Abstract: To model the stream of variation’s propagation and accumulation in multi- station manufacturing processes, the relationships among the input errors, system errors, random errors and output errors at a station are investigated and a corresponding model and its solution method are presented. Based on Taylor formula and the practical experiences assumptions, a semi-parametric regression model is proposed to denote the relationship between station input errors and output errors by the parameterized method and the relationship between station output errors and system errors by the non-parametric method. By calculation of the smoothing parameter using a generalized cross validation method and the regularize matrix on the practical experiences, a penalized least squares method is used to offer the parametric and non-parametric estimation of the proposed model. A two-station grinding example is taken to illustrate that the proposed model is able to not only model correctly the variation propagation and accumulation in multi-station manufacturing processes with the separation of system errors and random errors, but also show a good interpretability and applicability.

Key words: Penalized least squares method, Random errors, Semiparametric regression model, Stream of variation, System errors, Design efficiency, Fuzzy clustering, Fuzzy sets, Green design, Optimization strategy