From Profile to Surface Monitoring: SPC for Cylindrical Surfaces Via Gaussian Processes

References

• Ababou, R.; Amvrossios, C.; Bagtzoglou, C.; and Wood, E. F. (1994). “On the Condition Number of Covariance Matrices in Kriging Estimation, and Simulation of Random Fields”. Mathematical Geology 26, pp. 99–133.
   Google Scholar
• Abdel-Salam, A. G.; Birch, J. B.; and Jensen, W. A. (2010). “Nonparametric and Semiparametirc Mixed Models Methods for Phase I Profile Monitoring”. Technical Report, Department of Statistics, Virginia Polytechnic Institute # State University http://www.web-e.stat.vt.edu/dept/web-e/tech_reports/TechReport10-2.pdf.
   Google Scholar
• Banerjee, S. (2005). “On Geodetic Distance Computations in Spatial Modeling”. Biometrics 61, pp. 617–625.
   PubMed Web of Science ®Google Scholar
• Champ, C. W.; Jones-Farmer, A. L.; and Rigdon, S. E. (2005). “Properties of the T2 Control Chart When Parameters Are Estimated”. Technometrics 47, pp. 437–445.
   Web of Science ®Google Scholar
• Chenouri, S.; Steiner, S.; and Variyath, A. M. (2009). “A Multivariate Robust Control Chart for Individual Observations”. Journal of Quality Technology 41, pp. 259–271
   Web of Science ®Google Scholar
• Chipman, H. A.; MacKay, R. J.; and Steiner, S. H. (2010) “Comment: Nonparametric Profile Monitoring by Mixed Effects Modeling”. Technometrics 52 (3), pp. 280–283.
   Web of Science ®Google Scholar
• Cho, N. W. and Tu, J. F. (2001). “Roundness Modeling of Machined Parts for Tolerance Analysis”. Precision Engineering 25, pp. 35–47.
   Web of Science ®Google Scholar
• Colosimo, B. M. and Pacella, M. (2007). “On the Use of Principal Component Analysis to Identify Systematic Patterns in Roundness Profiles”. Quality and Reliability Engineering International 23, pp. 707–725.
   Web of Science ®Google Scholar
• Colosimo, B. M. and Pacella, M. (2010). “A Comparison Study of Control Charts for Statistical Monitoring of Functional Data”. International Journal of Production Research 48, pp. 1575–1601.
   Web of Science ®Google Scholar
• Colosimo, B. M. and Pacella, M. (2011). “Analyzing the Effect of Process Parameters on the Shape of 3D Profiles”. Journal of Quality Technology 43, pp. 169–195.
   Web of Science ®Google Scholar
• Colosimo, B. M. and Senin, N., eds. (2011). Geometric Tolerances. Impact on Product Design, Quality Inspection and Statistical Process Monitoring. London: Springer.
   Google Scholar
• Colosimo, B. M.; Mammarella, F.; and Petrò, S. (2010). “Quality Control of Manufactured Surfaces”. In Frontiers of Statistical Quality Control, Lenz, H. J. and Wilrich, P. T., eds. Springer.
   Google Scholar
• Colosimo, B. M.; Pacella, M.; and Semeraro, Q. (2008). “Statistical Process Control for Geometric Specifications: On the Monitoring of Roundness Profiles”. Journal of Quality Technology 40, pp. 1–18.
   Web of Science ®Google Scholar
• Colosimo, B. M.; Pacella, M.; and Semeraro, Q. (2011). “Statistical Process Control for Geometric Specifications”. In Statistical Analysis of Profile Monitoring, Noorossana, R.; Saghaei, A.; and Amiri, A., eds., pp. 217–252. Hoboken, NJ: John Wiley # Sons.
   Google Scholar
• Cressie, N. A. C. (1993). Statistics for Spatial Data, revised edition. New York, NY: John Wiley # Sons.
   Google Scholar
• Curriero, F. C. (2006). “On the Use of Non-Euclidean Distance Measures in Geostatistics”. Mathematical Geology 38, pp. 907–926.
   Google Scholar
• del Castillo, E.; Colosimo, B. M.; and Tajbakhsh, S. (2013). “Geodesic Gaussian Processes for the Reconstruction of a Free-Form Surface”, submitted paper. Available as technical report at http://www2.ie.psu.edu/Castillo/research/EngineeringStatistics/publications.htm.
   Google Scholar
• Forrester, A.; Sobester, A.; and Keane, A. (2008). Engineering Design Via Surrogate Modelling: A Practical Guide. New York, NY: John Wiley # Sons.
   Google Scholar
• Grimshaw, S. D.; Blades, N. J.; and Miles, M. P. (2013). “Spatial Control Charts for the Mean”. Journal of Quality Technology 45 (2), pp. 130–148.
   Web of Science ®Google Scholar
• Henke, R. P.; Summerhays, K. D.; Baldwin, J. M.; Cassou, R. M.; and Brown, C. W. (1999). “Methods for Evaluation of Systematic Geometric Deviations in Machined Parts and Their Relationships to Process Variables”. Precision Engineering 23, pp. 273–292.
   Web of Science ®Google Scholar
• Higham, N. J. (1996). Accuracy and Stability of Numerical Algorithms. SIAM.
   Google Scholar
• Higham, N. J. (2002). “Computing the Nearest Correlation Matrix: A Problem from Finance”. JIMA 22, pp. 329–343.
   Google Scholar
• ISO (2012). Geometrical Product Specifications (GPS)-Geometrical Tolerancing: Tolerances of Form, Orientation, Location and Run-Out. ISO 1101:2012, International Organization for Standardization.
   Google Scholar
• Johnson, M. E.; Moore, L. M.; and Ylvisaker, D. (1990). “Minimax and Maximin Distance Designs”. Journal of Statistical Planning and Inference 26, pp. 131–148.
   Web of Science ®Google Scholar
• Joseph, V. R. and Hung, Y. (2008). “Orthogonal-Maximum Latin Hypercube Designs”. Statistica Sinica 18, pp. 171–186.
   Web of Science ®Google Scholar
• Kang, L. and Albin, S. L. (2000). “On-Line Monitoring when the Process Yields a Linear Profile”. Journal of Quality Technology 32, pp. 418–426.
   Web of Science ®Google Scholar
• Kim, K.; Mahmoud, M. A.; and Woodall, W. H. (2003). “On the Monitoring of Linear Profiles”. Journal of Quality Technology 35, pp. 317–328.
   Web of Science ®Google Scholar
• Mahmoud, M. A. and Woodall, W. H. (2004). “Phase I Analysis of Linear Profiles with Calibration Applications”. Technometrics 46, pp. 377–391.
   Web of Science ®Google Scholar
• Matheron, G. (1963). “Principles of Geostatistics”. Economic Geology 58, pp. 1246–1266.
   Google Scholar
• McKay, M. D.; Beckman, R. J.; and Conover, W. J. (1979). “Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code”. Technometrics 21, pp. 239–245.
   Web of Science ®Google Scholar
• Megahed, F. M.; Woodall, H. W.; and Camelio, J. A. (2011). “A Review and Perspective on Control Charting with Image Data”. Journal of Quality Technology 43, pp. 83–98.
   Web of Science ®Google Scholar
• Montgomery, D. C. (2009). Introduction to Statistical Quality Control, 6th edition. New York, NY: John Wiley # Sons, Inc.
   Google Scholar
• Morris, M. D. and Mitchell, T. J. (1995). “Exploratory Designs for Computational Experiments”. Journal of Statistical Planning and Inference 43, pp. 381–402.
   Web of Science ®Google Scholar
• Noorossana, R. R.; Saghei, A.; and Amiri, A., eds. (2012). Statistical Analysis of Profile Monitoring. Wiley.
   Google Scholar
• Posa, D. (1989). “Conditioning of the Stationary Kriging Matrices for Some Well-Known Covariance Models”. Mathematical Geology 21, pp. 755–765.
   Google Scholar
• Prabhu, S. S. and Runger, G. C. (1997). “Designing a Multivariate EWMA Control Chart”. Journal of Quality Technology 29, pp. 8–15.
   Web of Science ®Google Scholar
• Qiu, P.; Zou, C.; and Wang, Z. (2010). “Nonparametric Profile Monitoring by Mixed Effects Modeling–with Discussion”. Technometrics 52 (3), pp. 265–293.
   Web of Science ®Google Scholar
• Rasmussen, C. E. and Nickisch, H. (2010). “Gaussian Process for Machine Learning Toolbox”. Journal of Machine Learning Research 11, pp. 3011–3015.
   Web of Science ®Google Scholar
• Rasmussen, C. E. and Nickisch, H. (2011). The GPML Toolbox–Version 3.1. url: www.GaussianProcess.org/gpml, accessed in May 2013.
   Google Scholar
• Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press.
   Google Scholar
• Stein, M. L. (1999). Statistical Interpolation of Spatial Data: Some Theory for Kriging. New York, NY: Springer.
   Google Scholar
• Wilkinson, J. H. (1961). “Error Analysis of Direct Methods of Matrix Inversion”. Journal of the Association for Computing Machinery 8, pp. 281–330.
   Google Scholar
• Woodall, W. H. (2007). “Current Research on Profile Monitoring”. Produção 17, pp. 420–425.
   Google Scholar
• Woodall, W. H.; Spitzner, D. J.; Montgomery, D. C.; and Gupta, S. (2004). “Using Control Charts to Monitor Process and Product Quality Profiles”. Journal of Quality Technology 36, pp. 309–320.
   Web of Science ®Google Scholar
• Xia, H.; Ding, Y.; and Wang, J. (2008). “Gaussian Process Method for Form Error Assessment Using Coordinate Measurements”. IIE Transactions 40, pp. 931–946.
   Web of Science ®Google Scholar
• Zhang, X.D.; Zhang, C.; Wang, B.; and Feng, S. C. (2005). “Unified Functional Tolerancing Approach for Precision Cylindrical Components”. International Journal of Production Research 43, pp. 25–47.
   Web of Science ®Google Scholar
• Zhang, Y.; He, Z.; Zhang, C.; and Woodall, W. H. (2013). Control Charts for Monitoring Linear Profiles with Within-Profile Correlation Using Gaussian Process Models. Quality and Reliability Engineering International.
   Google Scholar