Process Yield Improvement Through Optimum Design of Fixture Layouts in 3D Multistation Assembly Systems

Fixtures control the positions and orientations of parts in an assembly process. Inaccuracies of fixture locators or nonoptimal fixture layouts can result in the deviation of a workpiece from its design nominal and lead to overall product dimensional variability and low process yield. Major challenges involving the design of a set of fixture layouts for multistation assembly system can be enumerated into three categories: (1) high-dimensional design space since a large number of locators are involved in the multistation system, (2) large and complex design space for each locator since the design space represents the area of a particular part or subassembly surfaces on which a locator is placed, (here, the design space varies with a particular part design and is further expanded when parts are assembled into subassemblies), and (3) the nonlinear relations between locator nominal positions and key product characteristics. This paper presents a new approach to improve process yield by determining an optimum set of fixture layouts for a given multistation assembly system, which can satisfy (1) the part and subassembly locating stability in each fixture layout and (2) the fixture system robustness against environmental noises in order to minimize product dimensional variability. The proposed methodology is based on a two-step optimization which involves the integration of genetic algorithm and Hammersley sequence sampling. First, genetic algorithm is used for design space reduction by estimating the areas of optimal fixture locations in initial design spaces. Then, Hammersley sequence sampling uniformly samples the candidate sets of fixture layouts from those predetermined areas for the optimum. The process yield and part instability index are design objectives in evaluating candidate sets of fixture layouts. An industrial case study illustrates and validates the proposed methodology.

Process Yield Improvement Through Optimum Design of Fixture Layouts in 3D Multi-Station Assembly Systems

This paper presents a new approach to improve process yield by determining an optimum set of fixture layouts for a given multi-station assembly system which can satisfy: (i) parts and subassemblies locating stability in each fixture layout; and (ii) fixture system robustness against environmental noises in order to minimize product dimensional variability. Three major challenges of the multi-stage assembly processes are addressed: (i) high-dimensional design space; (ii) large and complex design space of each locator; and (iii) the nonlinear relations between locator positions, also called Key Control Characteristics, and Key Product Characteristics. The proposed methodology conducts two-step optimization based on the integration of Genetic Algorithm and Hammersley Sequence Sampling. First, Genetic Algorithm is used for design space reduction by determining the areas of optimal fixture locations in initial design spaces. Then, Hammersley Sequence Sampling uniformly samples the candidate sets of fixture layouts from the areas predetermined by GA for the optimum. The process yield and part instability index are design objectives in evaluating candidate sets of fixture layouts. An industrial case study illustrates and validates the proposed methodology.

A Quadrature-Based Sampling Technique for Robust Design With Computer Models

Several methods have been proposed for estimating transmitted variance to enable robust parameter design using computer models. This paper presents an alternative technique based on Gaussian quadrature which requires only 2n+1 or 4n+1 samples (depending on the accuracy desired) where n is the number of randomly varying inputs. The quadrature-based technique is assessed using a hierarchical probability model. The 4n+1 quadrature-based technique can estimate transmitted standard deviation within 5% in over 95% of systems which is much better than the accuracy of Hammersley Sequence Sampling, Latin Hypercube Sampling, and the Quadrature Factorial Method under similar resource constraints. If the most accurate existing method, Hammersley Sequence Sampling, is afforded ten times the number of samples, it provides approximately the same degree of accuracy as the quadrature-based method. Two case studies on robust design confirmed the main conclusions and also suggest the quadrature-based method becomes more accurate as robustness improvements are made.