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RETRACTED ARTICLE: Development of censored data-based robust design for pharmaceutical quality by design

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This article was retracted on 04 November 2020

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Abstract

Robust design techniques, which are based on the concept of building quality into products or processes, are increasingly popular in many manufacturing industries. In this paper, we propose a new robust design model in the context of pharmaceutical production research and development. Traditional robust design principles have often been applied to situations in which the quality characteristics of interest are typically time insensitive. In pharmaceutical manufacturing processes, time-oriented quality characteristics, such as the degradation of a drug, are often of interest. As a result, current robust design models for quality improvement which have been studied in the literature may not be effective in finding robust design solutions. To address such practical needs, this paper develops a robust design model using censored data, which is perhaps the first attempt in the robust design field. We then study estimation methods, such as the expectation–maximization algorithm and the maximum likelihood method, in the robust design context. Finally, comparative studies are discussed for model verification via a numerical example.

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Change history

  • 04 November 2020

    This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1007/s00170-020-06269-8

References

  1. Taguchi G (1986) Introduction to quality engineering. Asian productivity organization. UNIPUB/Kraus International, White Plains

    Google Scholar 

  2. Taguchi G (1987) Systems of experimental design: engineering methods to optimize quality and minimize cost. UNIPBUK/Kraus International, White Plains

    Google Scholar 

  3. Steinberg DM, Bursztyn D (1998) Noise factors, dispersion effects, and robust design. Stat Sin 8:67–85

    MathSciNet  MATH  Google Scholar 

  4. Leon RV, Shoemaker AC, Kackar RN (1987) Performance measures independent of adjustment: an explanation and extension of Taguchi signal-to-noise ratio. Technometrics 29:253–285

    Article  MathSciNet  Google Scholar 

  5. Box GEP (1988) Signal-to-noise ratios, performance criteria and transformations. Technometrics 30:1–17

    Article  MathSciNet  MATH  Google Scholar 

  6. Box GEP, Bisgaard S, Fung C (1988) An explanation and critique of Taguchi’s contributions to quality engineering. International Journal of Reliability Management 4:123–131

    Article  Google Scholar 

  7. Nair VN (1992) Taguchi’s parameter design: a panel discussion. Technometrics 34:127–161

    Article  MathSciNet  Google Scholar 

  8. Tsui KL (1992) An overview of Taguchi method and newly developed statistical methods for robust design. IIE Trans 24:44–57

    Article  Google Scholar 

  9. Vining GG, Myers RH (1990) Combining Taguchi and response surface philosophies: a dual response approach. J Qual Technol 22:38–45

    Article  Google Scholar 

  10. Del Castillo E, Montgomery DC (1993) A nonlinear programming solution to the dual response problem. J Qual Technol 25:199–204

    Article  Google Scholar 

  11. Copeland KAF, Nelson PR (1996) Dual response optimization via direct function minimization. J Qual Technol 28:331–336

    Article  Google Scholar 

  12. Khattree R (1996) Robust parameter design: a response surface approach. J Qual Technol 28:187–198

    Article  Google Scholar 

  13. Kim K, Lin DKJ (1998) Response surface optimization: a fuzzy modeling approach. J Qual Technol 30:1–10

    Article  Google Scholar 

  14. Lin DKJ, Tu W (1995) Dual response surface optimization. J Qual Technol 27:34–39

    Article  Google Scholar 

  15. Jayaram JSR, Ibrahim Y (1999) Multiple response robust design and yield maximization. Int J Qual Reliab Manage 6:826–837

    Article  Google Scholar 

  16. Cho BR, Kim YJ, Kimber DL, Phillips MD (2000) An integrated joint optimization procedure for robust and tolerance design. Int J Prod Res 38:2309–2325

    Article  MATH  Google Scholar 

  17. Kim YJ, Cho BR (2000) Economic integration of design optimization. Qual Eng 12:561–567

    Article  Google Scholar 

  18. Kim YJ, Cho BR (2003) Determining the optimum process mean for a skewed process. Int J Ind Eng 10(4):555–561

    Google Scholar 

  19. Yue RX (2002) Model-robust designs in multiresponse situations. Stat Probab Lett 58:369–379

    Article  MathSciNet  MATH  Google Scholar 

  20. Park C, Cho BR (2003) Development of robust design under contaminated and non-normal data. Qual Eng 15:463–469

    Article  Google Scholar 

  21. Miro-Quesada G, Del Castillo E (2004) Two approaches for improving the dual response method in robust parameter design. J Qual Technol 36:154–168

    Article  Google Scholar 

  22. Cho BR, Park C (2005) Robust design modeling and optimization with unbalanced data. Comput Ind Eng 48:173–180

    Article  Google Scholar 

  23. Govindaluri MS, Cho BR (2005) Integration of customer and designer preferences in robust design. International Journal of Six Sigma and Competitive Advantage 1:276–294

    Article  Google Scholar 

  24. Shin S, Cho BR (2005) Bias-specified robust design optimization and its analytical solutions. Computers and Industrial Engineering 48:129–140

    Article  Google Scholar 

  25. Shin S, Cho BR (2006) Robust design models for customer-specified bounds on process parameters. J Syst Sci Syst Eng 15:2–18

    Article  Google Scholar 

  26. Lee SB, Park C, Cho BR (2007) Development of a highly efficient and resistant robust design. Int J Prod Res 45:157–167

    Article  MATH  Google Scholar 

  27. Montgomery DC, Myers WR, Brenneman WA, Myers RH (2005) A dual-response approach to robust parameter design for a generalized linear model. J Qual Technol 37:130–138

    Article  Google Scholar 

  28. Park C, Cho BR (2005) Robust design modeling and optimization with unbalanced data. Comput Ind Eng 48:173–180

    Article  Google Scholar 

  29. Robinson TJ, Wulff SS, Montgomery DS, Khuri AI (2006) Robust parameter design using generalized linear mixed models. J Qual Technol 38:65–75

    Article  Google Scholar 

  30. Kovach J, Cho BR (2006) A D-optimal design approach to robust design under constraints: a new design for six sigma tool. International Journal of Six Sigma and Competitive Advantage 2:389–403

    Article  Google Scholar 

  31. Kovach J, Cho BR (2007) Development of a D-optimal robust design model for restricted experiments. Int J Ind Eng 14:117–128

    Google Scholar 

  32. Kovach J, Cho BR (2008) Solving multiresponse optimization problems using quality function-based robust design. Qual Eng 20:346–360

    Article  Google Scholar 

  33. Kovach J, Cho BR, Antony J (2008) Development of an experiment based robust design paradigm for multiple quality characteristics using physical programming. Int J Adv Manuf Technol 35:1100–1112

    Article  Google Scholar 

  34. Ginsburg H, Ben-Gal I (2006) Designing experiments for robust-optimization problems: the Vs-optimality criterion. IIE Trans 38:445–461

    Article  Google Scholar 

  35. Xu D, Albin SL (2003) Robust optimization of experimentally derived objective functions. IIE Trans 35:793–802

    Article  Google Scholar 

  36. Govindaluri MS, Cho BR (2007) Robust design modeling and optimization with correlated quality characteristics using a multicriteria decision framework. Int J Adv Manuf Technol 32:423–433

    Article  Google Scholar 

  37. Egorov IN, Kretinin GV, Leshchenko IA, Kuptzov SV (2007) Multi-objective approach for robust design optimization problems. Inverse Problems in Science and Engineering 15:47–59

    Article  MathSciNet  MATH  Google Scholar 

  38. Scheffé H (1958) Experiments with mixtures. J R Stat Soc, B 20(2):344–360

    MathSciNet  MATH  Google Scholar 

  39. Scheffé H (1963) The simplex-centroid design for experiments with mixtures. J R Stat Soc, B 25(2):235–263

    MathSciNet  MATH  Google Scholar 

  40. Cornell JA (1981) Experiments with mixtures: designs, models, and the analysis of mixture data. John Wiley, New York

    MATH  Google Scholar 

  41. McLean RA, Anderson VL (1966) Extreme vertices design of mixture experiments. Technometrics 8(3):477–454

    Article  MathSciNet  Google Scholar 

  42. Snee RD, Marquardt DW (1974) Extreme vertices designs for linear mixture models. Technometrics 16(3):399–408

    Article  MATH  Google Scholar 

  43. DuMouchel W, Jones B (1994) A simple bayesian modification of d-optimal designs to reduce dependence on an assumed model. Technometrics 36:37–47

    MATH  Google Scholar 

  44. Andere-Rendon J, Montgomery DC, Rollier DA (1997) Design of mixture experiments using Bayesian D-optimality. J Qual Technol 29(4):451–463

    Article  Google Scholar 

  45. Goos P, Donev AN (2006) The D-optimal design of blocked experiments with mixture components. J Qual Technol 38(4):319–332

    Article  Google Scholar 

  46. Donev AN (1989) Design of experiments with both mixture and qualitative factors. J R Stat Soc, B 51(2):297–302

    MathSciNet  MATH  Google Scholar 

  47. Nigam AK (1976) Corrections to blocking conditions for mixture experiments. Ann Stat 47:1294–1295

    Article  MATH  Google Scholar 

  48. John PWM (1984) Experiments with mixtures involving process variables. Technical Report 8, Center for Statistical Sciences. University of Texas, Austin

    Google Scholar 

  49. Piepel GF, Szychowski JM, Loeppky JL (2002) Augmenting Scheffe linear mixture models with squared and/or crossproduct terms. J Qual Technol 34:297–314

    Article  Google Scholar 

  50. Cornell JA, Gorman JW (1984) Fractional design plans for process variables in mixture experiments. J Qual Technol 16:20–38

    Article  Google Scholar 

  51. Snee RD, Rayner AA (1982) Assessing the accuracy of mixture model regression calculations. J Qual Technol 14:67–79

    Article  Google Scholar 

  52. Prescott P, Dean AM, Draper NR, Lewis SM (2002) Mixture experiments: Ill-conditioning and quadratic model specification. Technometrics 44:260–268

    Article  MathSciNet  Google Scholar 

  53. Sengupta TK, Nandy RK, Mukhopadhyay S, Hall RH, Sathyamoorthy V, Ghose AC, Draper NR, Pukelsheim F (1998) Mixture models based on homogeneous polynomials. J Stat Plan Inference 71:303–311

    Article  MathSciNet  Google Scholar 

  54. Steiner SH, Hamada M (1997) Making mixtures robust to noise and mixing measurement errors. J Qual Technol 29:441–450

    Article  Google Scholar 

  55. Goldfarb HB, Borror CM, Montgomery DC (2003) Mixture-process variable experiments with noise variables. J Qual Technol 35:393–405

    Article  Google Scholar 

  56. Goldfarb HB, Borror CM, Montgomery DC, Anderson-Cook CM (2004) Three-dimensional variance dispersion graphs for mixture-process experiments. J Qual Technol 36:109–124

    Article  Google Scholar 

  57. Goldfarb HB, Borror CM, Montgomery DC, Anderson-Cook CM (2005) Using genetic algorithms to generate mixture-process experimental designs involving control and noise variables. J Qual Technol 37:60–74

    Article  Google Scholar 

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Correspondence to Byung Rae Cho.

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Cho, B.R., Choi, Y. & Shin, S. RETRACTED ARTICLE: Development of censored data-based robust design for pharmaceutical quality by design. Int J Adv Manuf Technol 49, 839–851 (2010). https://doi.org/10.1007/s00170-009-2455-3

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  • DOI: https://doi.org/10.1007/s00170-009-2455-3

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