Monitoring Fuzzy Capability Index $\widetilde{C}_{pk}$ by Using the EWMA Control Chart with Imprecise Data

[1] L. Angstenberger, Dynamic fuzzy pattern recognition with application to finance and engineering,
Kluwer Academic Publishers, United States, 2001.
[2] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Acceptance single sampling plan
with fuzzy parameter, Iranian Journal of Fuzzy Systems, 8(2) (2011), 47{55.
[3] P. Castagliola, An EWMA control chart for monitoring the logarithm of the process sample
variance, Proceedings of the International Conference on Industrial Engineering and Production
Management, Glasgow, Scotland, (1999), 371{377.
[4] P. Castagliola, A new S2-EWMA control chart for monitoring the process variance, Quality
and Reliability Engineering International, 21(2005), 781{794.
[5] P. Castagliola, A R-EWMA control chart for monitoring the process range, International
Journal of Reliability, Quality and Safety Engineering, 12 (2005), 31{49.
[6] P. Castagliola, G. Celano and S. Fichera, Monitoring process variability using EWMA, Handbook
of Engineering Statistics, Springer, Berlin, (2006), 291{325.
[7] L. K. Chang, S. W. Cheng and F. A. Spiring, A new measure of process capability: Cpm,
Journal of Quality Technology, 20 (1988), 162{331.
[8] S. Chen and G. Li, Representation, ranking, and distance of fuzzy number with exponential
membership function using graded mean integration method, Tamsui Oxford Journal of
Mathematical Sciences, 16(2) (2000), 123{131

[9] T. W. Chen, K. S. Chen and J. Y. Lin, Fuzzy evaluation of process capability for bigger-thebest
type products, International Journal of Advanced Manufacturing Technology, 21 (2003),
820{826.
[10] C. B. Cheng, Fuzzy process control: construction of control charts with fuzzy numbers, Fuzzy
Sets and Systems, 154 (2005), 287{303.
[11] Y. Deng, Z. Zhenfu and L. Qi, Ranking fuzzy numbers with an area method using radius of
gyration, Computers and Mathematics with Applications, 51 (2006), 1127{1136.
[12] P. Grzegorzewski, Control charts for fuzzy data, In: Proceedings of the 5th European Congress
EUFIT97, Aachen, (1997), 1326{1330.
[13] P. Grzegorzewski and O. Hryniewicz, Soft methods in statistical quality control, Control and
Cybernetics, 29 (2000), 119{140.
[14] O. Hryniewicz, Statistics with fuzzy data in statistical quality control, Soft Computing, 12
(2008), 229{234.
[15] B. M. Hsu and M. H. Shu, Fuzzy inference to assess manufacturing process capability with
imprecise data, European Journal of Operational Research, 186(2) (2008), 652{670.
[16] J. M. Juran, Jurans quality control handbook, Third Edition, MacGraw Hill, New York, 1974.
[17] A. Kanagawa, F. Tamaki and H. Ohta, Control charts for process average and variability
based on linguistic data, International Journal of Production Research, 31 (1993), 913{922.
[18] V. E. Kane, Process capability indices, Journal of Quality Technology, 18 (1986), 41{52.
[19] I. Kaya and C. Kahraman, Fuzzy process capability analyses: An application to teaching
processes, Journal of Intelligent and Fuzzy Systems, 19 (2008), 259{272.
[20] S. K. Land, D. B. Smith and J. W. Walz, Practical support for lean six sigma software process
definition: using IEEE software engineering standards, Hoboken : Wiley ; Los Alamitos :
IEEE computer society, 2008.
[21] J. L. Meriam and L. G. Kraige, Engineering mechanics, Third Edition, Wiley, New York,
1992.
[22] D. C. Montgomery, Introduction to statistical quality control, Third Edition, Wiley, New
York, 1996.
[23] S. H. Nasseri and M. Sohrabi, Ranking fuzzy numbers by using radius of gyration, Australian
Journal of Basic and Applied Sciences, 4 (2010), 658{664.
[24] A. Parchami, M. Mashinchi, Fuzzy estimation for process capability indices, Information
Sciences, 177 (2007), 1452{1462.
[25] W. L. Pearn, S. Kotz and N. L. Johnson, Distributional and inferential properties of process
capability indices, Journal of Quality Technology, 24 (1992), 216{231.
[26] T. Raz and J. H. Wang, Probabilistic and membership approaches in the construction of
control charts for linguistic data, Production Planning and Control, 1 (1990), 147{157.
[27] B. Sadeghpour Gildeh and D. Gien, La distance-Dp;q et le coefficient de corrlation entre deux
variables alatoires floues, Rencontres Francophones sur la Logique Floue et ses Applications
LFA 01, Mons, Belgium, (2001), 97{102.
[28] W. A. Shewhart, Economic control of quality of manufactured product, D. Van Nostrand,
Inc., Princeton, NJ, 1931.
[29] H. Taleb and M. Limam, On fuzzy and probabilistic control charts, International Journal of
Production Research, 40 (2002), 2849{2863.
[30] J. D. T. Tannock, A fuzzy control charting methods for individuals, International Journal of
Production Research, 41 (2003), 1017{1032.
[31] C. C. Tsai and C. C. Chen, Making decision to evaluate process capability index Cp with fuzzy
numbers, International Journal of Advanced Manufacturing Technology, 30 (2006), 334{339.
[32] K. Vannman, A unified approach to capability indices, Statistica Sinica, 5 (1995), 805{820.
[33] K. Vannman and P. Castagliola, Monitoring capability indices using an EWMA approach,
Quality and Reliability Engineering International, 23 (2008), 769{790.
[34] D.Wang, A CUSUM control chart for fuzzy quality data, In: Lawry J, Miranda E, Bugarin A,
Li S, Gil MA, Grzegorzewski P, Hryniewicz O, eds., Soft Methods for Integrated Uncertainty
Modelling, Springer-Verlag, Heidelberg, (2006), 357{364.

[35] J. H. Wang and T. Raz, On the construction of control charts using linguistic variables,
International Journal of Production Research, 28 (1990), 477{487.
[36] C. W.Wu, Decision-making in testing process performance with fuzzy data. European Journal
of Operational Research, 193(2) (2009), 499{509.
[37] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.