In many situations, the system failures depend on the operating environmental conditions that vary on time, usually with periodical manners. We use nonhomogeneous Poisson processes whose rate functions exhibit cyclic behavior as well as a long-term evolutionary trend to model the stochastic process of the failures when the rate of occurrence of the failures varies periodically, for example from day to day or between seasons. In this study, we compare optimal policies under the nonho-mogeneous process with/without a cyclic component in the failure rate function. The analytical re-sults for various situations are presented along with numerical examples using simulated data.