Monitoring fuzzy linear quality profiles: A comparative study

Article history: Received August 17 2020 Received in Revised Format October 7 2020 Accepted October 15 2020 Available online October, 15 2020 Quality profiles representing the quality of a process or product as the functional relationship between one or more dependent variables and one or more explanatory variables, which are nowadays widely recognized in statistical process control (SPC) applications by both researchers and practitioners. Furthermore, in many real-world cases, evaluation of process or product characteristics is carried out with ambiguity or conducted using linguistic values. The theory of fuzzy sets provides an appropriate approach to deal with uncertainty due to ambiguity in human subjective evaluations or vagueness in linguistic variables. The purpose of this study is to introduce two novel methods based on fuzzy regression modeling for monitoring fuzzy linear profiles in phase II of SPC. To accomplish this, the fuzzified Hoteling’s T statistic and fuzzy hypothesis testing are used. Moreover, a simulation study is used to compare the performance of the proposed methods with previous methods, based on the average run length (ARL) criterion in order to assess the detectability of charts with regard to the step shifts in profile parameters. Finally, the results of a real-world example in the tile and ceramic industry are presented. © 2021 by the authors; licensee Growing Science, Canada

[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]  Changliang Zou,et al.  A control chart based on a change-point model for monitoring linear profiles , 2006 .

[3]  Gerhard-Wilhelm Weber,et al.  A Literature Review on the Fuzzy Control Chart; Classifications & Analysis , 2014 .

[4]  Kudret Demirli,et al.  Fuzzy logic based assignable cause diagnosis using control chart patterns , 2010, Inf. Sci..

[5]  Zhi-gang Su,et al.  Kernel based nonlinear fuzzy regression model , 2013, Eng. Appl. Artif. Intell..

[6]  A. Celmins.  Least squares model fitting to fuzzy vector data , 1987 .

[7]  Lan Kang,et al.  On-Line Monitoring When the Process Yields a Linear Profile , 2000 .

[8]  Hassan Hassanpour,et al.  A Goal Programming Approach to Fuzzy Linear Regression with Non-Fuzzy Input and Fuzzy Output Data , 2009, Asia Pac. J. Oper. Res..

[9]  Joseph C. Chen,et al.  Development of fuzzy logic-based statistical process control chart pattern recognition system , 2016 .

[10]  H. Tanka.  Fuzzy data analysis by possibilistic linear models , 1987 .

[11]  Vahid Amirzadeh,et al.  New fuzzy EWMA control charts for monitoring phase II fuzzy profiles , 2016 .

[12]  Mohammad Hossein Fazel Zarandi,et al.  A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts , 2010, Inf. Sci..

[13]  Mohammad Ghasem Akbari,et al.  Bootstrap Statistical Inference about the Regression Coefficients Based on Fuzzy Data , 2012 .

[14]  Seyed Mahmoud Taheri,et al.  Testing fuzzy hypotheses based on fuzzy test statistic , 2009, Soft Comput..

[15]  Jurgita Antucheviciene,et al.  Interval Type-2 Fuzzy c-Control Charts: An Application in a Food Company , 2017, Informatica.

[16]  Pierpaolo D'Urso,et al.  Least squares estimation of a linear regression model with LR fuzzy response , 2006, Comput. Stat. Data Anal..

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

[18]  Shahram Ghobadi,et al.  Developing a univariate approach to phase-I monitoring of fuzzy quality profiles , 2012 .

[19]  Mahmoud A. Mahmoud,et al.  On the Monitoring of Linear Profiles , 2003 .

[20]  Pierpaolo D'Urso,et al.  Linear regression analysis for fuzzy = crisp input and fuzzy = crisp output data , 2015 .

[21]  Fiorenzo Franceschini,et al.  CONTROL CHART FOR LINGUISTIC VARIABLES : A METHOD BASED ON THE USE OF LINGUISTIC QUANTIFIERS , 1999 .

[22]  Dug Hun Hong,et al.  Fuzzy Nonlinear Regression Model Based on LS-SVM in Feature Space , 2006, FSKD.

[23]  Rassoul Noorossana,et al.  Developing a multivariate approach to monitor fuzzy quality profiles , 2014 .

[24]  Hassen Taleb,et al.  On fuzzy and probabilistic control charts , 2002 .

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

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

[27]  Mahmoud A. Mahmoud,et al.  A change point method for linear profile data , 2007, Qual. Reliab. Eng. Int..

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

[29]  Vahid Amirzadeh,et al.  Developing new methods to monitor phase II fuzzy linear profiles , 2015 .

[30]  Adel Alaeddini,et al.  A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts , 2009, Inf. Sci..

[31]  Vahid Amirzadeh,et al.  A novel phase I fuzzy profile monitoring approach based on fuzzy change point analysis , 2018, Appl. Soft Comput..

[32]  M. Yasuda,et al.  Construction of Fuzzy Control Charts Based on Weighted Possibilistic Mean , 2014 .

[33]  Maria Nela Pastuizaca Fernandez,et al.  Fuzzy theory and quality control charts , 2017, 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[34]  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..

[35]  Wolfgang Näther,et al.  Linear Regression with Random Fuzzy Variables: Extended Classical Estimates, Best Linear Estimates, Least Squares Estimates , 1998, Inf. Sci..