In this paper, we try to propose four replacement policies including general age replacement policy (GARP), replacement first policy (RFP), replacement last policy (RLP), and replacement next policy (RNP) for a system based on a one-cycle criterion. The system is subject to two kinds of failures whose probabilities are age-dependent. We use minimal repair to fix the Type I failure (minor failure) and we do replacement to remove the Type II failure (catastrophic failure). We formulate all mathematical models for four replacement policies and we also discuss the optimal schedules that minimize the expected cost rate in one replacement cycle analytically. We present an optimal computational algorithm to determine the four replacement policies. Finally, we give some numerical examples to fit our research and also compare the expected cost rate function between one-cycle criterion and the infinite horizon (renewal reward) assumptions under four replacement policies.
