Gaussian process regression is widely used for modeling responses in both physical and computer experiments. In practice, data from physical experiments may include replications and be subject to censoring due to equipment limitations or contextual constraints, and such datasets can be large, posing a scalability challenge for standard Gaussian process inference. Motivated by a real-world industrial research study, we develop a Gaussian process modeling framework that efficiently analyzes large replicated and censored data. Our approach integrates a Vecchia approximation for computational scalability with a likelihood-based formulation that fully exploits replication and rigorously incorporates information from censored observations, analogous to exact simulation from truncated distributions. Through experiments on synthetic data and a real case study from industrial research, we demonstrate that the proposed method yields improved predictive accuracy and reliable uncertainty quantification compared to existing approaches, making it well suited for large-scale applications with structured replication and incomplete data.

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