Glasses are nonequilibrium materials that continuously relax toward the metastable supercooled liquid state. As such, the properties of a glass depend on both its composition and thermal history. When an initially cooled glass is subjected to additional thermal cycles, relaxation during the heat treatment is accelerated, leading to changes in the macroscopic properties of the glass. This relaxation behavior is intrinsic to the glassy state and of critical interest to the high-tech glass industry. In many practical cases, the magnitude of the relaxation is less important than the variability of the relaxation effects due to slight variations in the thermal history experienced by the glass. These fluctuations in thermal history can occur either during the initial glass formation or during the subsequent heat treatment cycle(s). Here we calculate the variation in relaxation behavior using a detailed enthalpy landscape model, showing that the relaxation variability can be reduced dramatically by increasing the fragility of the system.