Uncertainties in the performance of engineering systems arise due to idealizations of geometry, material behavior, and loading history. Uncertainties in the geometry are often related to manufacturing processes, while the uncertainty in the material behavior often arises out of materials processing. In this two-part study, we analyze the effect of uncertainty in material behavior on the performance of bonded assemblies in general, but motivated by the example of a fiber-optic system. In the fiber-optic system, the motion of the surface emitting laser relative to the substrate (to which the laser is bonded) due to the viscoelastic behavior of the bond epoxy causes a loss in the light coupled to the fiber. In the first part of the paper, we develop models to describe the shear displacement and the shear stress in bond layer of the fiber-optic assembly. In the second part, we characterize through extensive experimentation the uncertainty in the viscoelastic behavior of the bond epoxy and use it to develop guidelines for the design of the bonded system.