A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts

Despite their capability in monitoring the variability of the processes, control charts are not effective tools for identifying the real time of such changes. Identifying the real time of the change in a process is recognized as change-point estimation problem. Most of the change-point models in the literature are limited to fixed sampling control charts which are only a special case of more effective charts known as variable sampling charts. In this paper, we develop a general fuzzy-statistical clustering approach for estimating change-points in different types of control charts with either fixed or variable sampling strategy. For this purpose, we devise and evaluate a new similarity measure based on the definition of operation characteristics and power functions. We also develop and examine a new objective function and discuss its relation with maximum-likelihood estimator. Finally, we conduct extensive simulation studies to evaluate the performance of the proposed approach for different types of control charts with different sampling strategies.

[1]  H. Lenz,et al.  Frontiers in Statistical Quality Control 2. , 1984 .

[2]  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..

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

[4]  George C. Runger,et al.  Process Partitions from Time-Ordered Clusters , 2009 .

[5]  Joseph J. Pignatiello,et al.  Estimating the Change Point of a Poisson Rate Parameter with a Linear Trend Disturbance , 2006, Qual. Reliab. Eng. Int..

[6]  Seyed Taghi Akhavan Niaki,et al.  A clustering approach to identify the time of a step change in Shewhart control charts , 2008, Qual. Reliab. Eng. Int..

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

[8]  Douglas M. Hawkins,et al.  The Changepoint Model for Statistical Process Control , 2003 .

[9]  Reay‐Chen Wang,et al.  Economic statistical np‐control chart designs based on fuzzy optimization , 1995 .

[10]  James Tannock,et al.  A fuzzy control charting method for individuals , 2003 .

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

[12]  Olgierd Hryniewicz,et al.  Soft methods in statistical quality control , 2000 .

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

[14]  Cheng-Ru Wu,et al.  Using expert technology to select unstable slicing machine to control wafer slicing quality via fuzzy AHP , 2008, Expert Syst. Appl..

[15]  John W. Seaman,et al.  The efficacy of fuzzy representations of uncertainty , 1994, IEEE Trans. Fuzzy Syst..

[16]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A CHANGE IN A POISSON RATE PARAMETER , 1998 .

[17]  Douglas M. Hawkins,et al.  A Multivariate Change-Point Model for Statistical Process Control , 2006, Technometrics.

[18]  Yan-Kwang Chen,et al.  A fuzzy reasoning based diagnosis system for X control charts , 2001, J. Intell. Manuf..

[19]  Charles W. Bradshaw,et al.  A fuzzy set theoretic interpretation of economic control limits , 1983 .

[20]  W. Woodall,et al.  A probabilistic and statistical view of fuzzy methods , 1995 .

[21]  Cengiz Kahraman,et al.  Using triangular fuzzy numbers in the tests of control charts for unnatural patterns , 1995, Proceedings 1995 INRIA/IEEE Symposium on Emerging Technologies and Factory Automation. ETFA'95.

[22]  Min-Chia Wang,et al.  The application of control chart for defects and defect clustering in IC manufacturing based on fuzzy theory , 2007, Expert Syst. Appl..

[23]  Marcus B. Perry,et al.  Change point estimation for monotonically changing Poisson rates in SPC , 2007 .

[24]  Douglas M. Hawkins,et al.  Statistical Process Control for Shifts in Mean or Variance Using a Changepoint Formulation , 2005, Technometrics.

[25]  Olgierd Hryniewicz,et al.  User-preferred solutions of fuzzy optimization problems--an application in choosing user-preferred inspection intervals , 2003, Fuzzy Sets Syst..

[26]  Joseph J. Pignatiello,et al.  Estimating the Change Point of the Process Fraction Non‐conforming with a Monotonic Change Disturbance in SPC , 2007, Qual. Reliab. Eng. Int..

[27]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A STEP-CHANGE WITH X 2 CONTROL CHARTS , 1998 .

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

[29]  Douglas M. Hawkins,et al.  A Change-Point Model for a Shift in Variance , 2005 .

[30]  Oscar Castillo,et al.  AN INTELLIGENT HYBRID APPROACH FOR INDUSTRIAL QUALITY CONTROL COMBINING NEURAL NETWORKS, FUZZY LOGIC AND FRACTAL THEORY , 2004 .

[31]  Kwok-Leung Tsui,et al.  A Review of Statistical and Fuzzy Quality Control Charts Based on Categorical Data , 1997 .

[32]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A STEP CHANGE IN A NORMAL PROCESS VARIANCE , 1998 .

[33]  Kimmo Latva-Käyrä,et al.  TMP pulp quality observer , 2001 .

[34]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[35]  Cengiz Kahraman,et al.  Development of fuzzy process control charts and fuzzy unnatural pattern analyses , 2006, Comput. Stat. Data Anal..

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

[37]  Hsu-Hwa Chang,et al.  Optimization design of control charts based on minimax decision criterion and fuzzy process shifts , 2008, Expert Syst. Appl..

[38]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A STEP-CHANGE IN THE PROCESS FRACTION NONCONFORMING , 2001 .

[39]  Mohammad Hossein Fazel Zarandi,et al.  A Neuro-fuzzy Multi-objective Design of Shewhart Control Charts , 2007, Analysis and Design of Intelligent Systems using Soft Computing Techniques.

[40]  C. Chou,et al.  A Note on Selecting Target and Process Capability Index Based on Fuzzy Optimization , 2002 .

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

[42]  Steven E. Rigdon.  Properties of the Duane plot for repairable systems , 2002 .

[43]  Bah-Hwee Gwee,et al.  Self-adjusting diagnostic system for the manufacture of crystal resonators , 1993, Conference Record of the 1993 IEEE Industry Applications Conference Twenty-Eighth IAS Annual Meeting.

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

[45]  Ahmet Çelik,et al.  A fuzzy approach to define sample size for attributes control chart in multistage processes: An application in engine valve manufacturing process , 2008, Appl. Soft Comput..

[46]  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..

[47]  Joe H. Sullivan,et al.  Detection of Multiple Change Points from Clustering Individual Observations , 2002 .

[48]  Abraham Kandel,et al.  On the very real distinction between fuzzy and statistical methods , 1995 .

[49]  Mohammad Hossein Fazel Zarandi,et al.  A hybrid fuzzy adaptive sampling - Run rules for Shewhart control charts , 2008, Inf. Sci..

[50]  Joseph J. Pignatiello,et al.  IDENTIFYING THE TIME OF A STEP-CHANGE WITH X 2 CONTROL CHARTS , 1998 .

[51]  Abraham Kandel,et al.  Discussion: On the Very Real Distinction Between Fuzzy and Statistical Methods , 1995 .

[52]  Joseph J. Pignatiello,et al.  A magnitude‐robust control chart for monitoring and estimating step changes for normal process means , 2002 .

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

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