IEEE Trans. Circuits Syst. I Regul. Pap. 65(4), 1386–1394 (2018)

    Article  MathSciNet  Google Scholar 

  33. Wu, Y., Lu, R., Shi, P., Su, H., Wu, Z.-G.: Analysis and design of synchronization for heterogeneous network. IEEE Trans. Cybern. 48(4), 1253–1262 (2018)

    Article  Google Scholar 

  34. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)

    Article  Google Scholar 

  35. Zarandi, M.F., Alaeddini, A., Turksen, I.: A hybrid fuzzy adaptive sampling—run rules for Shewhart control charts. Inf. Sci. 178(4), 1152–1170 (2008)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are deeply thankful to the editor and the reviewers for their valuable suggestions to improve the quality of this manuscript. This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. D-260-130-1439. The authors, therefore, gratefully acknowledge the DSR technical and financial support.

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia

    Muhammad Aslam

  2. Department of Marine Geology, Faculty of Marine Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia

    Rashad A. R. Bantan

  3. Department of Statistics, Jhang Campus, University of Veterinary and Animal Sciences, Lahore, Pakistan

    Nasrullah Khan

Authors
  1. Muhammad Aslam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rashad A. R. Bantan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nasrullah Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Aslam.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aslam, M., Bantan, R.A.R. & Khan, N. Design of a New Attribute Control Chart Under Neutrosophic Statistics. Int. J. Fuzzy Syst. 21, 433–440 (2019). https://doi.org/10.1007/s40815-018-0577-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-018-0577-1

Keywords