This study aims to understand the viscosity variation of amorphous materials, and hence establish a theoretical model for reliable applications. The investigation was carried out by simplifying an amorphous system to a mixture of many subsystems which switch their energy states and relaxation processes stochastically. The response of the macroscopic system is then treated as an ensemble average of relaxations of individual subsystems. Our derivation illuminates the transition from exponential to nonexponential relaxation and that the sudden increase of fragility in the viscosity-temperature relation with reducing temperature could be attributed to the bifurcation from the harmonic mean of the subsystems towards the arithmetic mean. The successful application of our model to the amorphous selenium indicates that the model captures the fundamental mechanism of viscosity variation.