Design Evaluation of Multi-station Assembly Processes by Using State Space Approach

This paper considers the problem of evaluating and benchmarking process design configuration in a multi-station assembly process. We focus on the unique challenges brought by the multi-station system, namely, (1) a system level model to characterize the variation propagation in the entire process, and (2) the necessity to describe the system response to variation inputs at both global (system level) and local (station level and single fixture level) scales. State space representation is employed to recursively describe the propagation of variation in such a multi-station process, incorporating process design information such as fixture locating layout at individual stations and station-to-station locating layout change. Following the sensitivity analysis in control theory, a group of hierarchical sensitivity indices is defined and expressed in terms of the system matrices in the state space model, which are determined by the given process design configuration. Implication of these indices with respect to variation control is discussed and a three-step procedure of applying the sensitivity indices for selecting a better design and prioritizing the critical station/fixture is presented. We illustrate the proposed method using the group of sensitivity indices in design evaluation of the assembly process of a SUV (Sport Utility Vehicle) side panel. * Corresponding author, Tel: (608)265-3457, Fax: (608)262-8454, Email: [email protected] 2 NOMENCLATURE A dynamic matrix B input matrix C observation matrix KCC Key Control Characteristics KPC Key Product Characteristics K0 covariance matrix of part deviation Kp covariance matrix of fixture deviation KY covariance matrix of KPCs Kε covariance matrix of uncertainty term ε P fixture deviation vector W weighting coefficient matrix X part deviation vector Y observation vector k station index n dimension of part deviation vector X mk dimension of fixture deviation P(k) qk dimension of observation vector Y(k) state transition matrix uncertainty term ) (k the model matrix of station k, equals to ) ( ) ( k k , N B C , p the p th column vector in qp the q th element in column vector p 2 output variance vector of KPCs on the final product 2 kp variance of the p th locating feature at station k 2 k variance vector of all fixtures at station k, T 2 2 21 2 ] [ k km kp k k σ σ σ = " " 2 input variance vector of the entire process, T T 2 T 2 T 2 1 2 ] [ N k input " " = unmodeled process deviation additive sensor noise