A zero-inflated multivariate peaks-over-threshold model for serial multi-stage processing time data

초록

Serial multi-stage manufacturing process involves a sequence of interconnected processing steps. The complexity of each stage introduces challenges tied to the accumulation of variations, along with highly dependent structure among stages. A delayed or tardy process significantly affects the throughput of overall production by cumulative delays encountered across sequential stages. Incorporating zero-inflated data within target processing time limit and heavy-tailed characteristics, this study proposes two types of zero-inflated multivariate peaks-over-threshold (PoT) models called a zero-inflated multivariate generalized Pareto distribution. The propose models aim at extending the conventional multivariate PoT models by explicitly incorporating inflated zeros and dependence structure arising from evolutional manufacturing environments. By leveraging the angular representation and Pickands dependence, MLEs of the model parameters are derived. The inference procedure is developed using the asymptotic consistency and normality of MLEs. The proposed multivariate models are validated through real-world battery manufacturing process data. Zero inflation provides further insight into the underlying characteristics of processing time distributions in PoT applications within manufacturing systems. The proposed method facilitates improved industrial process optimization, especially in detecting and alleviating bottlenecks associated with both nominal operating conditions and sporadic extreme delays.

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