<p>In this study, a reliability model grounded in Markov reward processes is introduced to evaluate the performance behavior of <i>k</i>-out-of-<i>n</i> systems with competing risks. These risks stem from two failure modes: one occurs when the system reaches an absorbing condition, and the other arises once the number of transfers from a perfect to an imperfect functioning state reaches a specified threshold. Identifying the optimal component configuration and the best redundancy strategy is crucial for designing reliable and economical <i>k</i>-out-of-<i>n</i> systems. For this purpose, a two-stage optimization model is constructed with the objective of minimizing the expected overall cost with specified reliability requirements. Its first stage involves searching for the optimal values of <i>k</i> and <i>n</i>, while the second stage focuses on determining the optimal constraint regarding the number of transfers. By employing the theory of aggregate stochastic processes, necessary model parameters are defined and their analytical formulas are derived. Meanwhile, corresponding simulation procedures are presented to verify the accuracy of the obtained formulas. Subsequently, a 1-D search algorithm for addressing our two-stage optimization model is provided. A numerical example in the context of offshore oil platform power systems is showcased to elucidate the reliability model and two-stage optimization model.</p>