A methodology for data-driven adjustment of variation propagation models in multistage manufacturing processes

Abstract

In the current paradigm of Zero Defect Manufacturing, it is essential to obtain mathematical models that express the propagation of manufacturing deviations along Multistage Manufacturing Processes (MMPs). Linear physical-based models such as the Stream of Variation (SoV) model are commonly used, but its accuracy may be limited when applied to MMPs with a large amount of stages, mainly because of the modeling errors at each stage that are accumulated downstream. In this paper we propose a methodology to calibrate the SoV model using data from the inspection stations and prior engineering-based knowledge. The data used for calibration does not contain information about the sources of variation, and they must be estimated as part of the model adjustment procedure. The proposed methodology consists of a recursive algorithm that minimizes the difference between the sample covariance of the measured Key Product Characteristic (KPC) deviations and its estimation, which is a function of a variation propagation matrix and the covariance of the deviation of the variation sources. To solve the problem with standard convex optimization tools, Schur complements and Taylor series linearizations are applied. The output of the algorithm is an adjusted model, which consists of a variation propagation matrix and an estimation of the aforementioned variation source covariance. In order to validate the performance of the algorithm, a simulated case study is analyzed. The results, based on Monte Carlo simulations, show that the estimation errors of the KPC deviation covariances are proportional to the measurement noise variance and inversely proportional to the number of processed parts that have been used to train the algorithm, similarly to other process estimators in the literature.