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Robust Design in the Case of Data Contamination and Model Departure

  • Linhan Ouyang
  • Chanseok Park
  • Jai-Hyun Byun
  • Mark Leeds
Chapter
Part of the ICSA Book Series in Statistics book series (ICSABSS)

Abstract

In robust design, it is usually assumed that the experimental data are normally distributed and uncontaminated. However, in many practical applications, these assumptions can be easily violated. It is well known that normal model departure or data contamination can result in biased estimation of the optimal operating conditions of the control factors in the robust design framework. In this chapter, we investigate this possibility by examining these estimation effects on the optimal operating condition estimates in robust design. Proposed estimation methodologies for remedying the difficulties associated with data contamination and model departure are provided. Through the use of simulation, we show that the proposed methods are quite efficient when the standard assumptions hold and outperform the existing methods when the standard assumptions are violated.

Keywords

Robust design Outlier-resistance Contamination Model departure Relative efficiency 

Notes

Acknowledgements

The work of Professor Ouyang was supported by the National Natural Science Foundation of China under grants NSFC-71811540414 & 71702072 and the Natural Science Foundation for Jiangsu Institutions under grant BK20170810. The work of Professor Park was supported under the framework of the international cooperation program managed by the National Research Foundation of Korea (2018K2A9A2A06019662). The work of Professor Byun was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (2016R1D1A1B03935397).

References

  1. 1.
    Bendell, A., Disney, J., & Pridmore, W. A. (1987). Taguchi methods: Applications in world industry. London, UK: IFS Publications.Google Scholar
  2. 2.
    Dehnad, K. (1989). Quality control, robust design and the Taguchi method. Pacific Grove, CA: Wadsworth and Brooks/Cole.CrossRefGoogle Scholar
  3. 3.
    Taguchi, G., & Wu, Y. (1980). Introduction to off-line quality control. Nagoya: Central Japan Quality Control Association.Google Scholar
  4. 4.
    Taguchi, G. (1986). Introduction to quality engineering. White Plains, NY: Asian Productivity Organization.Google Scholar
  5. 5.
    Ross, P. J. (1988). Taguchi techniques for quality engineering. New York, NY: McGraw-Hill Book Company.Google Scholar
  6. 6.
    Kenett, R., & Zacks, S. (1998). Modern industrial statistics: Design and control of quality and reliability. Pacific Grove, CA: Duxbury.Google Scholar
  7. 7.
    Box, G. E. P. (1985). Discussion of off-line quality control, parameter design and the Taguchi methods. Journal of Quality Technology, 17, 198–206.CrossRefGoogle Scholar
  8. 8.
    Box, G. E. P. (1988). Signal-to-noise ratios, performance criteria, and transformations. Technometrics, 30, 1–17.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Vining, G. G., & Myers, R. H. (1990). Combining Taguchi and response surface philosophies: A dual response approach. Journal of Quality Technology, 22, 38–45.CrossRefGoogle Scholar
  10. 10.
    Pignatiello, J., & Ramberg, J. S. (1991). Top ten triumphs and tragedies of Genichi Taguchi. Quality Engineering, 4, 221–225.CrossRefGoogle Scholar
  11. 11.
    Myers, R. H., Khuri, A. I., & Vining, G. G. (1992). Response surface alternatives to the Taguchi robust design problem. The American Statistician, 46, 131–139.Google Scholar
  12. 12.
    Tiao, G. C., Bisgaard, S., Hill, W. J., Peña, D., & Stigler, S. M. (Eds.). (2000). Box on quality and discovery with design, control and robustness. New York, NY: Wiley.zbMATHGoogle Scholar
  13. 13.
    Myers, R. H., & Montgomery, D. C. (2002). Response surface methodology, 2nd Edn. New York, NY: Wiley.zbMATHGoogle Scholar
  14. 14.
    Gauri, S. K., & Pal, S. (2014). The principal component analysis (PCA)-based approaches for multi-response optimization: Some areas of concerns. The International Journal of Advanced Manufacturing Technology, 70(9), 1875–1887.CrossRefGoogle Scholar
  15. 15.
    Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response surface methodology: Process and product optimization using designed experiments, 4th Edn. New York, NY: Wiley.zbMATHGoogle Scholar
  16. 16.
    Del Castillo, E., & Montgomery, D. C. (1993) . A nonlinear programming solution to the dual response problem. Journal of Quality Technology, 25, 199–204.CrossRefGoogle Scholar
  17. 17.
    Lin, D. K. J., & Tu, W. (1995). Dual response surface optimization. Journal of Quality Technology, 27, 34–39.CrossRefGoogle Scholar
  18. 18.
    Copeland, K. A. F., & Nelson, P. R. (1996). Dual response optimization via direct function minimization. Journal of Quality Technology, 28, 331–336.CrossRefGoogle Scholar
  19. 19.
    Kim, K., & Lin, D. K. J. (1998). Dual response surface optimization: A fuzzy modeling approach. Journal of Quality Technology, 30, 1–10.CrossRefGoogle Scholar
  20. 20.
    Borror, C. M., & Montgomery, D. C. (2000). Mixed resolution designs as alternative to Taguchi inner/outer array designs for robust design problems. Quality and Reliability Engineering Inetrnational, 16, 1–11.CrossRefGoogle Scholar
  21. 21.
    Scibilia, B., Kobi, A., Barreau, A., & Chassagnon, R. (2003). Robust designs for quality improvement. IIE Transactions, 35, 487–492.CrossRefGoogle Scholar
  22. 22.
    Oyeyemi, G. M. (2004). Treatment of non-normal responses from designed experiments. Journal of the Nigerian Statistical Association, 17, 8–19.Google Scholar
  23. 23.
    Lee, M. K., Kwon, H. M., Kim, Y. J., & J. Bae. (2005). Determination of optimum target values for a production process based on two surrogate variables. In O. Gervasi, M. L. Gavrilova, V. Kumar, A. Laganá, H. P. Lee, Y. Mun, D. Taniar, & C. J. K. Tan (Eds.), Computational Science and Its Applications – ICCSA 2005. Lecture Notes in Computer Science (Vol. 3483, pp. 232–240). Berlin, Springer.CrossRefGoogle Scholar
  24. 24.
    Lee, S. B., & Park, C. (2006). Development of robust design optimization using incomplete data. Computers & Industrial Engineering, 50, 345–356.CrossRefGoogle Scholar
  25. 25.
    Lee, M. K., Kwon, H. M., Hong, S. H., & Kim, Y. J. (2007). Determination of the optimum target value for a production process with multiple products. International Journal of Production Economics, 107(1), 173–178. Special Section on Building Core-Competence through Operational Excellence.Google Scholar
  26. 26.
    Lee, S. B., Park, C., & Cho, B.-R. (2007). Development of a highly efficient and resistant robust design. International Journal of Production Research, 45, 157–167.CrossRefGoogle Scholar
  27. 27.
    Ardakani, M. K., & Wulff, S. S. (2013). An overview of optimization formulations for multiresponse surface problems. Quality and Reliability Engineering International, 29(1), 3–16.CrossRefGoogle Scholar
  28. 28.
    Park, C. (2013). Determination of the joint confidence region of optimal operating conditions in robust design by bootstrap technique. International Journal of Production Research, 51, 4695–4703.CrossRefGoogle Scholar
  29. 29.
    Ouyang, L., Ma, Y., Byun, J.-H., Wang, J., & Tu, Y. (2016). An interval approach to robust design with parameter uncertainty. International Journal of Production Research, 54(11), 3201–3215.CrossRefGoogle Scholar
  30. 30.
    Ardakani, M. K. (2016). The impacts of errors in factor levels on robust parameter design optimization. Quality and Reliability Engineering International, 32(5), 1929–1944.CrossRefGoogle Scholar
  31. 31.
    Park, C., & Leeds, M. (2016). A highly efficient robust design under data contamination. Computers & Industrial Engineering, 93, 131–142.CrossRefGoogle Scholar
  32. 32.
    Park, C., Ouyang, L., Byun, J.-H., & Leeds, M. (2017). Robust design under normal model departure. Computers & Industrial Engineering, 113, 206–220.CrossRefGoogle Scholar
  33. 33.
    Park, C., & Cho, B.-R. (2003). Development of robust design under contaminated and non-normal data. Quality Engineering, 15, 463–469.CrossRefGoogle Scholar
  34. 34.
    Hampel, F. R., Ronchetti, E., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust statistics: The approach based on influence functions. New York, NY: Wiley.zbMATHGoogle Scholar
  35. 35.
    Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35, 73–101.MathSciNetCrossRefGoogle Scholar
  36. 36.
    Huber, P. J., & Ronchetti, E. M. (2009). Robust statistics, 2nd Edn. New York, NY: Wiley.CrossRefGoogle Scholar
  37. 37.
    Rousseeuw, P., & Croux, C. (1993). Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273–1283.MathSciNetCrossRefGoogle Scholar
  38. 38.
    Bartlett, M. S., & Kendall, D. G. (1946). The statistical analysis of variance-heterogeneity and the logarithmic transformation. Journal of the Royal Statistical Society, 8, 128–138.MathSciNetzbMATHGoogle Scholar
  39. 39.
    Lindsay, B. G. (1994). Efficiency versus robustness: The case for minimum Hellinger distance and related methods. Annals of Statistics, 22, 1081–1114.MathSciNetCrossRefGoogle Scholar
  40. 40.
    Tukey, J. W. (1960). A survey of sampling from contaminated distributions. In I. Olkin, S. Ghurye, W. Hoeffding, W. Madow, & H. Mann (Eds.), Contributions to probability and statistics (pp. 448–485). Stanford: Stanford University Press.Google Scholar
  41. 41.
    Park, C., Basu, A., & Basu, S. (1995). Robust minimum distance inference based on combined distances. Communications in Statistics: Simulation and Computation, 24, 653–673.CrossRefGoogle Scholar
  42. 42.
    Park, C., & Basu, A. (2003). The generalized Kullback-Leibler divergence and robust inference. Journal of Statistical Computation and Simulation, 73, 311–332.MathSciNetCrossRefGoogle Scholar
  43. 43.
    Basu, A., Shioya, H., & Park, C. (2011). Statistical inference: The minimum distance approach. Monographs on Statistics and Applied Probability. London: Chapman & Hall.Google Scholar
  44. 44.
    Shamos, M. I. (1976). Geometry and statistics: Problems at the interface. In J. F. Traub (Ed.), Algorithms and complexity: New directions and recent results (pp. 251–280). New York, NY: Academic Press.Google Scholar
  45. 45.
    Hogg, R. V., McKean, J. W., & Craig, A. T. (2013). Introduction to mathematical statistics, 7th Edn. London: Pearson.Google Scholar
  46. 46.
    Hettmansperger, T. P., & McKean, J. W. (2010). Robust nonparametric statistical methods, 2nd Edn. Boca Raton, FL: Chapman & Hall/CRC.CrossRefGoogle Scholar
  47. 47.
    Lehmann, E. L. (1999). Elements of large-sample theory. New York, NY: Springer.CrossRefGoogle Scholar
  48. 48.
    Serfling, R. J. (2011). Asymptotic relative efficiency in estimation. In M. Lovric (Ed.), Encyclopedia of statistical science, Part I (pp. 68–82). Berlin: Springer.CrossRefGoogle Scholar
  49. 49.
    Huber, P. J. (1981). Robust statistics. New York, NY: Wiley.CrossRefGoogle Scholar
  50. 50.
    Dixon, W. J. (1960). Simplified estimation for censored normal samples. Annals of Mathematical Statistics, 31, 385–391.MathSciNetCrossRefGoogle Scholar
  51. 51.
    Lèvy-Leduc, C., Boistard, H., Moulines, E., Taqqu, M. S., & Reisen, V. A. (2011). Large sample behaviour of some well-known robust estimators under long-range dependence. Statistics, 45, 59–71.MathSciNetCrossRefGoogle Scholar
  52. 52.
    Huber, P. J. (1984). Finite sample breakdown of M- and P-estimators. Annals of Statistics, 12, 119–126.MathSciNetCrossRefGoogle Scholar
  53. 53.
    Staudte, R. G., & Sheather, S. J. (1900). Robust estimation and testing. New York, NY: Wiley.zbMATHGoogle Scholar
  54. 54.
    R Core Team. (2018). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.Google Scholar
  55. 55.
    Hampel, F. R., Marazzi, A., Ronchetti, E., Rousseeuw, P. J., Stahel, W. A., & Welsch, R. E. (1982). Handouts for the instructional meeting on robust statistical methods. In The 15th European Meeting of Statisticians, Palermo, Italy.Google Scholar
  56. 56.
    Park, C., & Basu, A. (2011). Minimum disparity inference based on tangent disparities. International Journal of Information and Management Sciences, 22, 1–25.MathSciNetzbMATHGoogle Scholar
  57. 57.
    Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman & Hall.CrossRefGoogle Scholar
  58. 58.
    Anderson, T. W. (1993). An introduction to multivariate statistical analysis. London: Wiley.Google Scholar
  59. 59.
    Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis, 6th Ed. Englewood Cliffs, NJ: Prentice-Hall.zbMATHGoogle Scholar
  60. 60.
    DeCarlo, L. T. (1997). On the meaning and use of kurtosis. Psychological Methods, 2, 292–307.CrossRefGoogle Scholar
  61. 61.
    Westfall, P. H. (2014). Kurtosis and peakedness, 1095–2014. R.I.P. The American Statistician, 68, 191–195.MathSciNetCrossRefGoogle Scholar
  62. 62.
    Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society B, 52, 105–124.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Linhan Ouyang
    • 1
  • Chanseok Park
    • 2
  • Jai-Hyun Byun
    • 3
  • Mark Leeds
    • 4
  1. 1.Department of Management Science and EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Applied Statistics Laboratory, Department of Industrial EngineeringPusan National UniversityBusanSouth Korea
  3. 3.Department of Industrial and Systems EngineeringGyeongsang National UniversityJinjuSouth Korea
  4. 4.Statematics ConsultingNew YorkUSA

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