This paper conducts a reliability assessment of the tunnel face stability induced by an adjacent tunnel under incomplete information. The evaluation indicator in this study is the limit support pressure (LSP) for the tunnel excavation face, which is first determined through a detailed finite element analysis. Relying on the numerical results, a hybrid particle swarm optimization-neural network (PSO-NN) is developed to construct the meta-model for LSP. This study develops a framework of Monte Carlo simulation combing with the trivariate copula analysis of the cohesive strength, Poisson ratio, and internal friction angle, to assess the probability distribution of LSP with incomplete information. This study proposes an index α greater than 1.0, to quantify the copula's effect in forty-six illustrative cases. Finally, this paper examines the reliability of different existing formulas of LSP in the tunneling excavation procedure. Rankine and Terzaghi's formulas show a higher reliability value above 0.8. Furthermore, this study proposes a new safety factor for engineering design considering the uncertainties and copula's effect. Through further examining the performance of the new safety factor based on the Rankine and Terzaghi approaches, this study proposes a new procedure to determine LSP for a safe and efficient engineering design practice.