Sensitizing Rules for Fuzzy Control Charts

Quality control charts indicate out of control conditions if any nonrandom pattern of the points is observed or any point is plotted beyond the control limits. Nonrandom patterns of Shewhart control charts are tested with sensitizing rules. When the processes are defined with fuzzy set theory, traditional sensitizing rules are insufficient for defining all out of control conditions. This is due to the fact that fuzzy numbers increase the number of out of control conditions. The purpose of the study is to develop a set of fuzzy sensitizing rules, which increase the flexibility and sensitivity of fuzzy control charts. Fuzzy sensitizing rules simplify the identification of out of control situations that results in a decrease in the calculation time and number of evaluations in fuzzy control chart approach.




References:
[1] D.C. Montgomery, Introduction to Statistical Quality Control, 5th
edition, John Wiley & Sons Inc., NY, USA, 1996.
[2] Western Electric Company, Statistical Quality Control handbook, 1th
edition, AT & T Technologies, Indianapolis, Indiana, 1956.
[3] L.S. Nelson, "The Shewhart control chart-tests for special causes",
Journal of Quality Technology, 16, 237-239 1984.
[4] L.S. Nelson, "Interpreting Shewhart x-bar control charts", Journal of
Quality Technology, 17, 114-116, 1985.
[5] L.A. Zadeh, "Fuzzy sets", Information and Control, 8, 338-353, 1965.
[6] T. Raz and J.H. Wang, "Probabilistic and memberships a roaches in the
construction of control charts for linguistic data", Production Planning
and Control, 1, 147-157, 1990.
[7] J.H. Wang and T. Raz, "On the construction of control charts using
linguistic variables", Intelligent Journal of Production Research, 28,
477-487, 1990.
[8] A. Kanagawa, F. Tamaki and H. Ohta, "Control charts for process
average and variability based on linguistic data", Intelligent Journal of
Production Research, 31 (4), 913-922, 1993.
[9] H. Taleb and M. Limam, "On fuzzy and probabilistic control charts",
International Journal of Production Research, 40 12(15), 2849 - 2863,
2002.
[10] M. G├╝lbay, C. Kahraman and D. Ruan, "╬▒ - Cuts fuzzy control charts
for linguistic data", International Journal of Intelligent Systems, 19,
1173-1196, 2004.
[11] C.B. Cheng, "Fuzzy process control: construction of control charts with
fuzzy numbers", Fuzzy Sets and Systems, 154 2, 287-303, 2005.
[12] M. G├╝lbay and C. Kahraman, "An alternative approach to fuzzy control
charts: direct fuzzy approach", Information Sciences, 77 (6), 1463-1480,
2007.
[13] O. Hryniewicz, "Statistics with fuzzy data in statistical quality control,
Soft Computing - A Fusion of Foundations", Methodologies and
Applications, 12 3, 229 - 234, 2007.
[14] V. Amirzadeh, M. Mashinchi and A. Parchami, "Construction of pcharts
using degree of nonconformity", Information Sciences, 179 (1-2),
1501-60, 2009.
[15] A. Faraz and M.B. Moghadam, "Fuzzy control chart a better alternative
for Shewhart average chart", Quality and Quantity, 41 3(11), 375-385,
2007.
[16] S. Senturk and N. Erginel, "Development of fuzzy X~ R~
− and X~ S~

control charts using ╬▒ - cuts", Information Sciences, 179, 1542-1551,
2009.
[17] A. Faraz, R.B. Kazemzadeh, M.B. Moghadam and A. Bazdar,
"Constructing a fuzzy Shewhart control chart for variables when
uncertainty and randomness are combined", Journal of Quality &
Quantity, 44 5, 905-914, 2009.
[18] A. Faraz and A.F. Shapiro, "An application of fuzzy random variables to
control charts", Fuzzy Sets and Systems, vol. 161, pp. 2684-2694, 2010.
[19] M.H. Shu and H.C. Wu, "Fuzzy X and R control charts: Fuzzy
dominance approach", Computers & Industrial Engineering, 613, 676-
686, 2011.
[20] B.H. Gwee, M.H. Lim and B.H. Soong, "Self-Adjusting Diagnostic
System for the Manufacture of Crystal Resonators", Proceedings of
IEEE Industry Application Society Annual Meeting, IAS-93, Toronto,
Canada, 3, 2014-2020, 1993.
[21] C. Kahraman, E. Tolga and Z. Ulukan, "Using triangular fuzzy numbers
in the tests of control charts for unnatural patterns", in: Proceedings of
INRIA/IEEE Conference on Emerging Technologies and Factory
Automation, Paris, France, 291-298, 1995.
[22] L.R. Wang and H. Rowlands, "A fuzzy logic application in SPC
evaluation and control", in: Proceedings of IEEE International
Conference on Emerging Technologies and Factory Automation, 1, 679-
684, 1999.
[23] H.M. Hsu and Y.K. Chen, "A fuzzy reasoning based diagnosis system
for X control charts", Journal of Intelligent Manufacturing, 12, 2001.
[24] J.D.T. Tannock, "A fuzzy control charting method for individuals",
International Journal of Production Research, 41 5, 2003.
[25] M .G├╝lbay and C. Kahraman, "Development of fuzzy process control
charts and fuzzy unnatural pattern analyses", Computational Statistics
and Data Analysis, 51, 434-451, 2006.
[26] M.H. Fazel Zarandi, A. Alaeddini and I.B. T├╝rksen, "A hybrid fuzzy
adaptive sampling - Run rules for Shewhart control charts", Information
Sciences, 178 4, 1152-1170, 2008.
[27] K. Demirli and S. Vijayakumar, "Fuzzy logic based assignable cause
diagnosis using control chart patterns", Information Sciences, 180, 3258-
3272, 2010.
[28] G. Bortolan and R. Degani, "A review of some methods for ranking
fuzzy numbers", Fuzzy Sets and Systems, 15, 1 - 19, 1985.
[29] X. Wang and E. E. Kerre, "Reasonable properties for the ordering of
fuzzy quantities (I)", Fuzzy Sets and Systems, 118 (3), 375-385, 2001.
[30] X. Wang and E. E. Kerre, "Reasonable properties for the ordering of
fuzzy quantities (II)", Fuzzy Sets and Systems, 118 (3), 387-405, 2001.