Advertisement

International Journal of Fuzzy Systems

, Volume 21, Issue 2, pp 433–440 | Cite as

Design of a New Attribute Control Chart Under Neutrosophic Statistics

  • Muhammad AslamEmail author
  • Rashad A. R. Bantan
  • Nasrullah Khan
Article

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.

Keywords

Neutrosophic statistics Neutrosophic average run length Neutrosophic algorithm Classical statistics Simulation 

Notes

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.

Compliance with Ethical Standards

Conflicts of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Alipour, H., Noorossana, R.: Fuzzy multivariate exponentially weighted moving average control chart. Int. J. Adv. Manuf. Technol. 48(9–12), 1001–1007 (2010)CrossRefGoogle Scholar
  2. 2.
    Aslam, M.: A new sampling plan using neutrosophic process loss consideration. Symmetry 10(5), 132 (2018)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Aslam, M., Arif, O.A.: Testing of grouped product for the Weibull distribution using neutrosophic statistics. Symmetry 10(9), 403 (2018)CrossRefGoogle Scholar
  4. 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. 5.
    Bradshaw Jr., C.W.: A fuzzy set theoretic interpretation of economic control limits. Eur. J. Oper. Res. 13(4), 403–408 (1983)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Duncan, A.: A Chi square chart for controlling a set of percentages. Ind. Qual. Control 7(11), 11–15 (1950)Google Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    Faraz, A., Shapiro, A.F.: An application of fuzzy random variables to control charts. Fuzzy Sets Syst. 161(20), 2684–2694 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gülbay, M., Kahraman, C.: An alternative approach to fuzzy control charts: direct fuzzy approach. Inf. Sci. 177(6), 1463–1480 (2007)CrossRefzbMATHGoogle Scholar
  15. 15.
    Gülbay, M., Kahraman, C., Ruan, D.: α-Cut fuzzy control charts for linguistic data. Int. J. Intell. Syst. 19(12), 1173–1195 (2004)CrossRefzbMATHGoogle Scholar
  16. 16.
    Hou, S., Wang, H., Feng, S.: Attribute control chart construction based on fuzzy score number. Symmetry 8(12), 139 (2016)MathSciNetCrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 18.
    Montgomery, D.C.: Introduction to statistical quality control. Wiley, Hoboken (2007)zbMATHGoogle Scholar
  19. 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)CrossRefGoogle Scholar
  20. 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. 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)CrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 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. 24.
    Smarandache, F.: Neutrosophic logic-generalization of the intuitionistic fuzzy logic. arXiv preprint arXiv: math/0303009 (2003)Google Scholar
  25. 25.
    Smarandache, F.: Introduction to neutrosophic statistics. Infinite Study (2014). https://arxiv.org/pdf/1406.2000
  26. 26.
    Sorooshian, S.: Fuzzy approach to statistical control charts. J. Appl. Math. 2013, 1–6 (2013)MathSciNetGoogle Scholar
  27. 27.
    Taleb, H., Limam, M.: On fuzzy and probabilistic control charts. Int. J. Prod. Res. 40(12), 2849–2863 (2002)CrossRefGoogle Scholar
  28. 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. 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)CrossRefGoogle Scholar
  30. 30.
    Williams, R.H., Zigli, R.M.: Ambiguity impedes quality in the service industries. Qual. Progress 20(7), 14–17 (1987)Google Scholar
  31. 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. 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)MathSciNetCrossRefGoogle Scholar
  33. 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)CrossRefGoogle Scholar
  34. 34.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)CrossRefGoogle Scholar
  35. 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)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Muhammad Aslam
    • 1
    Email author
  • Rashad A. R. Bantan
    • 2
  • Nasrullah Khan
    • 3
  1. 1.Department of Statistics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Marine Geology, Faculty of Marine ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of StatisticsJhang Campus, University of Veterinary and Animal SciencesLahorePakistan

Personalised recommendations