Holistic modeling and analysis of multistage manufacturing processes with sparse effective inputs and mixed profile outputs

In a Multistage Manufacturing Process (MMP), multiple types of sensors are deployed to collect intermediate product quality measurements after each stage of manufacturing. This study aims at modeling the relationship between these quality outputs of mixed profiles and sparse effective process inputs. We propose an analytical framework based on four process characteristics: (i) every input only affects the outputs of the same and the later stages; (ii) the outputs from all stages are smooth functional curves or images; (iii) only a small number of inputs influence the outputs; and (iv) the inputs cause a few variation patterns on the outputs. We formulate an optimization problem that simultaneously estimates the effects of process inputs on the outputs across the entire MMP. An ADMM consensus algorithm is developed to solve this problem. This algorithm is highly parallelizable and can handle a large amount of data of mixed types obtained from multiple stages. The ability of this algorithm in estimations, selecting effective inputs, and identifying the variation patterns of each stage is validated with simulation experiments.