Due to changes of the thermal environment, thermal stresses are produced in structures. Two approaches based on the stochastic process theory are used to describe this phenomenon. The structure is idealized as a long hollow viscoelastic cylinder. Two sites are considered: Barrow (AK) and Yuma (AZ). First passage concepts are applied to characterize the reliability of the system. Crossings are assumed to follow either the behavior of the Poisson process or Markov process. In both cases, the distribution of the time to first passage is taken to be the exponential distribution. Because the material is viscoelastic, statistically and time varying barriers (strengths) with Normal, Log-Normal, or Neibull distributions are considered. Degradation of the barriers by aging and cumulative damage are incorporated in the analysis. / Ph. D. / incomplete_metadata