Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 20, No. 3 (October 2007) 233-242   

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  A GENERALIZED LINEAR STATISTICAL MODEL APPROACH TO MONITOR PROFILES
 
 
Seyed Taghi Akhavan Niaki* and Babak Abbasi

Department of Industrial Engineering, Sharif University of Technology
P.O. Box 11155-9414, Tehran, Iran
Niaki@Sharif.edu - b_abbasi@mehr.sharif.edu

Jamal Arkat


Department of Industrial Engineering, Iran University of Science and Technology
Tehran, Iran
j.arkat@gmail.com

*Corresponding Author

 
 
( Received: August 01, 2006 – Accepted in Revised Form: September 13, 2007 )
 
 

Abstract    Statistical process control methods for monitoring processes with univariate ormultivariate measurements are used widely when the quality variables fit to known probabilitydistributions. Some processes, however, are better characterized by a profile or a function of qualityvariables. For each profile, it is assumed that a collection of data on the response variable along withthe values of the corresponding quality variables is measured. While the linear function is thesimplest, it occurs frequently that many of the nonlinear functions may be transferred to linearfunctions easily. This paper proposes a control chart based on the generalized linear test (GLT) tomonitor coefficients of the linear profiles and an R-chart to monitor the error variance, thecombination of which is called GLT/R chart. While fixed values of the explanatory variables arecornerstones in other control charts proposed to monitor profiles, in GLT/R chart, it is not a necessarycondition. In order to illustrate the robustness of the GLT/R chart a simulation study has been done intwo different cases, i.e. fixed and non-fixed values of the explanatory variables. Then, the resultsobtained from GLT/R charts are compared to the ones from a multivariate T2 and ExponentiallyWeighted Moving Average/R (EWMA/R) control charts.

 

Keywords    General Linear Models, Multivariate Quality Control, Profile Monitoring, Statistical Control Chart

 

References   


1. Shewhart, W. A., “Economic Control of Quality of Manufactured Product”, D. Van Nostrand, New York, NY., (Republished in 1980 by the American Society for Quality Control, Milwaukee, WI), (1931).

2. Montgomery, D. C.,“Introduction to Statistical Quality Control”, 4th Edition, John Wiley and Sons, New York, NY, (2001).


3. Gardner, M. M., Lu, J. C., Gyurcsik, R. S., Wortman, J. J., Hornung, B. E., Heinisch, H. H., Rying, E. A., Rao, S., Davis, J. C. and Muzumder, P. K., “Equipment Fault Detection Using Spatial Signatures”, IEEE Transactions on Components, Packaging, and Manufacturing Technology-Part C., Vol. 20, (1997), 295-304.


4. Jin, J. and Shi, J., “Automatic Feature Extraction of Waveform Signals for In-Process Diagnostic Performance Improvement”, Journal of Intelligent Manufacturing, Vol. 12, (2001), 257-268.


5. Kang, L. and Albin, S. L., “On-Line Monitoring When the Process Yields a Linear Profile”, Journal of Quality Technology, Vol. 32, (2000), 418-426.


6. Jin, J. and Shi, J., “Feature-Preserving Data Compression of Stamping Tonnage Information Using Wavelets”, Technometrics, Vol. 41, (1999), 327-339.


7. Mahmoud, M. A. and Woodall, W. H., “Phase I Analysis of Linear Profiles with Calibration Applications”, Technometrics, Vol. 46, (2004), 277-391.


8. Kim, K., Mahmoud, M. A. and Woodall, W. H., “On the Monitoring of Linear Profiles”, Journal of Quality Technology, Vol. 35, (2003), 317-328.


9. Jensen, D. R., Hui, Y. V. and Ghare, P. M., “Monitoring an Input-Output Model for Production. I: The Control Charts”, Management Science, Vol. 30, (1984), 1197-1206.


10. Walker, E. and Wright, S. P. “Comparing Curves Using Additive Models”, Journal of Quality Technology, Vol. 34, (2002), 118-129.


11. Miller, A., “Analysis of Parameter Design Experiments for Signal-Response System”, Journal of Quality Technology, Vol. 34, (2002), 139-151.


12. Nair, V. N., Taam, W. and Ye, K. Q. “Analysis of Functional Responses from Robust Design Studies”, Journal of Quality Technology, Vol. 34, (2002), 355-370.


13. Ramsay, J. O. and Silverman, B. W., “Functional Data Analysis”, Springer-Verlag, New York, NY, (1997).


14. Brill, R. V., “A Case Study for Control Charting a Product Quality Measure that is a Continuous Function over Time”, Presented at the 45th Annual Fall Technical Conference, Toronto, Ontario, (2001).


15. Williams, J. D., Woodall, W. H. and Berch, J. B., “Phase I monitoring of nonlinear Profiles”, Presented at the 2003 Quality and Productivity Research Conference, Yorktown Heights, New York, (2003).


16. Lada, E. K. and Wilson, J. C. L., “A Wavelet-based Procedure for Process Fault Detection”, IEEE Transactions on Semiconductor Manufacturing, Vol. 15, (2002), 79-90.


17. Williams, J. D., Woodall, W. H., Spitzner, J., Montgomery, D. C. and Gupta, S., “Using Control Charts to Monitor Process and Product Quality Profiles”, Journal of Quality Technology, Vol. 36, (2004), 309-320.


18. Chang, S. I. and Samuel, T. R., “Intelligent CUSUM Scheme for Monitoring Process Variation Using Fuzzy Control”, International Journal of Smart Engineering System Design, Vol. 2, (1999), 1-15.


19. Neter, M. Kutner, H., Nachtsheim, C. J. and Wasserman, W., “Applied Linear Regression Models”, 3rd Edition, Irwin, Chicago, (1996).


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