In this article we consider the problem of determining the reliability of a series chain consisting of k identical links. The stress acting on the chain is known a prior, i.e., deterministic. We consider the case of repeated applications of stresses, i.e., cycles of stresses. We also consider the change of the distribution of strengths of the links with time, i.e., (the change of the distribution) during different cycles of stresses. We find an expression of the reliability function after m cycles of stresses. The strengths of the links of the chain could be random independent, random fixed or deterministic. A two-sided confidence interval for the reliability is obtained. As an application, the cases of exponential and Rayleigh distributions are studied. In order to highlight the results obtained a numerical illustration is performed.