The aim of this paper is to present a stochastic model to characterize the failure distribution of multi-unit systems when the current units state is imperfectly monitored. The definition of the hazard rate process existing with perfect monitoring is extended to the realistic case where the units failure time are not always detected (non-detection events). The so defined observed hazard rate process gives a better representation of the system behavior than the classical failure rate calculated without any information on the units state and than the hazard rate process based on perfect monitoring information. The quality of this representation is, however, conditioned by the monotony property of the process. This problem is mainly discussed and illustrated on a practical example (two parallel units). The results obtained motivate the use of the observed hazard rate process to characterize the stochastic behavior of the multi-unit systems and to optimize for example preventive maintenance policies.