At the time of the new information technolo-gies, computer networks are inescapable in any large organization, where they are organized so as to form powerful internal means of communication. In a context of dependability, the reliability parameter proves to be fundamental to evaluate the performances of such sys-tems. In this paper, we study the reliability evaluation of a real computer network, through three reliability models. The computer network considered (set of PCs and server interconnected) is localized in a company established in the west of Algeria and dedicated to the production of ammonia and fertilizers. The result permits to compare between the three models to determine the most appropriate reliability model to the studied network, and thus, contribute to improving the quality of the network. In order to anticipate system failures as well as improve the reliability and availability of the latter, we must put in place a policy of adequate and effective maintenance based on a new model of the most common competing risks in maintenance, Alert-Delay model. At the end, dependability measures such as MTBF and reliability are calculated to assess the effectiveness of maintenance strategies and thus, validate the alert delay model.