Skip to main content
SpringerLink
Log in

Quality Improvement via Optimization of Tolerance Intervals During the Design Stage

  • Chapter
Applications of Interval Computations

Part of the book series: Applied Optimization ((APOP,volume 3))

Abstract

A deterministic model-based approach to quality improvement is proposed, along Taguchi’s ideas for off-line quality control. This new approach takes into account fluctuations in the factors; these fluctuations are characterized in terms of tolerance intervals.

The case of an a priori known model (i.e., known dependency of the performance characteristics on the factors) is considered first. The optimal factor design is chosen by worst-case optimization.

If the model’s parameters are unknown, a bounded-error approach is used to characterize their uncertainty. A min-max optimization is then performed, taking into account the fluctuations of the quality of the product components as well as the uncertainty on the model parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Belforte, B. Bona and V. Cerone, “Parameter estimation algorithms for a set-membership description of uncertainty”, Automatica, 1990, Vol. 26, pp. 887–898.

    Article  MATH  Google Scholar 

  2. G. Belforte and T. T. Tay, “Recursive estimation for linear models with set membership measurement errors”, Prep. 9th IFAC/IFORS Symp. Identification and System Parameter Estimation, Budapest, 8-12 July, 1991, pp. 872–877.

    Google Scholar 

  3. V. Broman and M. J. Shensa, “A compact algorithm for the intersection and approximation of N—dimensional polytopes”, Math, and Comput. in Simulation, 1990, Vol. 32, pp. 469–480.

    Article  MathSciNet  Google Scholar 

  4. G. Cagnac, E. Ramis and J. Commeau, Nouveau cours de mathématiques spéciales, Masson, Paris, 1965, Vol. 3, pp. 17–19.

    Google Scholar 

  5. V. Cerone, “Feasible parameter sets for linear models with bounded errors in all variables”, Automatica, 1993, Vol. 29, pp. 1551–1555.

    Article  MATH  Google Scholar 

  6. L. Chisci, A. Garulli and G. Zappa, “Recursive set membership state estimation via parallelotopes”, Prep. 10th IF AC Symp. on System Identification, Copenhagen, 4–6 July, 1994, Vol. 3, pp. 383–388.

    Google Scholar 

  7. T. Clement and S. Gentil, “Reformulation of parameter identification with unknown but bounded errors”, Math, and Comput. in Simulation, 1988, Vol. 30, pp. 257–270.

    Article  MATH  MathSciNet  Google Scholar 

  8. T. Clément and S. Gentil, “Recursive membership set estimation for output-error models”, Math. Comput. in Simulation, 1990, Vol. 32, pp. 505–513.

    Article  Google Scholar 

  9. P. Combettes, “The foundations of set theoretic estimation”, Proc. of the IEEE, 1993, Vol. 81, pp. 182–208.

    Article  Google Scholar 

  10. J. R. Deller, “Set membership identification in digital signal processing”, IEEE ASSP Magazine, 1989, Vol. 6, pp. 4–20.

    Article  Google Scholar 

  11. J. R. Deller, M. Nayeri and S. F. Odeh, “Least-square identification with error bounds for real-time signal processing and control”, Proc. of the IEEE, 1993, Vol. 81, pp. 813–849.

    Article  Google Scholar 

  12. E. Fogel and Y. F. Huang, “On the value of information in system identification — bounded noise case”, Automatica, 1982, Vol. 18, pp. 229–238.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. R. Hansen, “Global optimization using interval analysis — the multidimensional case”, Numer. Math., 1980, Vol. 34, pp. 247–270.

    Article  MATH  MathSciNet  Google Scholar 

  14. K. Ishikawa, “Quality and standardization: progress for economic success”, Quality Progress, 1984, Vol. 1, pp. 16–20.

    Google Scholar 

  15. J. M. Lucas, “Optimum composite designs”, Technometrics, 1974, Vol. 16, pp. 561–567.

    Article  MATH  MathSciNet  Google Scholar 

  16. Y. A. Merkuryev, “Identification of objects with unknown bounded disturbances”, Int. J. Control, 1989, Vol. 50, pp. 2333–2340.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Messaoud and G. Favier, “Recursive determination of parameter uncertainty intervals for linear models with unknown but bounded errors”, Prep. 10th IFAC Symp. on System Identification, Copenhagen, 4–6 July, 1994, Vol. 3, pp. 365–369.

    Google Scholar 

  18. H. Messaoud, G. Favier and R. Santos Mendes, “Adaptative robust pole placement by connecting identification and control”, Prep. 4th IFAC Int. Symp. Adaptative Systems in Control and Signal Processing, Grenoble, 1992, pp. 41–46.

    Google Scholar 

  19. M. Milanese and G. Belforte, “Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: linear families of models and estimators”, IEEE Trans. Autom. Control, 1982, Vol. 27, pp. 408–414.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Milanese and A. Vicino, “Optimal estimation theory for dynamic systems with set membership uncertainty: an overview”, Automatica, 1991, Vol. 27, pp. 997–1009.

    Article  MATH  MathSciNet  Google Scholar 

  21. S. H. Mo and J. P. Norton, “Fast and robust algorithms to compute exact polytope parameter bounds”, Math. and Comput. in Simulation, 1990, Vol. 32, pp. 481–493.

    Article  MathSciNet  Google Scholar 

  22. R. E. Moore, Methods and Applications of Interval Analysis, SIAM Studies in Applied Mathematics, Philadelphia, 1979.

    MATH  Google Scholar 

  23. J. P. Norton, “Identification of parameter bounds for ARMAX models from records with bounded noise”, Int. J. Control, 1987, Vol. 45, pp. 375–390.

    Article  MATH  Google Scholar 

  24. J. P. Norton, “Identification and application of bounded-parameter models”, Automatica, 1987, Vol. 23, pp. 497–507.

    Article  MATH  Google Scholar 

  25. J. P. Norton (Ed.), “Special issue on bounded-error estimation”, Issues I and II, Int. J. of Adapt. Contr. and Signal Proc., 1994, Vol. 8, and 1995, Vol. 9.

    Google Scholar 

  26. J. P. Norton (Ed.), “Special issue on bounded-error estimation”, Issues I and II, Int. J. of Adapt. Contr. and Signal Proc., 1994, Vol. 8, and 1995, Vol. 9.

    Google Scholar 

  27. H. Piet-Lahanier and E. Walter, “Polyhedric approximation and tracking for bounded-error models”, Proc. IEEE Int. Symp. Circuits and Systems, Chicago, 1993, pp. 782–785.

    Google Scholar 

  28. L. Pronzato and E. Walter, “Minimum-volume ellipsoids containing compact sets: application to parameter bounding”, Automatica, 1994, Vol. 30, pp. 1731–1739.

    Article  MATH  MathSciNet  Google Scholar 

  29. L. Pronzato, E. Walter and H. Piet-Lahanier, “Mathematical equivalence of two ellipsoidal algorithms for bounded-error estimation”, Proc. 28th IEEE Conference on Decision and Control, Tampa, 1989, pp. 1952–1955.

    Chapter  Google Scholar 

  30. L. Pronzato, E. Walter, A. Venot and J. -F. Lebruchec, “A general purpose global optimizer: implementation and applications”, Math, and Computers in Simulation, 1984, Vol. 26, pp. 412–422.

    Article  MathSciNet  Google Scholar 

  31. B. Pschenichnyy and V. S. Pokotilo, “A minmax approach to the estimation of linear regression parameters”, Engrg. Cybernetics, 1983, pp. 77–85.

    Google Scholar 

  32. F. S. Schweppe, Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, 1973.

    Google Scholar 

  33. K. Shimitzu and E. Aiyoshi, “Necessary conditions for min-max problems and algorithm by a relaxation procedure”, IEEE Trans. Autom. Control, 1980, Vol. 25, pp. 62–66.

    Article  Google Scholar 

  34. G. Taguchi, Introduction to Quality Engineering, APO, Tokyo, 1986.

    Google Scholar 

  35. G. Taguchi and M. S. Phadke, “Quality engineering through design optimization”, IEEE Global Telecommunications Conference, Atlanta, GA, 1984, pp. 1106–1113

    Google Scholar 

  36. S. M. Veres and J. P. Norton, “Parameter-bounding algorithms for linear errors in variables models”, Prep. 9th IFAC/IFORS Symp. on Identification and System Parameter Estimation, Budapest, 1991, pp. 1038–1043.

    Google Scholar 

  37. I. N. Vuchkov and L. N. Boyadjieva, “The robustness against tolerances of performance characteristics described by second order polynomials”, in Optimal design and analysis of experiments (Eds. Y. Dodge, V. Fedorov and H. Wynn ), North Holland, Amsterdam, 1988, pp. 293–309.

    Google Scholar 

  38. I. N. Vuchkov and L. N. Boyadjieva, “A model-based approach to the robustness against tolerances”, Proc. 33rd EOQC Annual Conference, Vienna, 1989, pp. 585–592.

    Google Scholar 

  39. I. N. Vuchkov and L. N. Boyadjieva, “Quality improvement through design of experiments with both product parameters and external noise factors”, in Model Oriented Data Analysis. A Survey of Recent Methods (Eds. V. Fedorov, W. G. Müller and I. N. Vuchkov ), Physica Verlag, Heildelberg, 1992.

    Google Scholar 

  40. E. Walter and H. Piet-Lahanier, “Exact recursive polyhedral description of the feasible parameter set for bounded-error models”, IEEE Trans. Autom. Control, 1989, Vol. 34, No. 8, pp. 911–915.

    Article  MATH  MathSciNet  Google Scholar 

  41. E. Walter and H. Piet-Lahanier, “Estimation of parameter bounds from bounded — error data: a survey”, Math. Comput. in Simulation, 1990, Vol. 32, pp. 449–468.

    Article  MathSciNet  Google Scholar 

  42. E. Walter and L. Pronzato, “Characterizing sets defined by inequalities”, Prep. 10th IFAC Symp. on System Identification, Copenhagen, 4–6 July, 1994, Vol. 2, pp. 15–26.

    Google Scholar 

  43. H. P. Wynn and A. Winterbottom, Lectures on Experimental Design and Off-line Quality Control (Taguchi methods), City University, London, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS/ESE, Plateau de Moulon, 91192, Gif sur Yvette, France

    Sevgui Hadjihassan & Eric Walter

  2. Laboratoire I3S, CNRS URA-1376, 250 av. A. Einstein, Sophia Antipolis, 66560, Valbonne, France

    Luc Pronzato

Authors
  1. Sevgui Hadjihassan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eric Walter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luc Pronzato
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Southwestern Louisiana, USA

    R. Baker Kearfott

  2. University of Texas at El Paso, USA

    Vladik Kreinovich

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Kluwer Academic Publishers

About this chapter

Cite this chapter

Hadjihassan, S., Walter, E., Pronzato, L. (1996). Quality Improvement via Optimization of Tolerance Intervals During the Design Stage. In: Kearfott, R.B., Kreinovich, V. (eds) Applications of Interval Computations. Applied Optimization, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3440-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3440-8_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3442-2

  • Online ISBN: 978-1-4613-3440-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation