On the multivariate process capability vector in fuzzy environment

Document Type : Research Paper


Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran


The production of a process is expected to meet customer demands, specifications or engineering tolerances. The ability of a process to meet these expectations is expresed as a single number using a process capability index. When the quality of the products relates to more than one characteristic, multivariate process capability indices are applied. As it is known, in some circumstances we are faced with imprecise data. So, fuzzy logic is engaged to deal with them. In this article, the specification limits and the target value of each characteristic and also, the data gathered from the process are assumed to be imprecise and a new fuzzy multivariate capability vector is introduced. As a whole, the present article provides a research of the application of fuzzy logic in multivariate capability vector.


[1] M. A. Basaran, Calculating fuzzy inverse matrix using fuzzy linear equation system, Applied
Soft Computing, 12 (2012), 1810{1813.
[2] K. S. Chen and W. L. Pearn, Capability indices for processes with asymmetric tolerances,
Journal of the Chinese Institute of Engineers, 24(5) (2001), 559{568.
[3] M. Dehghan, M. Ghatee and B. Hashemi, Inverse of a fuzzy matrix of fuzzy numbers, International
Journal of Computer Mathematics, 86(8) (2009), 1433{1452.
[4] P. Fortemps and M. Roubens, Ranking and defuzzification methods based on area compensation,
Fuzzy Sets and Systems, 82 (1996) 319{330.
[5] J. E. Jackson, Quality control methods for two related variables, Industrial Quality Control,
(1956), 4{8.
[6] I. Kaya and C. Kahraman, Fuzzy process capability analyses: An application to teaching
processes, Journal of Intelligent and Fuzzy Systems, 19(4-5) (2008), 259{272.
[7] I. Kaya and C. Kahraman, Fuzzy robust process capability indices for risk assessment of air
pollution, Stochastic Environmental Research and Risk Assessment, 23(4) (2009), 529{541.
[8] I. Kaya and C. Kahraman, Development of fuzzy process accuracy index for decision making
problems, Information Sciences, 180(6) (2010), 861{872.
[9] A. Parchami, M. Mashinchi and H. R. Maleki, Fuzzy confidence interval for fuzzy process
capability index, Journal of Intelligent and Fuzzy Systems, 17 (2006), 287{295.
[10] A. Parchami and M. Mashinchi, Fuzzy estimation for process capability indices, Information
Sciences, 177 (2007), 1452{1462.
[11] A. Parchami, B. Sadeghpour Gildeh, M. Nourbakhsh and M. Mashinchi, A new generation
of process capability indices based on fuzzy measurements, Journal of Applied Statistics, 41
(2014), 1122{1136.
[12] W. L. Pearn, S. Kotz and N. L. Johnson, Distributional and inferential properties of process
capability indices, Journal of Quality Technology, 24 (1992), 216{233.
[13] B. Sadeghpour Gildeh, Comparison of and process capability indices in the case of measurement
error occurrence, IFSA World Congress, Istanbul, Turkey, (2003), 563{567.
[14] B. Sadeghpour Gildeh, Measurement error effects on the performance of the process capability
index based on fuzzy tolerance interval, Annals of Fuzzy Mathematica and Informatics, 2
(2011), 17{32.
[15] B. Sadeghpour Gildeh and V. Moradi, Fuzzy tolerance region and process capability analysis,
Advances in Intelligent and Soft Computing, 157 (2012), 183{193.
[16] H. Shahriari and M. Abdollahzadeh, A new multivariate process capability vector, Quality
Engineering, 21(3) (2009), 290{299.
[17] J. J. H. Shiau, C. L. Yen, W. L. Pearn and W. T. Lee, Yield-Related process capability
indices for processes of multiple quality characteristics, Quality and Reliability Engineering
International, 29 (2013), 487{507.
[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
[19] M. Zhang, G. A. Wang, H. E. Shuguang and H. E. Zhen, Modified multivariate process capability
index using principal component analysis, Chinese Journal of Mechanical Engineering,
27(2) (2014), 249{259.