A long hollow cylinder with five layers, subjected to a random thermal environment is analyzed. The random thermal environment includes the ambient air temperature, solar radiation and wind speed. The location of interest is Phoenix, Arizona. The governing differential equation is the so-called one-dimensional Fourier heat conduction equation in cylindrical coordinates. An implicit finite difference scheme is developed to obtain temperature responses inside the cylinder. Given the linear elastic behavior of materials involved, induced stresses and strains are evaluated at the end of each time step of the finite difference scheme. A statistical analysis is then carried out to determine the probability of failure of the propellant and hence the service life of the motor can be computed. / Ph. D.