M. Kehoe, “Tolerance assignment for minimizing manufacturing cost,” in International Optical Design Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuF5.

R. Bates, “Performance and tolerance sensitivity optimization of highly aspheric miniature camera lenses,” Proc. SPIE 7793, 779302 (2010).

[CrossRef]

H. I. Choi, Y. Lee, D. H. Choi, and J. S. Maeng, “Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency,” Struct. Multidisc. Optim. 40, 537–548 (2010).

[CrossRef]

C.-C. Hsueh, P. D. Lin, and J. Sasian, “Worst-case-based methodology for tolerance analysis and tolerance allocation of optical systems,” Appl. Opt. 49, 6179–6188 (2010).

[CrossRef]

PIAnO user’s manual, version 3.0, FRAMAX, Inc. (2009).

S. H. Lee and W. Chen, “A comparative study of uncertainty propagation methods for black-box-type problems,” Struct. Multidisc. Optim. 37, 239–253 (2009).

[CrossRef]

D. J. Kim, J. H. Kim, and Y. B. Yoon, “A study of lens assembly deformation for mobile phone camera,” in Proceedings of the Annual Spring Conference of Korean Society of Mechanical Engineers (KSME, 2008), pp. 93–94.

G. Cassar, E. Vigier-Blanc, and T. Lépine, “Improved tolerancing for production yield anticipation of optical micro-modules for cameraphones,” Proc. SPIE 7100, 71000F (2008).

[CrossRef]

CODE V 9.7 reference manual, Optical Research Associates (2007).

B. D. Youn, Z. Xi, L. J. Wells, and D. J. Gorsich, “Sensitivity-free approach for reliability-based robust design optimization,” in Proceedings of the 33rd Design Automation Conference, Presented at—2007 American Society of Mechanical Engineers International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (ASME, 2007), pp. 1309–1320.

S. K. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-Based Structural Design (Springer, 2007).

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” in International Optical Design, OSA Technical Digest (CD) (Optical Society of America, 2006), paper TuA5.

R. N. Youngworth, “21st century optical tolerancing: a look at the past and improvements for the future,” in International Optical Design, Technical Digest (CD) (Optical Society of America, 2006), paper MB3.

S. H. Lee and B. M. Kwak, “Reliability based design optimization using response surface augmented moment method,” in Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization (ISSMO, 2005).

S. Rahman and H. Xu, “A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics,” Prob. Eng. Mech. 19, 393–408 (2004).

[CrossRef]

H. Xu and S. Rahman, “A generalized dimension-reduction method for multidimensional integration in stochastic mechanics,” Int. J. Numer. Meth. Eng. 61, 1992–2019 (2004).

[CrossRef]

M. Isshiki, L. Gardner, and G. G. Gregory, “Automated control of manufacturing sensitivity during optimization,” Proc. SPIE 5249, 343–352 (2004).

[CrossRef]

R. N. Youngworth and B. D. Stone, “Elements of cost-based tolerancing,” Opt. Rev. 8, 276–280 (2001).

[CrossRef]

S. Rahman and B. N. Rao, “A perturbation method for stochastic meshless analysis in elastostatics,” Int. J. Numer. Meth. Eng. 50, 1969–1991 (2001).

[CrossRef]

K. J. Hong, M. S. Kim, and D. H. Choi, “Efficient approximation method for constructing quadratic response surface model,” KSME Int. J. 15, 876–888 (2001).

[CrossRef]

A. Haldar and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design (Wiley, 2000), Sec. 1.2.

A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods (SIAM, 2000).

[CrossRef]

R. N. Youngworth and B. D. Stone, “Cost-based tolerancing of optical systems,” Appl. Opt. 39, 4501–4512 (2000).

[CrossRef]

D. E. Huntington and C. S. Lyrintzis, “Improvements to and limitations of Latin hypercube sampling,” Prob. Eng. Mech. 13, 245–253 (1998).

[CrossRef]

C. Y. Lin, W. H. Huang, M. C. Jeng, and J. L. Doong, “Study of an assembly tolerance allocation model based on Monte Carlo simulation,” J. Mater. Process. Technol. 70, 9–16 (1997).

[CrossRef]

N. Alexandrov, “Robustness properties of a trust-region framework for managing approximations in engineering optimization,” in Proceedings of the 6th AIAA/NASA/USAF Symposium on Multidisciplinary Analysis and Optimization (AIAA, 1996), pp. 1056–1059.

R. M. Lewis, “A trust region framework for managing approximation models in engineering optimization,” in Proceedings of the 6th AIAA/NASA/USAF Symposium on Multidisciplinary Analysis and Optimization (AIAA, 1996), pp. 1053–1055.

F. Yamazaki, M. Shinozuka, and G. Dasgupta, “Neumann expansion for stochastic finite element analysis,” J. Eng. Mech. ASCE 114, 1335–1354 (1988).

[CrossRef]

M. Stein, “Large sample properties of simulations using Latin hypercube sampling,” Technometrics 29, 143–151 (1987).

[CrossRef]

G. Adams, “Tolerancing of optical systems,” Ph.D. thesis (Imperial College, 1987).

R. Fletcher, Practical Methods of Optimization (Wiley, 1987).

B. Fiessler, H.-J. Neumann, and R. Rackwitz, “Quadratic limit states in structural reliability,” J. Eng. Mech. Div. ASCE 105, 661–676 (1979).

M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, 239–245 (1979).

[CrossRef]

M. J. D. Powell, “Convergence properties of a class of minimization algorithms,” in Nonlinear Programming(Academic, 1975).

R. Fletcher, “An algorithm for solving linearly constrained optimization problem,” Math. Prog. 2, 133–165 (1972).

[CrossRef]

C. A. Cornell, “A probability-based structural code,” Am. Concrete Inst. J. 66, 974–985 (1969).

G. Adams, “Tolerancing of optical systems,” Ph.D. thesis (Imperial College, 1987).

N. Alexandrov, “Robustness properties of a trust-region framework for managing approximations in engineering optimization,” in Proceedings of the 6th AIAA/NASA/USAF Symposium on Multidisciplinary Analysis and Optimization (AIAA, 1996), pp. 1056–1059.

R. Bates, “Performance and tolerance sensitivity optimization of highly aspheric miniature camera lenses,” Proc. SPIE 7793, 779302 (2010).

[CrossRef]

M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, 239–245 (1979).

[CrossRef]

S. K. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-Based Structural Design (Springer, 2007).

G. Cassar, E. Vigier-Blanc, and T. Lépine, “Improved tolerancing for production yield anticipation of optical micro-modules for cameraphones,” Proc. SPIE 7100, 71000F (2008).

[CrossRef]

S. H. Lee and W. Chen, “A comparative study of uncertainty propagation methods for black-box-type problems,” Struct. Multidisc. Optim. 37, 239–253 (2009).

[CrossRef]

H. I. Choi, Y. Lee, D. H. Choi, and J. S. Maeng, “Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency,” Struct. Multidisc. Optim. 40, 537–548 (2010).

[CrossRef]

K. J. Hong, M. S. Kim, and D. H. Choi, “Efficient approximation method for constructing quadratic response surface model,” KSME Int. J. 15, 876–888 (2001).

[CrossRef]

H. I. Choi, Y. Lee, D. H. Choi, and J. S. Maeng, “Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency,” Struct. Multidisc. Optim. 40, 537–548 (2010).

[CrossRef]

S. K. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-Based Structural Design (Springer, 2007).

A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods (SIAM, 2000).

[CrossRef]

M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, 239–245 (1979).

[CrossRef]

C. A. Cornell, “A probability-based structural code,” Am. Concrete Inst. J. 66, 974–985 (1969).

F. Yamazaki, M. Shinozuka, and G. Dasgupta, “Neumann expansion for stochastic finite element analysis,” J. Eng. Mech. ASCE 114, 1335–1354 (1988).

[CrossRef]

C. Y. Lin, W. H. Huang, M. C. Jeng, and J. L. Doong, “Study of an assembly tolerance allocation model based on Monte Carlo simulation,” J. Mater. Process. Technol. 70, 9–16 (1997).

[CrossRef]

B. Fiessler, H.-J. Neumann, and R. Rackwitz, “Quadratic limit states in structural reliability,” J. Eng. Mech. Div. ASCE 105, 661–676 (1979).

R. Fletcher, Practical Methods of Optimization (Wiley, 1987).

R. Fletcher, “An algorithm for solving linearly constrained optimization problem,” Math. Prog. 2, 133–165 (1972).

[CrossRef]

M. Isshiki, L. Gardner, and G. G. Gregory, “Automated control of manufacturing sensitivity during optimization,” Proc. SPIE 5249, 343–352 (2004).

[CrossRef]

B. D. Youn, Z. Xi, L. J. Wells, and D. J. Gorsich, “Sensitivity-free approach for reliability-based robust design optimization,” in Proceedings of the 33rd Design Automation Conference, Presented at—2007 American Society of Mechanical Engineers International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (ASME, 2007), pp. 1309–1320.

A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods (SIAM, 2000).

[CrossRef]

S. K. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-Based Structural Design (Springer, 2007).

M. Isshiki, L. Gardner, and G. G. Gregory, “Automated control of manufacturing sensitivity during optimization,” Proc. SPIE 5249, 343–352 (2004).

[CrossRef]

A. Haldar and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design (Wiley, 2000), Sec. 1.2.

K. J. Hong, M. S. Kim, and D. H. Choi, “Efficient approximation method for constructing quadratic response surface model,” KSME Int. J. 15, 876–888 (2001).

[CrossRef]

C. Y. Lin, W. H. Huang, M. C. Jeng, and J. L. Doong, “Study of an assembly tolerance allocation model based on Monte Carlo simulation,” J. Mater. Process. Technol. 70, 9–16 (1997).

[CrossRef]

D. E. Huntington and C. S. Lyrintzis, “Improvements to and limitations of Latin hypercube sampling,” Prob. Eng. Mech. 13, 245–253 (1998).

[CrossRef]

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” in International Optical Design, OSA Technical Digest (CD) (Optical Society of America, 2006), paper TuA5.

M. Isshiki, L. Gardner, and G. G. Gregory, “Automated control of manufacturing sensitivity during optimization,” Proc. SPIE 5249, 343–352 (2004).

[CrossRef]

C. Y. Lin, W. H. Huang, M. C. Jeng, and J. L. Doong, “Study of an assembly tolerance allocation model based on Monte Carlo simulation,” J. Mater. Process. Technol. 70, 9–16 (1997).

[CrossRef]

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” in International Optical Design, OSA Technical Digest (CD) (Optical Society of America, 2006), paper TuA5.

M. Kehoe, “Tolerance assignment for minimizing manufacturing cost,” in International Optical Design Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuF5.

D. J. Kim, J. H. Kim, and Y. B. Yoon, “A study of lens assembly deformation for mobile phone camera,” in Proceedings of the Annual Spring Conference of Korean Society of Mechanical Engineers (KSME, 2008), pp. 93–94.

D. J. Kim, J. H. Kim, and Y. B. Yoon, “A study of lens assembly deformation for mobile phone camera,” in Proceedings of the Annual Spring Conference of Korean Society of Mechanical Engineers (KSME, 2008), pp. 93–94.

K. J. Hong, M. S. Kim, and D. H. Choi, “Efficient approximation method for constructing quadratic response surface model,” KSME Int. J. 15, 876–888 (2001).

[CrossRef]

S. H. Lee and B. M. Kwak, “Reliability based design optimization using response surface augmented moment method,” in Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization (ISSMO, 2005).

S. H. Lee and W. Chen, “A comparative study of uncertainty propagation methods for black-box-type problems,” Struct. Multidisc. Optim. 37, 239–253 (2009).

[CrossRef]

S. H. Lee and B. M. Kwak, “Reliability based design optimization using response surface augmented moment method,” in Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization (ISSMO, 2005).

H. I. Choi, Y. Lee, D. H. Choi, and J. S. Maeng, “Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency,” Struct. Multidisc. Optim. 40, 537–548 (2010).

[CrossRef]

G. Cassar, E. Vigier-Blanc, and T. Lépine, “Improved tolerancing for production yield anticipation of optical micro-modules for cameraphones,” Proc. SPIE 7100, 71000F (2008).

[CrossRef]

R. M. Lewis, “A trust region framework for managing approximation models in engineering optimization,” in Proceedings of the 6th AIAA/NASA/USAF Symposium on Multidisciplinary Analysis and Optimization (AIAA, 1996), pp. 1053–1055.

C. Y. Lin, W. H. Huang, M. C. Jeng, and J. L. Doong, “Study of an assembly tolerance allocation model based on Monte Carlo simulation,” J. Mater. Process. Technol. 70, 9–16 (1997).

[CrossRef]

D. E. Huntington and C. S. Lyrintzis, “Improvements to and limitations of Latin hypercube sampling,” Prob. Eng. Mech. 13, 245–253 (1998).

[CrossRef]

H. I. Choi, Y. Lee, D. H. Choi, and J. S. Maeng, “Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency,” Struct. Multidisc. Optim. 40, 537–548 (2010).

[CrossRef]

A. Haldar and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design (Wiley, 2000), Sec. 1.2.

M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, 239–245 (1979).

[CrossRef]

B. Fiessler, H.-J. Neumann, and R. Rackwitz, “Quadratic limit states in structural reliability,” J. Eng. Mech. Div. ASCE 105, 661–676 (1979).

M. J. D. Powell, “Convergence properties of a class of minimization algorithms,” in Nonlinear Programming(Academic, 1975).

B. Fiessler, H.-J. Neumann, and R. Rackwitz, “Quadratic limit states in structural reliability,” J. Eng. Mech. Div. ASCE 105, 661–676 (1979).

H. Xu and S. Rahman, “A generalized dimension-reduction method for multidimensional integration in stochastic mechanics,” Int. J. Numer. Meth. Eng. 61, 1992–2019 (2004).

[CrossRef]

S. Rahman and H. Xu, “A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics,” Prob. Eng. Mech. 19, 393–408 (2004).

[CrossRef]

S. Rahman and B. N. Rao, “A perturbation method for stochastic meshless analysis in elastostatics,” Int. J. Numer. Meth. Eng. 50, 1969–1991 (2001).

[CrossRef]

S. Rahman and B. N. Rao, “A perturbation method for stochastic meshless analysis in elastostatics,” Int. J. Numer. Meth. Eng. 50, 1969–1991 (2001).

[CrossRef]

F. Yamazaki, M. Shinozuka, and G. Dasgupta, “Neumann expansion for stochastic finite element analysis,” J. Eng. Mech. ASCE 114, 1335–1354 (1988).

[CrossRef]

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” in International Optical Design, OSA Technical Digest (CD) (Optical Society of America, 2006), paper TuA5.

M. Stein, “Large sample properties of simulations using Latin hypercube sampling,” Technometrics 29, 143–151 (1987).

[CrossRef]

A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods (SIAM, 2000).

[CrossRef]

G. Cassar, E. Vigier-Blanc, and T. Lépine, “Improved tolerancing for production yield anticipation of optical micro-modules for cameraphones,” Proc. SPIE 7100, 71000F (2008).

[CrossRef]

B. D. Youn, Z. Xi, L. J. Wells, and D. J. Gorsich, “Sensitivity-free approach for reliability-based robust design optimization,” in Proceedings of the 33rd Design Automation Conference, Presented at—2007 American Society of Mechanical Engineers International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (ASME, 2007), pp. 1309–1320.

B. D. Youn, Z. Xi, L. J. Wells, and D. J. Gorsich, “Sensitivity-free approach for reliability-based robust design optimization,” in Proceedings of the 33rd Design Automation Conference, Presented at—2007 American Society of Mechanical Engineers International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (ASME, 2007), pp. 1309–1320.

S. Rahman and H. Xu, “A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics,” Prob. Eng. Mech. 19, 393–408 (2004).

[CrossRef]

H. Xu and S. Rahman, “A generalized dimension-reduction method for multidimensional integration in stochastic mechanics,” Int. J. Numer. Meth. Eng. 61, 1992–2019 (2004).

[CrossRef]

F. Yamazaki, M. Shinozuka, and G. Dasgupta, “Neumann expansion for stochastic finite element analysis,” J. Eng. Mech. ASCE 114, 1335–1354 (1988).

[CrossRef]

D. J. Kim, J. H. Kim, and Y. B. Yoon, “A study of lens assembly deformation for mobile phone camera,” in Proceedings of the Annual Spring Conference of Korean Society of Mechanical Engineers (KSME, 2008), pp. 93–94.

B. D. Youn, Z. Xi, L. J. Wells, and D. J. Gorsich, “Sensitivity-free approach for reliability-based robust design optimization,” in Proceedings of the 33rd Design Automation Conference, Presented at—2007 American Society of Mechanical Engineers International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (ASME, 2007), pp. 1309–1320.

R. N. Youngworth, “21st century optical tolerancing: a look at the past and improvements for the future,” in International Optical Design, Technical Digest (CD) (Optical Society of America, 2006), paper MB3.

R. N. Youngworth and B. D. Stone, “Elements of cost-based tolerancing,” Opt. Rev. 8, 276–280 (2001).

[CrossRef]

R. N. Youngworth and B. D. Stone, “Cost-based tolerancing of optical systems,” Appl. Opt. 39, 4501–4512 (2000).

[CrossRef]

C. A. Cornell, “A probability-based structural code,” Am. Concrete Inst. J. 66, 974–985 (1969).

D. S. Grey, “Tolerance sensitivity and optimization,” Appl. Opt. 9, 523–526 (1970).

[CrossRef]
[PubMed]

L. W. Grossman and R. W. Faaland, “Minimum resolution specification of intraocular lens implants using the modulation transfer function,” Appl. Opt. 32, 3497–3503 (1993).

[CrossRef]
[PubMed]

R. N. Youngworth and B. D. Stone, “Cost-based tolerancing of optical systems,” Appl. Opt. 39, 4501–4512 (2000).

[CrossRef]

C.-C. Hsueh, P. D. Lin, and J. Sasian, “Worst-case-based methodology for tolerance analysis and tolerance allocation of optical systems,” Appl. Opt. 49, 6179–6188 (2010).

[CrossRef]

H. Xu and S. Rahman, “A generalized dimension-reduction method for multidimensional integration in stochastic mechanics,” Int. J. Numer. Meth. Eng. 61, 1992–2019 (2004).

[CrossRef]

S. Rahman and B. N. Rao, “A perturbation method for stochastic meshless analysis in elastostatics,” Int. J. Numer. Meth. Eng. 50, 1969–1991 (2001).

[CrossRef]

F. Yamazaki, M. Shinozuka, and G. Dasgupta, “Neumann expansion for stochastic finite element analysis,” J. Eng. Mech. ASCE 114, 1335–1354 (1988).

[CrossRef]

B. Fiessler, H.-J. Neumann, and R. Rackwitz, “Quadratic limit states in structural reliability,” J. Eng. Mech. Div. ASCE 105, 661–676 (1979).

C. Y. Lin, W. H. Huang, M. C. Jeng, and J. L. Doong, “Study of an assembly tolerance allocation model based on Monte Carlo simulation,” J. Mater. Process. Technol. 70, 9–16 (1997).

[CrossRef]

K. J. Hong, M. S. Kim, and D. H. Choi, “Efficient approximation method for constructing quadratic response surface model,” KSME Int. J. 15, 876–888 (2001).

[CrossRef]

R. Fletcher, “An algorithm for solving linearly constrained optimization problem,” Math. Prog. 2, 133–165 (1972).

[CrossRef]

R. N. Youngworth and B. D. Stone, “Elements of cost-based tolerancing,” Opt. Rev. 8, 276–280 (2001).

[CrossRef]

S. Rahman and H. Xu, “A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics,” Prob. Eng. Mech. 19, 393–408 (2004).

[CrossRef]

D. E. Huntington and C. S. Lyrintzis, “Improvements to and limitations of Latin hypercube sampling,” Prob. Eng. Mech. 13, 245–253 (1998).

[CrossRef]

R. Bates, “Performance and tolerance sensitivity optimization of highly aspheric miniature camera lenses,” Proc. SPIE 7793, 779302 (2010).

[CrossRef]

G. Cassar, E. Vigier-Blanc, and T. Lépine, “Improved tolerancing for production yield anticipation of optical micro-modules for cameraphones,” Proc. SPIE 7100, 71000F (2008).

[CrossRef]

M. Isshiki, L. Gardner, and G. G. Gregory, “Automated control of manufacturing sensitivity during optimization,” Proc. SPIE 5249, 343–352 (2004).

[CrossRef]

S. H. Lee and W. Chen, “A comparative study of uncertainty propagation methods for black-box-type problems,” Struct. Multidisc. Optim. 37, 239–253 (2009).

[CrossRef]

H. I. Choi, Y. Lee, D. H. Choi, and J. S. Maeng, “Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency,” Struct. Multidisc. Optim. 40, 537–548 (2010).

[CrossRef]

M. Stein, “Large sample properties of simulations using Latin hypercube sampling,” Technometrics 29, 143–151 (1987).

[CrossRef]

M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, 239–245 (1979).

[CrossRef]

S. K. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-Based Structural Design (Springer, 2007).

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” in International Optical Design, OSA Technical Digest (CD) (Optical Society of America, 2006), paper TuA5.

R. N. Youngworth, “21st century optical tolerancing: a look at the past and improvements for the future,” in International Optical Design, Technical Digest (CD) (Optical Society of America, 2006), paper MB3.

S. H. Lee and B. M. Kwak, “Reliability based design optimization using response surface augmented moment method,” in Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization (ISSMO, 2005).

D. J. Kim, J. H. Kim, and Y. B. Yoon, “A study of lens assembly deformation for mobile phone camera,” in Proceedings of the Annual Spring Conference of Korean Society of Mechanical Engineers (KSME, 2008), pp. 93–94.

B. D. Youn, Z. Xi, L. J. Wells, and D. J. Gorsich, “Sensitivity-free approach for reliability-based robust design optimization,” in Proceedings of the 33rd Design Automation Conference, Presented at—2007 American Society of Mechanical Engineers International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (ASME, 2007), pp. 1309–1320.

CODE V 9.7 reference manual, Optical Research Associates (2007).

PIAnO user’s manual, version 3.0, FRAMAX, Inc. (2009).

A. Haldar and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design (Wiley, 2000), Sec. 1.2.

M. Kehoe, “Tolerance assignment for minimizing manufacturing cost,” in International Optical Design Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuF5.

R. Fletcher, Practical Methods of Optimization (Wiley, 1987).

N. Alexandrov, “Robustness properties of a trust-region framework for managing approximations in engineering optimization,” in Proceedings of the 6th AIAA/NASA/USAF Symposium on Multidisciplinary Analysis and Optimization (AIAA, 1996), pp. 1056–1059.

R. M. Lewis, “A trust region framework for managing approximation models in engineering optimization,” in Proceedings of the 6th AIAA/NASA/USAF Symposium on Multidisciplinary Analysis and Optimization (AIAA, 1996), pp. 1053–1055.

A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods (SIAM, 2000).

[CrossRef]

M. J. D. Powell, “Convergence properties of a class of minimization algorithms,” in Nonlinear Programming(Academic, 1975).

G. Adams, “Tolerancing of optical systems,” Ph.D. thesis (Imperial College, 1987).