The researchers aimed to show that their models can accurately predict the durability of glass made from High Level Waste Sludge Batch 4. They conducted a variability study to test the models' reliability in predicting the quality of the vitrified waste product. By analyzing the chemical composition of the glass and comparing it to the predicted durability, they confirmed that the models are effective in controlling the process of making glass from the sludge batch. This study helps ensure that the glass produced meets the required standards for safe disposal.