Network of several test benches for a turbomachine, each test bench for a turbomachine comprising a system for managing the predictive maintenance of the bench, each bench comprising a plurality of appliances (A, B, C,...) and means to maintain these appliances, the system being implemented on a computing device and being configured to carry out a maintenance method, the maintenance method comprising the following steps: - estimate n parameters (p 1A, p 2A,..., p nA) corresponding to a respective appliance (A, B, C...) of the test bench and its use, the n parameters comprising parameters of which the value is obtained from measurements at a given time and parameters of which the value is pre-determined at that given time; - increment, with the estimated parameters, a database including data relating to the bench and its use; - determine, at a given time and for each appliance, an index (i A) which varies according to the content of the database at that given time as well as at preceding times according to the following formula: i A = 1 ∑ j = 1 j = n γ jA γ 1 A γ 2 A... γ nA. p 1 A ∈ α 1 A β 1 A t 1 A p 2 A ∈ α 2 A β 2 A t 2 A... p nA ∈ α nA β nA t nA in which the coefficients γ are weighting factors to be applied to each parameter respectively; the row j of the matrix has the value of 1 if the parameter p j resulting from a measurement has been present in the predefined interval [α jA,β jA] for a duration of at least t jA; otherwise, the value of the row j is 0; and when the parameter p j is estimated by predetermination, the row j of the matrix has the value of p j; - generating an information that an action is to be carried out on a given appliance (A, B, C,...) when the index (i A) of the corresponding appliance is greater than or equal to a given criterion (i AC), the method further comprising, following the generation of the information, a step of maintenance of the given appliance during which the action to be taken is carried out, preferably by an operator; the network being such that when an action is carried out on a piece of appliance (A, B, C,...) of one of the benches, the database of the bench in question is shared with the other benches of the network and the definition (p, α, β, t, γ et i C), as a function of the database, of the criterion of the said piece of appliance (A, B, C,...) on which an action was carried out, is updated by means of self-learning on all of the benches (2, 2') of the network. - estimate n parameters (p 1A, p 2A,..., p nA) corresponding to a respective appliance (A, B, C...) of the test bench and its use, the n parameters comprising parameters of which the value is obtained from measurements at a given time and parameters of which the value is pre-determined at that given time; - increment, with the estimated parameters, a database including data relating to the bench and its use; - determine, at a given time and for each appliance, an index (i A) which varies according to the content of the database at that given time as well as at preceding times according to the following formula: i A = 1 ∑ j = 1 j = n γ jA γ 1 A γ 2 A... γ nA. p 1 A ∈ α 1 A β 1 A t 1 A p 2 A ∈ α 2 A β 2 A t 2 A... p nA ∈ α nA β nA t nA in which the coefficients γ are weighting factors to be applied to each parameter respectively; the row j of the matrix has the value of 1 if the parameter p j resulting from a measurement has been present in the predefined interval [α jA,β jA] for a duration of at least t jA; otherwise, the value of the row j is 0; and when the parameter p j is estimated by predetermination, the row j of the matrix has the value of p j; - generating an information that an action is to be carried out on a given appliance (A, B, C,...) when the index (i A) of the corresponding appliance is greater than or equal to a given criterion (i AC), the method further comprising, following the generation of the information, a step of maintenance of the given appliance during which the action to be taken is carried out, preferably by an operator; the network being such that when an action is carried out on a piece of appliance (A, B, C,...) of one of the benches, the database of the bench in question is shared with the other benches of the network and the definition (p, α, β, t, γ et i C), as a function of the database, of the criterion of the said piece of appliance (A, B, C,...) on which an action was carried out, is updated by means of self-learning on all of the benches (2, 2') of the network. the method further comprising, following the generation of the information, a step of maintenance of the given appliance during which the action to be taken is carried out, preferably by an operator; the network being such that when an action is carried out on a piece of appliance (A, B, C,...) of one of the benches, the database of the bench in question is shared with the other benches of the network and the definition (p, α, β, t, γ et i C), as a function of the database, of the criterion of the said piece of appliance (A, B, C,...) on which an action was carried out, is updated by means of self-learning on all of the benches (2, 2') of the network.