Abstract
This paper presents a general method for maximizing manufacturing yield when the realizations of system components are independent random variables with arbitrary distributions. Design specifications define a feasible region which, in the nonlinear case, is linearized using a first-order approximation. The method attempts to place the given tolerance hypercube of the uncertain parameters such that the area with higher yield lies in the feasible region. The yield is estimated by using the joint cumulative density function over the portion of the tolerance hypercube that is contained in the feasible region. A double-bounded density function is used to approximate various bounded distributions for which optimal designs are demonstrated on a tutorial example. Monte Carlo simulation is used to evaluate the actual yields of optimal designs.
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References
R.K. Brayton, S.W. Director and G.D. Hatchel, Yield maximization and worst-case design with arbitrary statistical distributions, IEEE Transactions on Circuits and Systems CAS-27(9) (1980) 756–764.
S.W. Director, P. Feldmann and K. Krishna, Optimization of parametric yield: a tutorial, International Journal of High Speed Electronics 3(1) (1992) 95–136.
G. Kjellstrom and L. Taxén, Stochastic optimization in system design, IEEE Transactions on Circuits and Systems CAS-28(7) (1981) 702–715.
D. Kontsoyiannis and T. Xanthopoulos, On the parametric approach to unit hydrograph identification, Water Resources Management 3 (1989) 107–128.
P. Kumaraswamy, A generalized probability density function for double-bounded random processes, Journal of Hydrology 46 (1980) 79–88.
M.S. Lobo, L. Vandenberghe and S. Boyd, Second-order cone programming, Working Paper, Information Systems Laboratory, Electrical Engineering Department, Stanford University, Stanford, CA 94305 (1997).
H.O.Madsen, S. Krenk and N.C. Lind, Methods of Structural Safety (Prentice-Hall, Englewood Cliffs, NJ, 1986).
A. Seifi, K. Ponnambalam and J. Vlach, Probabilistic design of integrated circuits with correlated input parameters, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 18(8) (1999) 1214–1219.
A. Seifi, K. Ponnambalam and J. Vlach, A unified approach to statistical design centering of integrated circuits with correlated parameters, IEEE Transactions on Circuits and Systems I 46(1) (1999) 190–196.
L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Review 38(1) (1996) 49–95.
J.Wojciechowski, J. Vlach and L. Opalski, Design for non-symmetrical statistical distributions, IEEE Transactions on Circuits and Systems I 44(1) (1997) 29–37.
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Seifi, A., Ponnambalam, K. & Vlach, J. Maximization of Manufacturing Yield of Systems with Arbitrary Distributions of Component Values. Annals of Operations Research 99, 373–383 (2000). https://doi.org/10.1023/A:1019288220413
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DOI: https://doi.org/10.1023/A:1019288220413