Design and analysis of process capability indices cpm and cpmk by neutrosophic sets

Document Type : Research Paper

Authors

1 Department of Industrial Engineering, Beykent University, 34398, Sariyer, Istanbul, Turkey

2 Department of Industrial Engineering, Yildiz Technical University, 34349, Yildiz, Istanbul, Turkey

Abstract

Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices  C_{pm}  and  C_{pmk}  have been developed to consider customers' ideal value that called target value ( T ). Although, these indices have similar features of the well-known indices C_{p}  and  C_{pk} , one of the most important differences is to consider \textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices  C_{pm} and C_{pmk} have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} have been obtained and the main formulas of them have been produced. Additionally, the proposed \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} have been applied on real case studies from manufacturing industry. The obtained results show that the indices \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} include more informative and flexible results to evaluate capability of process.

Keywords

References

[1] F. Ahmad, A. Y. Adhami, Neutrosophic programming approach to multiobjective nonlinear transportation problem with fuzzy parameters, International Journal of Management Science and Engineering Management, 14(3) (2019), 218-229.
[2] F. Ahmad, A. Y. Adhami, F. Smarandache, Single valued neutrosophic hesitant fuzzy computational algorithm for multiobjective nonlinear optimization problem, Neutrosophic Sets Systems, 22 (2018), 76-86.
[3] M. Aslam, A variable acceptance sampling plan under neutrosophic statistical interval method, Symmetry, 11(114) (2019), 1-7.
[4] M. Aslam, M. Albassam, Inspection plan based on the process capability index using the neutrosophic statistical method, Mathematics, 7(7) (2019), 1-10.
[5] K. T. Atanassov, Intuitionistic fuzzy sets: Theory and applications, Physica-Verlag Heidelberg, 1999.
[6] S. Ayber, N. Erginel, Developing the neutrosophic fuzzy FMEA method as evaluating risk assessment tool, in Advances in Intelligent Systems and Computing, 1029 (2020), 1130-1137.
[7] S. Aydın, A. Aktas, M. Kabak, Neutrosophic fuzzy analytic hierarchy process approach for safe cities evaluation criteria, Advances in Intelligent Systems and Computing, 896 (2019), 958-965.
[8] P. Biswas, S. Pramanik, B. C. Giri, Value and ambiguity index based ranking method of single-valued trapezoidal neutrosophic numbers and its application to multi-attribute decision making, Neutrosophic Sets Systems, 12 (2016), 127-138.
[9] S. Broumi, A. Bakali, M. Talea, F. Smarandache, L. Vladareanu, Computation of shortest path problem in a network with SV-Trapezoidal neutrosophic numbers, in International Conference on Advanced Mechatronic Systems, ICAMechS, IEEE, (2016), 417-422.
[10] S. Broumi, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari, M. Parimala, Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: An overview, Complex and Intelligent Systems, 5(4) (2019), 371-378.
[11] Y. Cao, Z. Wu, T. Liu, Z. Gao, J. Yang, Multivariate process capability evaluation of cloud manufacturing resource based on intuitionistic fuzzy set, The International Journal of Advanced Manufacturing Technology, 84(1-4) (2016), 227-237.
[12] A. Chakraborty, S. P. Mondal, A. Ahmadian, N. Senu, S. Alam, S. Salahshour, Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications, Symmetry, 10(327) (2018), 1-27.
[13] A. Chakraborty, S. P. Mondal, A. Mahata, S. Alam, Different linear and non-linear form of trapezoidal neutrosophic numbers, de-neutrosophication techniques and its application in time-cost optimization technique, sequencing problem, RAIRO-Operations Research, 55 (2021), S97-S118.
[14] L. K. Chan, S. W. Cheng, F. A. Spiring, A new measure of process capability: Cpm, Journal of Quality Technolocy, 20(3) (1988), 162-175.
[15] Y. C. Chang, Interval estimation of capability index cpmk for manufacturing processes with asymmetric tolerances, Computers and Industrial Engineering, 56(1) (2009), 312-322.
[16] S. K. Das, A. Chakraborty, A new approach to evaluate linear programming problem in pentagonal neutrosophic environment, Complex and Intelligent Systems, 7(1) (2021), 101-110.
[17] İ. Deli, A novel defuzzification method of SV-trapezoidal neutrosophic numbers and multi-attribute decision making: A comparative analysis, Soft Computing, 23(23) (2019), 12529-12545.
[18] İ. Deli, Y. Şubaş, Single valued neutrosophic numbers and their applications to multicriteria decision making problem, Neutrosophic Sets Systems, 2(1) (2014), 1-13.
[19] İ. Deli, Y. Şubaş, A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems, International Journal of Machine Learning and Cybernetics, 8(4) (2017), 1309-1322.
[20] O. Engin, A. Çelik, İ. Kaya, A fuzzy approach to define sample size for attributes control chart in multistage processes: An application in engine valve manufacturing process, Applied Soft Computing Journal, 8(4) (2008), 1654-1663.
[21] P. Gupta, Applications of fuzzy logic in daily life, International Journal of Advanced Research in Computer Science, 8(5) (2017), 1795-1800.
[22] M. Gülbay, C. Kahraman, Development of fuzzy process control charts: Direct fuzzy approach, Itüdergisi/d mühendislik, 7(2) (2008), 95-105.
[23] G. Hesamian, M. G. Akbari, A process capability index for normal random variable with intuitionistic fuzzy information, Operational Research, (2019), 1-14.
[24] T. C. Hsiang, A tutorial on quality control and assurance-the Taguchi methods, ASA Annual Meeting LA, 1985.
[25] C. Kahraman, A. Parchami, S. Cevik Onar, B. Oztaysi, Process capability analysis using intuitionistic fuzzy sets, Journal of Intelligent and Fuzzy Systems, 32(3) (2017), 1659-1671.
[26] İ. Kaya, A genetic algorithm approach to determine the sample size for attribute control charts, Information Sciences, 179 (2009), 1552-1566.
[27] İ. Kaya, A genetic algorithm approach to determine the sample size for control charts with variables and attributes, Expert Systems with Applications, 36(5) (2009), 8719-8734.
[28] İ. Kaya, M. Çolak, A literature review on fuzzy process capability analysis, Journal of Testing and Evaluation, 48(5) (2020), 3963-3985.
[29] İ. Kaya, O. Engin, A new approach to define sample size at attributes control chart in multistage processes: An application in engine piston manufacturing process, Journal of Materials Processing Technology, 183(1) (2007), 38-48.
[30] İ. Kaya, C. Kahraman, A new perspective on fuzzy process capability indices: Robustness, Expert Systems, 37(6) (2010), 4593-4600.
[31] İ. Kaya, C. Kahraman, Fuzzy process capability analyses with fuzzy normal distribution, Expert Systems with Applications, 37(7) (2010), 5390-5403.
[32] İ. Kaya, C. Kahraman, Fuzzy process capability indices with asymmetric tolerances, Expert Systems, 38(12) (2011), 14882-14890.
[33] İ. Kaya, C. Kahraman, Process capability analyses with fuzzy parameters, Expert Systems with Applications, 38 (2011), 11918-11927.
[34] B. Kosko, S. Isaka, Fuzzy logic, Scientific American, 269(1) (1993), 76-81.
[35] S. Kotz, N. L. Johnson, Process capability indices-A review 1992-2000, Journal of Quality Technolocy, 34(1) (2002), 2-19.
[36] R. Kumar, S. A. Edaltpanah, S. Jha, S. Broumi, A. Dey, Neutrosophic shortest path problem, Neutrosophic Sets Systems, 23 (2018), 5-15.
[37] R. Kumar, S. A. Edalatpanah, S. Jha, S. Broumi, R. Singh, A. Dey, A multi objective programming approach to solve integer valued neutrosophic shortest path problems, Neutrosophic Sets Systems, 24 (2019), 134-149.
[38] D. F. Li, J. B. Yang, Fuzzy linear programming technique for multiattribute group decision making in fuzzy environments, Information Sciences, 158 (2004), 263-275.
[39] İ. Otay, C. Kahraman, Analytic network process with neutrosophic sets, in Studies in Fuzziness and Soft Computing, Springer, Cham, 369 (2019), 525-542.
[40] A. Parchami, M. Mashinchi, Fuzzy estimation for process capability indices, Information Sciences, 177(6) (2007), 1452-1462.
[41] A. Parchami, S. Ç. Onar, B. Öztayşi, C. Kahraman, Process capability analysis using interval type-2 fuzzy sets, International Journal of Computational Intelligence Systems, 10(1) (2017), 721-733.
[42] W. L. Pearn, S. Kotz, N. L. Johnson, Distributional and inferential properties of process capability indices, Journal of Quality Technology, 24(4) (1992), 216-231.
[43] S. Pramanik, P. P. Dey, Bi-level linear programming problem with neutrosophic numbers, Neutrosophic Sets Systems, 21 (2018), 110-121.
[44] N. M. Radwan, M. B. Senousy, A. E. D. M. Riad, A new expert system for learning management systems evaluation based on neutrosophic sets, Expert Systems, 33(6) (2016), 548-558.
[45] R. M. Rizk-Allah, A. E. Hassanien, M. Elhoseny, A multi-objective transportation model under neutrosophic environment, Computers and Electrical Engineering, 69 (2018), 705-719.
[46] M. U. J. Sastri, I. P. Jayasimman, A. Rajkumar, Industrial robots using single valued neutrosophic fuzzy numbers, Advances in Mathematics: Scientific Journal, 9(10) (2020), 7865-7869.
[47] O. Senvar, C. Kahraman, Type-2 fuzzy process capability indices for non-normal processes, Journal of Intelligent and Fuzzy Systems, 27(2) (2014), 769-781.
[48] F. Smarandache, A unifying field in logics: Neutrosophic logic, Philosophy, American Research Press, 1999.
[49] S. Subasri, K. Selvakumari, Neutrosophic travelling salesman problem in trapezoidal fuzzy number using branch and bound technique, Journal of Physics: Conference Series, 1362 (2019), 1-9, Doi:10.1088/1742-6596/1362/1/012098.
[50] H. X. Sun, H. X. Yang, J. Z. Wu, Y. Ouyang, Interval neutrosophic numbers Choquet integral operator for multicriteria decision making, Journal of Intelligent and Fuzzy Systems, 28(6) (2015), 2443-2455.
[51] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets, Infinite Study, 2010.
[52] J. Wang, G. Wei, M. Lu, TODIM method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment, Symmetry, 10(486) (2018), 1-15.
[53] C. W. Wu, W. L. Pearn, S. Kotz, An overview of theory and practice on process capability indices for quality assurance, International Journal of Production Economics, 117(2) (2009), 338-359.
[54] Y. Yang, J. Hu, R. Sun, X. Chen, Medical tourism destinations prioritization using group decision making method with neutrosophic fuzzy preference relations, Scientia Iranica, 25(6) (2018), 3744-3764.
[55] W. Yang, Y. Pang, New multiple attribute decision making method based on DEMATEL and TOPSIS for multivalued interval neutrosophic sets, Symmetry, 10(115) (2018), 1-16.
[56] J. Ye, Trapezoidal neutrosophic set and its application to multiple attribute decision-making, Neural Computing and Applications, 26(5) (2015), 1157-1166.
[57] J. Ye, Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method, Informatica, 28(2) (2017), 387-402.
[58] L. A. Zadeh, Fuzzy sets, Information and Control, 177(8) (1965), 338-353.
Iranian Journal of Fuzzy Systems
Volume 19, Issue 1
January and February 2022
Pages 13-30

Files

Share

How to cite

Statistics