The fundamental idea behind the expected quantile improvement (EQI) acquisition function is 'tunable precision' where a particular observation's precision can be adjusted using more computational budget. In a physical system, noise can come from various sources, including environmental variables that are outside of our control and measurement errors. In this paper for in silico experiments, noise was added to the model predictions to imitate noise in a physical system. Mathematically, tunable precision can be implemented by taking a sample mean of N independent Monte Carlo drawings: