Maintaining the reliability of components or systems that are subject to degradation failures is an old and challenging problem. The traditional way to deal with this problem has been to systematically replace parts so that certain reliability, and possibly cost, criteria are satisfied. More recently, new technologies have been developed that allow nondestructive inspections of increasing precision. Thus, replacements may be based now on observations made at these inspections. In a first model, we consider the important case where degradation and failure result from the growth of a crack that has developed within the component of interest, this growth being assumed deterministic. A probabilistic model is presented for the fatigue reliability and cost analysis of such components subject to periodic nondestructive inspections. Some figures of merit considered include the hazard function, an approximation of the cost per unit of service time, and the mean time between failures. A numerical example is given that focuses on the effect of inspections on the hazard function. This model is then extended in order both to handle the possible stochasticity of different parameters, and to allow the dynamic scheduling of inspections from observations. The model is not restricted to the crack growth type degradation. Finally, a computer code with an interface between the Fortran and S-plus languages is developed so that important quantities like the probabilities of failure, of replacements, or the hazard function are calculated in the case where the degradation law parameters are random. The code also provides graphs for the failure time density and the hazard function. Thus, for these functions, the effect of modifying model inputs may be appreciated both numerically and graphically. Numerical examples are given for two crack growth degradation cases, where the growth obeys Paris Law;