Construction of control charts by using Fuzzy Multinomial -FM and EWMA Chart “Comparative study"

1 Kawa M. Jamal Rashid, 2 Suzan S. Haydar
Department of Statistics, School of Administrations and Economics, Sulamani University

The control chart is a graphical tool for monitoring the activities of a manufacturing process.
It plays a vital role in Statistical Process Control (SPC). These charts help us to take correct

decisions. The use of statistical methods in statistical quality control has a long history. The P-
chart plays the important role in controlling the fraction of nonconforming article produced.

The use of fuzzy has an effective role with inaccurate data. Great efforts have been made in the
direction of combining the Quality Control with fuzzy concept. Therefore; Fuzzy control chart
are connecting link between fuzzy logic and Quality Control technique, the goal of this
connection is to combine the advantage of both disciplines in order to process deal with linguistic
concepts and classified each item in more than two categories such as bad, medium, good, very
good and excellent.
This paper presents an extension of standard control chart to deal with linguistic categories
and the variable sampling size (VSS), it is named as fuzzy multinomial charts (FM-chart), and
we illustrate this approach by numerical example. This paper is comparing FM-chart with the
conventional p – chart and EWMA Control Chart. It is seen that FM chart with VSS performs
better than the conventional charts, this method is more sensitive, accurate and more economic
for assisting decision maker to control the operation system as early time, especially when there
is a change in sample sizes.

Keywords: Quality Control- Process, FM chart, P- chart, variable sampling size, linguistic terms and
Fuzzy control charts and EWMA-chart.


[1] Amirzadeh V., Mashinchi M., Yaghoobi M. A., "Construction of Control Charts Using
Fuzzy Multinomial Quality", Journal of Mathematics and Statistics 4 (1) ISSN 1549-3644,
pp. 26-31, (2008).
[2] Cheng C., "Fuzzy process control: construction of control charts with fuzzy numbers",
Fuzzy sets and systems, Vol. 154, Issue 2, pp. 287-303, (2005).
[3] Douglas M. C., "Introduction to Statistical Quality Control", Sixth Edition, (2009).

[4] Grant E. L. and Leavenworth R. S., "Statistical Quality Control", 6th edition, McGraw-
Hill book, (1988).

[5] Hunter J. S., "The Exponentially Weighted Moving Average", Journal of Quality
Technology, Vol. 18, No. 4, pp. 203-210, (1986).
[6] Kanagawa A., Tamaki F., and Ohta H., "Control charts for process average and variability
based on linguistic data", International Journal of production Research.31, pp. 913-922,
[7] Neubauer A. S., "The EWMA Control Chart: Properties and Comparison with other
Quality-Control Procedures by Computer Simulation", Clinical Chemistry, Vol. 43,
pp. 594-601, (1997).
[8] Oakliand J., "Statistical Process Control", Sixth edition, (2008).
[9] Pandian S.S. and Puthiyanayagam P., "Triangular fuzzy multinomial control chart with
variable sample size using α – cuts", International Journal of Engineering Science and
Technology (IJEST), Vol. 5, No.03, pp. 699-707, (2013).
[10] Taleb H., Limam M. and Hirota K., "Multivariate Fuzzy Multinomial Control Charts",
Vol. 3, No. 4, pp. 437-453, (2006).
[11] Wang J. H., Raz T., "On the Construction of Control Charts Using Linguistic
Variables", International Journal of Production Research, Vol. 28, Issue 3, pp. 477-487,
[12] Xie M., Goh T. N., and Kuralmani V.,2002 "Statistical Models and Control Charts for
High Quality Processes", (2002).