In this study, we explore the impact of a system administrator's risk preference on the process of selecting the optimal maintenance policy for systems that experience continuous-time Markovian deterioration and may encounter non-self-announcing failures. Our focus lies in the comparative evaluation of various maintenance strategies. The decision maker periodically inspects the system at designated decision epochs, identifying its current state as good, poor, or failed. Based on this assessment, the decision maker chooses an available action, such as doing nothing, repairing, or replacing the system. When the system fails, the failure may go undetected until the next inspection epoch. The primary objective is minimizing the expected long-run cost rate, encompassing various cost components, including inspection, downtime, and maintenance expenses. Through simulation examples, we analyze the effect of various cost parameters on the optimum inspection period and policy using the mean-variance approach, demonstrating a practical application in the process. By examining the system administrator's risk preference, we aim to shed light on its influence on optimal policy selection, thereby providing valuable insights for effective maintenance decision-making in scenarios involving continuous-time Markovian deterioration and non-self-announcing failures.