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Yield-based sensitivity analysis methods and algorithms are developed for process capability evaluation in this paper. Yield, the conformity to product specifications, is subject to critical design parameters such as dimensions, tolerances, and specification limits. The uncertainties in determining these parameters in design and manufacturing affect the process capability of producing high-quality products. Yield is a transparent and thus a desirable index, especially for multivariate process capability evaluation. Thus, yield sensitivity with respect to these design parameters indicates key contributors to final product quality, providing valuable information in design for quality control. Yield is formulated as a high dimension probability integral over a specification region. In multistage assembly processes, an assembly variation model links the quality characteristics to design parameters. This model is adopted in yield sensitivity analysis. Derivatives of yield with respect to the design parameters are developed using matrix calculus. Three sensitivity analysis algorithms, i.e., finite difference, yield derivative, and regression modeling, are implemented. Monte Carlo simulation is used for yield estimation in the three algorithms. A case study using floor pan assembly in automotive body manufacturing is presented for the validation of the proposed methodology.

Recent developments in modeling stream of variation in multistage manufacturing system along with the urgent need for yield enhancement in the semiconductor industry has led to complex large scale simulation problems in design and performance prediction, thus challenging current Monte Carlo (MC) based simulation techniques. MC method prevails in statistical simulation approaches for multi-dimensional cases with general (i.e., non-Gaussian) distributions and/or complex response functions. A method is proposed based on number theory (NT-net) to reduce computing effort and the variability of MC's results in tolerance design and circuit performance simulation. The sampling strategy is improved by introducing NT-net that can provide better convergent rate over MC. The new method is presented and verified using several case studies, including analytical and industrial cases of a filter design and analyses of a four-bar mechanism. Results indicate a 90–95% reduction of computation effort with significant improvement in accuracy that can be achieved by the proposed technique.

Tolerancing is one of the most important tasks in product and manufacturing process design. In the literature, both Monte Carlo simulation and numerical optimization method have been widely used in the process of statistical tolerance analysis and synthesis, but the computational effort is huge. This paper presents two techniques, quasi random numbers based on the Number Theoretic Method and sequential algorithm based on the Number Theoretic net, to calculate yield and to perform tolerance allocation. An example demonstrates the optimal tolerance allocation design and is employed to investigate the efficiency and accuracy of this solution. This algorithm can efficiently obtain the global optimum, and the amount of calculation is considerably reduced.

Monte Carlo (MC) technique prevails in probabilistic design simulation, such as in statistical tolerance analysis and synthesis. A quasi-Monte Carlo (e.g., number theoretic net method (NT-net)) with better computation efficiency over MC has recently attracted interests in application. In spite of a comprehensive case study (Huang et al., 2004, “Tolerance Analysis for Design of Multistage Manufacturing Processes Using Number-Theoretical Net Method (NT-net),” Int. J. Flexible Manuf. Syst., 16, pp. 65–90 and Zhou et al., 2001, “Sequential Algorithm Based on Number Theoretic Method for Tolerance Analysis and Synthesis,” ASME J. Manuf. Sci. Eng., 123(3), pp. 490–493) for comparison between NT-net and MC, a method for sample size determination of NT-net is still not available. Combinatorial theory and the solution of occupancy problem are used for estimating equivalent sample sizes of MC and NT-net, allowing the NT-net sample size determination in application. A multivariate Chebyshev polynomial with variant coefficients is used to represent generic design functions for validation. The results are verified by case studies.

A stream-of variation analysis (SOVA) model for 3D rigid body assemblies in single station is developed. Both product and process information such as part and fixture locating errors are integrated in the model. The model represents a linear relationship of the variations between Key Product Characteristics (KPCs) and Key Control Characteristics (KCCs). The generic modeling procedure and framework are provided, which involves: (1) an assembly graph (AG) to represent the kinematical constraints among parts and fixtures; (2) a unified method to transform all constraints (mating interface and fixture locators etc.) into a 3-2-1 locating scheme; and (3) a 3D rigid model for variation flow in a single station. The generality of the model is achieved by formulating all these constraints with a unified generalized fixture model. Thus, the new model accommodates various types of assemblies. This model provides a building block for complex multi station assembly model, in which the inter-station interactions are taken into account. The model has been verified by using Monte Carlo (MC) simulation and a standardized industrial software. It provides the basis for variation control through tolerance design analysis, synthesis and diagnosis in manufacturing systems.Copyright © 2006 by ASME

Tolerance synthesis for complex assemblies is formulated as a probabilistic optimization problem. A main challenge in statistical tolerance synthesis for complex assembly system design is the computation intensity in estimating the conformity probability of Key Product Characteristics (KPCs) or yield of assembled products. In assemblies with multiple KPCs, the yield can only be obtained numerically through simulation techniques such as Monte Carlo (MC) algorithm. The existing tolerance synthesis methods require a large number of yield assessments in optimization. A new approach is developed for yield model approximation based on computer experiment, multivariate distribution transformation (MDT) and regression analysis. An explicit yield function can thus be approximated. Therefore, the widely used gradient-based approaches (such as Sequential Quadratic Programming) can be applied and the intensive computation in direct optimization can be avoided. An industrial case study is presented to illustrate and validate the proposed methodology and compared with the existed tolerance synthesis methods.Copyright © 2006 by ASME