Applied Soft Computing 51 (2017) 370–381 Contents lists available at ScienceDirect Applied Soft Computing j ourna l ho me page: www.elsevier.com/locate /asoc Analysis and control of variability by using fuzzy individual control charts ˙ Ihsan Kaya ∗ , Melike Erdo˘ gan, Cansın Yıldız Yıldız Technical University, Department of Industrial Engineering, 34349, Bes ¸ iktas ¸ ˙ Istanbul, Turkey a r t i c l e i n f o Article history: Received 11 July 2016 Received in revised form 15 November 2016 Accepted 30 November 2016 Available online 9 December 2016 Keywords: Control charts Forecasting Fuzzy logic BIST-30 Index Statistical process control Variability a b s t r a c t The detection of changes in a process within shortest time provides significant benefits in terms of cost and quality. When considering the cost which would show up because of delays in identifying variability, detecting the deviation in the process accurately and quickly has a great importance for investors. In this paper, return volatility in the Borsa Istanbul-30 index (BIST-30) has been analyzed and a fuzzy control chart for individual measurements (FCCIM) has been proposed for use in determining and controlling in the variables of the BIST-30 index. For this purpose, firstly exponential smoothing method is used to forecast the variability of stock price of BIST-30 index by using MINITAB statistical software, and then a fuzzy control chart for individual measurements (FCCIM) which are fuzzy individual control chart (FICC) and fuzzy moving range control chart (FMRCC) with fuzzy control rules have been developed to be used in determining the variability of the process. For this aim, some fuzzy rules have been defined by using Ms EXCEL in fuzzy control chart for individual measurements. A real case application from Istanbul Stock Exchange for BIST-30 has been managed to check the effectiveness of suggested fuzzy control charts. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Control charts monitor whether or not a process is under con- trol. The chart contains three parts: a centerline that represents the average value of the quality characteristic corresponding to in- control state, and two other lines, called upper control limit (UCL) and lower control limit (LCL), which are chosen to assure that if the process is in-control, nearly all of the sample points will fall between them. Control charts have been widely used for moni- toring process stability and capability [31]. Control charts can be applied in finance sector for the statistical analysis of the variables. Control charts, which developed W.A. Shewhart, today still con- tinue its development by integrating new applications in different disciplines [45]. The use of classic control charts to analyze the vari- ation in the process is suitable when the data are known precisely and exactly. However, it may not always be possible to determine the data clearly. When human subjectivity plays an important role in defining the quality characteristics, the classical control charts may not be applicable since they require certain information. The major contribution of fuzzy set theory lies in its capability of repre- senting vague data. Fuzzy logic offers a systematic base to deal with ∗ Corresponding author. E-mail addresses: iekaya@yahoo.com, ihkaya@yildiz.edu.tr ( ˙ I. Kaya). situations, which are ambiguous or not well defined. Fuzzy control charts are inevitable to use when the statistical data in consider- ation are uncertain or vague; or available information about the process is incomplete or includes human subjectivity [47]. Deci- sion analysis under uncertainty is often carried out with using the fuzzy set theory (FST). The FST developed by Zadeh is an effective tool for modelling uncertainties arising from mental structure of human [58]. Using the FST is inevitable with the situations such as uncertain, imprecise or the cases that include linguistic expres- sions. Because of the complexity, dynamism and high volatility in stock prices, the data cannot be fully determined. Fuzzy logic is a branch of mathematics that allows a computer to model the real world in the same way that people do. It provides a simple way to reason with vague, ambiguous, and imprecise input or knowl- edge [16,32,33,52]. Therefore the use of fuzzy control chart instead of the traditional control charts to analyze the variability in the process is required. For this aim, the FST has been integrated with control charts for individual measurements and two new fuzzy con- trol charts named fuzzy individual measurements control chart for (FIMCC) and fuzzy moving range control chart for (FMRCC) have been proposed first time in this paper. The use of FST in control charts has gained importance with the paper of Wang and Raz [55]. This paper was followed by the studies of Raz and Wang [43] and Taleb and Limam [48]. Wang and Raz [55] presented a probabilistic and membership approach to the control http://dx.doi.org/10.1016/j.asoc.2016.11.048 1568-4946/© 2016 Elsevier B.V. All rights reserved.