Skip to main content
SpringerLink
Log in

A computational algorithm for selecting robust designs in safety and quality critical processes

  • Published:
Sankhya B Aims and scope Submit manuscript

Abstract

This article considers robust designs for safety and quality critical processes. In critical processes, the choice of control settings should ensure that the product quality remains near the target for each and every value of the noise variable. This objective is realized by using a min-max approach which minimizes the maximum possible deviation (caused by noise) of the estimated response from the target value. An algorithm for computing such control settings based on entropic regularization is discussed. The proposed method is used on automobile crash test data to select maximally safe designs for the interior rim of cars. A second example on the design of drug granulation parameters to produce uniformly sized granules is also included.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Copeland, K.A.F., and P.R. Nelson. 1996. Dual response optimization via direct function minimization. Journal of Quality Technology 28:331–336.

    Google Scholar 

  • Del Castillo, E., S.K. Fan, and J. Semple. 1997. Computation of global optima in dual response systems. Journal of Quality Technology 29:347–353.

    Google Scholar 

  • Del Castillo, E., and D.C. Montgomery. 1993. A nonlinear programming solution to the dual response problem. Journal of Quality Technology 25:199–204.

    Google Scholar 

  • Dette, H., L. Haines, and L. Imhof. 2003. Bayesian and maximin optimal designs for heteroscedastic regression models. Canadian Journal of Statistics 33:221–241.

    Article  MathSciNet  Google Scholar 

  • Evans, L.C., and R.F. Gariepy. 1992. Measure theory and fine properties of functions 2nd edn. Boca Raton, Florida: CRC Press.

    MATH  Google Scholar 

  • Fan, S.K.S. 2000. A generalized global optimization algorithm for dual response systems. Journal of Quality Technology 32:444–456.

    Google Scholar 

  • Huyer, W., and A. Neumaier. 1999. Global optimization by multilevel coordinate search. Journal of Global Optimization 14:331–355.

    Article  MathSciNet  MATH  Google Scholar 

  • Jones, D.R., C.D. Perttunen, and B.E. Stuckman. 1993. Lipschitzian optimization without the lipschitz constant. Journal of Optimization Theory and Applications 79:157–181.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacker, R.N. 1985. Off-line quality control, parameter design, and the Taguchi method. Journal of Quality Technology 17:176–209.

    Google Scholar 

  • Kiwiel, K. 1987. A direct method of linearization for continuous minimax problems. Journal of Optimization Theory and Applications 55:271–287.

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, D.K.J., and W. Tu. 1995. Dual response surface optimization. Journal of Quality Technology 27:34–39.

    Google Scholar 

  • Mukherjee, R., and S. Huda. 1985. Minimax second- and third-order designs to estimate the slope of a response surface. Biometrika 72:173–178.

    Article  MathSciNet  Google Scholar 

  • Myers, R.H., A.I. Khuri, and G.G. Vining. 1992. Response surface alternatives to the Taguchi robust parameter design approach. The American Statistician 46:131–139.

    Article  Google Scholar 

  • Nair, V.N. 1992. Taguchi’s parameter design: A panel discussion. Technometrics 34:127–161.

    Article  MathSciNet  Google Scholar 

  • Ogawa, S., T. Kamijima, Y. Miyamoto, M. Miyajima, H.K.T. Sato, and T. Nagai. 1994. A new attempt to solve the scale-up problem for granulation using response surface methodology. Journal of Pharmaceutical Sciences 83:439–443.

    Article  Google Scholar 

  • Parpas, P., B. Rustem, and C. Pantelides. 2009. An algorithm for the global optimization of a class of continuous minimax problems. Journal of Optimization Theory and Applications 141:461–473.

    Article  MathSciNet  MATH  Google Scholar 

  • Pickle, S.M., T.J. Robinson, J.B. Bircha, and C.M. Anderson-Cook. 2008. A semi-parametric approach to robust parameter design. Journal of Statistical Planning and Inference 138:114–131.

    Article  MathSciNet  MATH  Google Scholar 

  • Polak, E. 1994. Optimization: Algorithms and consistent approximations 2nd edn. New York: Springer.

    Google Scholar 

  • Polyak, R.A. 1988. Smooth optimization methods for minimax problems. SIAM Journal on Control and Optimization 26:1274–1286.

    Article  MathSciNet  MATH  Google Scholar 

  • Rai, B., N. Singh, and M. Ahmed. 2005. Robust design of an interior hard trim to improve occupant safety in a vehicle crash. Reliability Engineering and System Safety 89:296–304.

    Article  Google Scholar 

  • Robinson, T.J., C.M. Borror, and R.H. Myers. 2004. Robust parameter design: A review. Quality and Reliability Engineering International 20:81–101.

    Article  Google Scholar 

  • Rustem, B., and Q. Nguyen. 1998. An algorithm for inequality constrained discrete min-max problems. SIAM Journal on Optimization 8:256–283.

    Article  MathSciNet  Google Scholar 

  • Rustem, B., S. Zakovic, and P. Parpas. 2008. An interior point algorithm for continuous minimax: Implementation and computation. Optimization Methods and Software 23:911–928.

    Article  MathSciNet  MATH  Google Scholar 

  • Sasai, H. 1974. An interior penalty method for minimax problems with constraints. SIAM Journal of Control 12:643–649.

    Article  MathSciNet  MATH  Google Scholar 

  • Sheu, R.L., and J.Y. Lin. 2004. Solving continuous min-max problems by an iterative entropic regularization method. Journal of Optimization Theory and Applications 121:597–612.

    Article  MathSciNet  MATH  Google Scholar 

  • Sitter, R.R. 1992. Robust designs for binary data. Biometrics 48:1145–1155.

    Article  MathSciNet  Google Scholar 

  • Taguchi, G. 1986. Introduction to quality engineering. White Plains, NY: UNIPUB/Kraus International.

    Google Scholar 

  • Taguchi, G., and Y. Wu. 1985. Introduction to off-line quality control. Nagoya, Japan: Central Japan Quality Control Association.

    Google Scholar 

  • Vining, G.G., and R.H. Myers. 1990. Combining Taguchi and response surface philosophies: A dual response approach. Journal of Quality Technology 22:38–45.

    Google Scholar 

  • Vojnovic, D., D. Chicco, and H. El Zenary. 1996. Doehlert experimental design applied to optimization and quality control of a granulation process in a high shear mixer. International Journal of Pharmaceutics 145:203–213.

    Article  Google Scholar 

  • Vojnovic, D., M. Moneghini, F. Rubessa, and A. Zanchetta. 1993. Simultaneous optimization of several response variables in a granulation process. Drug Development and Industrial Pharmacy 19:1479–1496.

    Article  Google Scholar 

  • Welch, W.J., T.K. Yu, S.M. Kang, and J. Sacks. 1990. Computer experiments for quality control by parameter design. Journal of Quality Technology 22:15–22.

    Google Scholar 

  • Zakovic, S., B. Rustem, and C. Pantelides. 2000. An interior point algorithm for computing saddle points of constrained continuous minimax. Annals of Operational Research 99:59–78.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, 400076, India

    S. Mukhopadhyay

  2. Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    D. Chakraborty

Authors
  1. S. Mukhopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Mukhopadhyay.

Additional information

Grant Sponsor: Department of Science and Technology, SR/FTP/MS-13/2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mukhopadhyay, S., Chakraborty, D. A computational algorithm for selecting robust designs in safety and quality critical processes. Sankhya B 73, 105–122 (2011). https://doi.org/10.1007/s13571-011-0021-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13571-011-0021-0

Keywords

AMS (2000) Subject Classifications

Search

Navigation