Research Papers

Diagnosing Multistage Manufacturing Processes With Engineering-Driven Factor Analysis Considering Sampling Uncertainty

[+] Author and Article Information
Jian Liu

Department Systems and Industrial Engineering,
The University of Arizona,
Tucson, AZ 85721
e-mail: jianliu@email.arizoan.edu

Jionghua Jin

Department Industrial and Operations Engineering,
The University of Michigan,
Ann Arbor, MI 48109
e-mail: jhjin@umich.edu

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received December 7, 2012; final manuscript received May 15, 2013; published online July 17, 2013. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 135(4), 041020 (Jul 17, 2013) (9 pages) Paper No: MANU-12-1359; doi: 10.1115/1.4024661 History: Received December 07, 2012; Revised May 15, 2013; Accepted May 17, 2013

A new engineering-driven factor analysis (EDFA) method has been developed to assist the variation source identification for multistage manufacturing processes (MMPs). The proposed method investigated how to fully utilize qualitative engineering knowledge of the spatial variation patterns to guide the factor rotation. It is shown that ideal identification can be achieved by matching the rotated factor loading vectors with the qualitative indicator vectors (IV) that are defined according to spatial variation patterns based on the design constraints. However, the random sampling variability may significantly affect the estimation of the rotated factor loading vectors, leading to the deviations from their true values. These deviations may change the matching results and cause misidentification of the actual variation sources. By using implicit differentiation approach, this paper derives the asymptotic distribution and the associated variance-covariance matrix of the rotated factor loading vectors. Therefore, by considering the effect of sample estimation variability, the variation sources identification problem is reformulated as an asymptotic statistical test of the hypothesized match between the rotated factor loading vectors and the indicator vectors. A real-world case study is provided to demonstrate the effectiveness of the proposed matching method and its robustness to the sample uncertainty.

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Shi, J., 2006, Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes, CRC Press, Taylor & Francis Group, Boca Raton, FL, p. 469.
Wolbrecht, E., D'Ambrosio, B., Paasch, R., and Kirby, D., 2000, “Monitoring and Diagnosis of a Multistage Manufacturing Process Using Bayesian Networks,” Artif. Intell. Eng. Des. Anal. Manuf., 14(1), pp. 53–67. Available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=38559
Ceglarek, D., and Shi, J., 1996, “Fixture Failure Diagnosis for Auto Body Assembly Using Pattern Recognition,” ASME J. Eng. Ind., 118, pp. 55–65. [CrossRef]
Li, Z., and Zhou, S., 2006, “Robust Method of Multiple Variation Sources Identification in Manufacturing Processes For Quality Improvement,” ASME J. Manuf. Sci. Eng., 128, pp. 326–336. [CrossRef]
Apley, D. W., and Shi, J., 2001, “A Factor-Analysis Method for Diagnosing Variability in Multivariate Manufacturing Processes,” Technometrics, 43(1), pp. 84–95. [CrossRef]
Liu, J., Li, J., and Shi, J., 2005, “Engineering Driven Cause-Effect Modeling and Statistical Analysis for Multi-Operational Machining Process Diagnosis,” Trans. NAMRI/SME, 33, pp. 65–72.
Apley, D. W., and Lee, H. Y., 2003, “Identifying Spatial Variation Patterns in Multivariate Manufacturing Processes: A Blind Separation Approach,” Technometrics, 45(3), pp. 187–198. [CrossRef]
Jin, J., and Shi, J., 1999, “State Space Modeling of Sheet Metal Assembly for Dimensional Control,” ASME J. Manuf. Sci. Eng., 121, pp. 756–762. [CrossRef]
Liu, J., Jin, J., and Shi, J., 2010, “State Space Modeling for 3-D Variation Propagation in Rigid-Body Multistage Assembly Processes,” IEEE Trans. Autom. Sci. Eng., 7(4), pp. 724–735. [CrossRef]
Mantripragada, R., and Whitney, D. E., 1999, “Modeling and Controlling Variation Propagation in Mechanical Assemblies Using State Transition Models,” IEEE Trans. Rob. Autom., 15(1), pp. 124–140. [CrossRef]
Zhou, S., Huang, Q., and Shi, J., 2003, “State Space Modeling of Dimensional Variation Propagation in Multistage Machining Process Using Differential Motion Vector,” IEEE Trans. Rob. Autom., 19(2), pp. 296–309. [CrossRef]
Li, B., Yu, H., Yang, X., and Hu, Y., 2010, “Variation Analysis and Robust Fixture Design of a Flexible Fixturing System for Sheet Metal Assembly,” ASME J. Manuf. Sci. Eng., 132(4), p. 041014. [CrossRef]
Ding, Y., Ceglarek, D., and Shi, J., 2002, “Fault Diagnosis of Multistage Manufacturing Processes by Using State Space Approach,” ASME J. Manuf. Sci. Eng., 124(2), pp. 313–322. [CrossRef]
Zhou, S., Chen, Y., and Shi, J., 2004, “Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes,” IEEE Trans. Autom. Sci. Eng., 1(1), pp. 73–83. [CrossRef]
Kong, Z., Huang, W., and Oztekin, A., 2009, “Variation Propagation Analysis for Multi-Station Assembly Process With Consideration of GD&T Factors,” ASME J. Manuf. Sci. Eng., 131(5), p. 051010. [CrossRef]
Huang, W., Lin, J., Bezdecny, M., Kong, Z., and Ceglarek, D., 2007, “Stream-of-Variation Modeling I: A Generic 3D Variation Model for Rigid Body Assembly in Single Station Assembly Processes,” ASME J. Manuf. Sci. Eng., 129(4), pp. 821–831. [CrossRef]
Huang, W., Lin, J., Kong, Z., and Ceglarek, D., 2007, “Stream-of-Variation Modeling II: A Generic 3D Variation Model for Rigid Body Assembly in Multi Station Assembly Processes,” ASME J. Manuf. Sci. Eng., 131(5), 129(4), pp. 832–842. [CrossRef]
Abellan-Nebot, J.V., Liu, J., Subiron, F. R., and Shi, J., 2012, “State Space Modeling of Variation Propagation in Multistation Machining Processes Considering Machining-Induced Variations,” ASME J. Manuf. Sci. Eng., 134, p. 021002. [CrossRef]
Liu, J., Shi, J., and Hu, S. J., 2008, “Engineering-Driven Factor Analysis for Variation Source Identification in Multistage Manufacturing Processes,” ASME J. Manuf. Sci. Eng., 130(4), p. 041009. [CrossRef]
Kollo, T., and Neudecker, H., 1997, “Asymptotics of Pearson-Hotelling Principal-Component Vectors of Sample Variance and Correlation Matrices,” Behaviormetrika, 24(1), pp. 51–69. [CrossRef]
Jin, N., and Zhou, S., 2006, “Signature Construction and Matching for Fault Diagnosis in Manufacturing Processes Through Fault Space Analysis,” IIE Trans. Qual. Reliab. Eng., 38, pp. 341–354. [CrossRef]
Lawley, D. N., and Maxwell, A. E., 1971, Factor Analysis as a Statistical Method, Butterworths, London, p. 153.
Archer, C. O., and Jennrich, R.I., 1973, “Standard Errors for Rotated Factor Loadings,” Psychometrika, 38(4), pp. 581–592. [CrossRef]
Jennrich, R., 1973, “Standard Errors for Obliquely Rotated Factor Loadings,” Psychometrika, 38(4), pp. 593–604. [CrossRef]
Ogasawara, H., 2002, “Concise Formulas for the Standard Errors of Component Loading Estimates,” Psychometrika, 67(2), pp. 289–297. [CrossRef]
Girshick, M. A., 1939, “On the Sampling Theory of Roots of Determinantal Equations,” Ann. Math. Stat., 10, pp. 203–224. [CrossRef]


Grahic Jump Location
Fig. 2

Matching of estimated SPV with IVs

Grahic Jump Location
Fig. 1

Illustration of impacts of variation sources on KPCs

Grahic Jump Location
Fig. 5

Visualization of estimated SPVs

Grahic Jump Location
Fig. 6

Performance comparison in terms of robustness to sample uncertainty

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Fig. 3

The procedure of EDFA based variation source identification

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Fig. 4

Comparison of standardized SPVs



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