A Fuzzy EWMA Attribute Control Chart to Monitor Process Mean

Conventional control charts are one of the most important techniques in statistical process control which are used to assess the performance of processes to see whether they are in- or out-of-control. As traditional control charts deal with crisp data, they are not suitable to study unclear, vague, and fuzzy data. In many real-world applications, however, the data to be used in a control charting method are not crisp since they are approximated due to environmental uncertainties and systematic ambiguities involved in the systems under investigation. In these situations, fuzzy numbers and linguistic variables are used to grab such uncertainties. That is why the use of a fuzzy control chart, in which fuzzy data are used, is justified. As an exponentially weighted moving average (EWMA) scheme is usually used to detect small shifts, in this paper a fuzzy EWMA (F-EWMA) control chart is proposed to detect small shifts in the process mean when fuzzy data are available. The application of the newly developed fuzzy control chart is illustrated using real-life data.

[1]  Cengiz Kahraman,et al.  Fuzzy exponentially weighted moving average control chart for univariate data with a real case application , 2014, Appl. Soft Comput..

[2]  Hiroshi Ohta,et al.  Control charts for process average and variability based on linguistic data , 1993 .

[3]  Alan S. Morris,et al.  A fuzzy rule-based algorithm to improve the performance of statistical process control in quality systems , 2000, J. Intell. Fuzzy Syst..

[4]  Smiley W. Cheng,et al.  Monitoring process mean with a new EWMA control chart , 2011 .

[5]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[6]  M. Khademi,et al.  Fuzzy rules for fuzzy $overline{X}$ and $R$ control charts , 2014 .

[7]  Nihal Erginel,et al.  Fuzzy individual and moving range control charts with α-cuts , 2008 .

[8]  W. A. Rosenblith.  Information and Control in Organ Systems , 1959 .

[9]  Cengiz Kahraman,et al.  Fuzzy Shewhart Control Charts , 2016 .

[10]  Rassoul Noorossana,et al.  Fuzzy multivariate exponentially weighted moving average control chart , 2010 .

[11]  Hefin Rowlands,et al.  An approach of fuzzy logic evaluation and control in SPC , 2000 .

[12]  Sevil Sentürk,et al.  Fuzzy Regression Control Chart Based on α-cut Approximation , 2010, Int. J. Comput. Intell. Syst..

[13]  Tzvi Raz,et al.  On the construction of control charts using linguistic variables , 1990 .

[14]  Chi-Bin Cheng,et al.  Fuzzy process control: construction of control charts with fuzzy numbers , 2005, Fuzzy Sets Syst..

[15]  Cengiz Kahraman,et al.  Process capability analyses based on fuzzy measurements and fuzzy control charts , 2011, Expert Syst. Appl..

[16]  Da Ruan,et al.  α‐Cut fuzzy control charts for linguistic data , 2004, Int. J. Intell. Syst..

[17]  Richard E. DeVor,et al.  Statistical Quality Design and Control: Contemporary Concepts and Methods , 1992 .

[18]  Cengiz Kahraman,et al.  Design of Fuzzy u~ Control Charts , 2011, J. Multiple Valued Log. Soft Comput..

[19]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[20]  Cengiz Kahraman,et al.  An alternative approach to fuzzy control charts: Direct fuzzy approach , 2007, Inf. Sci..

[21]  Nihal Erginel,et al.  Development of fuzzy X-R and X-S control charts using alpha-cuts , 2009, Inf. Sci..

[22]  T. Raz,et al.  Probabilistic and membership approaches in the construction of control charts for linguistic data , 1990 .

[23]  Alireza Faraz,et al.  Fuzzy Control Chart A Better Alternative for Shewhart Average Chart , 2007 .

[24]  M. Khademi,et al.  FUZZY RULES FOR FUZZY X AND R CONTROL CHARTS , 2014 .