Diagnosing Quality Problems on a Complex CNC Machine via Process-oriented Basis Representations
Abstract
A Process-oriented basis representation (POBREP) can be used to express a multivariate quality vector as a linear combination of fault patterns, plus a residual. Monitoring the estimated coefficients of the linear relationship is especially useful when the quality vector contains the same kind of measurements at different locations on a product. Such an application is the subject of this study. POBREPs are derived for different types of quality problems for a 9-axis CNC drilling machine; complicated geometry involved in the drilling operation makes the derivation process a challenging task. Therefore a thorough treatment of the derivation process is presented. Next, diagnostic power of the POBREP is demonstrated by an application to multivariate process data.
Keywords
References
- [1] R. R. Barton and D. R. González-Barreto, “Process Oriented Basis Representations for Multivariate Process Diagnostics”, Quality Engineering, Vol. 9, pp. 107-118, 1996. [2] B. Birgoren, Multivariate Statistical Process Control for Quality Diagnostics and Applications to Process Oriented Basis Representations, Ph.D. Thesis, PennState University, Pennsylvania, 1998. [3] B. Birgören, “A Method for Problem Diagnosis in Multivariate Quality Control: Constrained Solution Spaces for Process Oriented Basis Representations”, Teknoloji, Vol. 7 No. 1, pp. 19-28, 2004. [4] H. I. Espada Colon and D. R. Gonzalez-Barreto, “Component Registration Diagnosis for Printed Circuit Boards using Process-Oriented Basis Elements”, Computers & Industrial Engineering, Vol. 33, pp. 389-392, 1997. [5] E. J. Foster, R. R. Barton, N. Gautam, L. T. Truss and J. D. Tew, “The Process-oriented Multivariate Capability Index”, International Journal of Production Research, Vol. 43, No. 10, pp. 2135-2148, 2005. [6] G. C. Runger, R. R. Barton, E. D. Castillo and W. H. Woodall, “Optimal Monitoring of Multivariate Data for Fault Patterns”, Journal of Quality Technology, Vol. 39, No. 2, pp. 159-172, 2007. [7] C. A. Lowry and D. C. Montgomery, “A Review of Multivariate Control Charts”, IIE Transactions, Vol. 27, pp. 800-810, 1995. [8] D. W. Apley and J. Shi, “A Factor-Analysis Method for Diagnosing Variability in Multivariate Manufacturing Processes”, Technometrics, Vol. 43, pp 84-95, 2001. [9] H. Y. Lee and D. W. Apley, “Diagnosing Manufacturing Variation Using Second-Order and Fourth-Order Statistics”, International Journal of Flexible Manufacturing Systems, Vol. 16, pp 45-64, 2004. [10] R. L. Mason, J. C. Young, Multivariate Statistical Process Control with Industrial Application, ASA-SIAM, Philadelphia, PA, 2001. [11] Y. Ding, L. Zheng and S. Zhou, “Phase-I Analysis for Monitoring Nonlinear Profile Signals in Manufacturing Processes”, Journal of Quality Technology, Vol. 38, pp 199-216, 2006. [12] D. W. Apley and H. Y. Lee, “Identifying Spatial Variation Patterns in Multivariate Manufacturing Processes: A Blind Search Approach”, Technometrics, Vol. 45, pp 220-234, 2003. [13] N. Jin and S. Zhou, “Data-Driven Variation Source Identification of Manufacturing Processes Based on Eigenspace Comparison”, Naval Search Logistics, Vol. 53, pp. 383-396, 2006. [14] J. Neter, M. H. Kutner, C. J. Nachtsheim and W. Wasserman, Applied Linear Statistical Models (4th edition), McGraw-Hill/Irwin, IL, 1996.