## The Annals of Applied Statistics

### Model transfer across additive manufacturing processes via mean effect equivalence of lurking variables

#### Abstract

Shape deviation models constitute an important component in quality control for additive manufacturing (AM) systems. However, specified models have a limited scope of application across the vast spectrum of processes in a system that are characterized by different settings of process variables, including lurking variables. We develop a new effect equivalence framework and Bayesian method that enables deviation model transfer across processes in an AM system with limited experimental runs. Model transfer is performed via inference on the equivalent effects of lurking variables in terms of an observed factor whose effect has been modeled under a previously learned process. Studies on stereolithography illustrate the ability of our framework to broaden both the scope of deviation models and the comprehensive understanding of AM systems.

#### Article information

Source
Ann. Appl. Stat., Volume 12, Number 4 (2018), 2409-2429.

Dates
Revised: January 2018
First available in Project Euclid: 13 November 2018

https://projecteuclid.org/euclid.aoas/1542078050

Digital Object Identifier
doi:10.1214/18-AOAS1158

Mathematical Reviews number (MathSciNet)
MR3875706

#### Citation

Sabbaghi, Arman; Huang, Qiang. Model transfer across additive manufacturing processes via mean effect equivalence of lurking variables. Ann. Appl. Stat. 12 (2018), no. 4, 2409--2429. doi:10.1214/18-AOAS1158. https://projecteuclid.org/euclid.aoas/1542078050

#### References

• Bareinboim, E. and Pearl, J. (2016). Causal inference and the data-fusion problem. In Proceedings of the National Academy of Sciences 113 7345–7352.
• Box, G. E. P. (1966). Use and abuse of regression. Technometrics 8 625–629.
• Buckholtz, B., Ragai, I. and Wang, L. (2015). Cloud manufacturing: Current trends and future implementations. J. Manuf. Sci. Eng. 137 040902.
• Campbell, T., Williams, C., Ivanova, O. and Garrett, B. (2011). Could 3D Printing Change the World? Technologies, Potential, and Implications of Additive Manufacturing. Atlantic Council, Washington, DC.
• Cook, R. D. and Critchley, F. (2000). Identifying regression outliers and mixtures graphically. J. Amer. Statist. Assoc. 95 781–794.
• Dai, W., Yang, Q., Xue, G.-R. and Yu, Y. (2007). Boosting for transfer learning. In Proceedings of the 24th International Conference on Machine Learning.
• Duane, S., Kennedy, A., Pendleton, B. J. and Roweth, D. (1987). Hybrid Monte Carlo. Phys. Lett. B 195 216–222.
• Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457–472.
• Germany Trade & Invest (2014). Industrie 4.0: Smart manufacturing for the future. Online.
• Gibson, I., Rosen, D. W. and Stucker, B. (2009). Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing. Springer, New York.
• Huang, Q., Nouri, H., Xu, K., Chen, Y., Sosina, S. and Dasgupta, T. (2014). Statistical predictive modeling and compensation of geometric deviations of 3D printed products. J. Manuf. Sci. Eng. 136 061008.
• Huang, Q., Zhang, J., Sabbaghi, A. and Dasgupta, T. (2015). Optimal offline compensation of shape shrinkage for 3D printing processes. IIE Trans. Qual. Reliab. 47 431–441.
• Imbens, G. W. and Rubin, D. B. (2015). Causal Inference—For Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge Univ. Press, New York.
• Jin, Y., Qin, S. and Huang, Q. (2016). Offline predictive control of out-of-plane geometric errors for additive manufacturing. J. Manuf. Sci. Eng. 138 121005.
• Joiner, B. L. (1981). Lurking variables: Some examples. Amer. Statist. 35 227–233.
• Luan, H. and Huang, Q. (2017). Prescriptive modeling and compensation of in-plane geometric deviations for 3D printed freeform products. IEEE Trans. Autom. Sci. Eng. 14 73–82.
• Meng, X.-L. (1994). Posterior predictive $p$-values. Ann. Statist. 22 1142–1160.
• Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In Handbook of Markov Chain Monte Carlo (S. Brooks, A. Gelman, G. L. Jones and X.-L. Meng, eds.). 113–162. CRC Press, Boca Raton, FL.
• Pan, S. J. and Yang, Q. (2010). A survey on transfer learning. IEEE Trans. Knowl. Data Eng. 22 1345–1359.
• Pardoe, D. and Stone, P. (2010). Boosting for regression transfer. In Proceedings of the 27th International Conference on Machine Learning.
• Pearl, J. (1995). Causal diagrams for empirical research. Biometrika 82 669–710.
• Pearl, J. and Bareinboim, E. (2014). External validity: From do-calculus to transportability across populations. Statist. Sci. 29 579–595.
• Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Statist. 12 1151–1172.
• Sabbaghi, A., Huang, Q. and Dasgupta, T. (2018). Bayesian model building from small samples of disparate data for capturing in-plane deviation in additive manufacturing. Technometrics. DOI:10.1080/00401706.2017.1391715.
• Sabbaghi, A., Dasgupta, T., Huang, Q. and Zhang, J. (2014). Inference for deformation and interference in 3D printing. Ann. Appl. Stat. 8 1395–1415.
• Shewhart, W. A. (1931). Economic Control of Quality of Manufacturing Product, 1st ed. Van Nostrand Reinhold, New York.
• Tong, K., Joshi, S. and Lehtihet, E. A. (2008). Error compensation for fused deposition modeling (FDM) machine by correcting slice files. Rapid Prototyping J. 14 4–14.
• Tong, K., Lehtihet, E. A. and Joshi, S. (2003). Parametric error modeling and software error compensation for rapid prototyping. Rapid Prototyping J. 9 301–313.
• Wang, H. and Huang, Q. (2006). Error cancellation modeling and its application to machining process control. IIE Trans. 38 355–364.
• Wang, H. and Huang, Q. (2007). Using error equivalence concept to automatically adjust discrete manufacturing processes for dimensional variation control. J. Manuf. Sci. Eng. 129 644–652.
• Wang, H., Huang, Q. and Katz, R. (2005). Multi-operational machining processes modeling for sequential root cause identification and measurement reduction. J. Manuf. Sci. Eng. 127 512–521.
• Wu, D., Rosen, D. W., Wang, L. and Schaefer, D. (2015). Cloud-based design and manufacturing: A new paradigm in digital manufacturing and design innovation. Comput.-Aided Design 59 1–14.
• Yates, F. and Cochran, W. G. (1938). The analysis of groups of experiments. J. Agric. Sci. 28 556–580.
• Zhou, C. and Chen, Y. (2012). Additive manufacturing based on optimized mask video projection for improved accuracy and resolution. J. Manuf. Process. 14 107–118.
• Zhou, C., Chen, Y. and Waltz, R. A. (2009). Optimized mask image projection for solid freeform fabrication. J. Manuf. Sci. Eng. 131 061004.