Signatures (D-spectra) are used successfully in the recent years for analysis of complex systems consisting of unreliable components. This paper presents a general description of systems whose analysis is performed by means of signature. This approach is applied to an investigation of a queueing system with an unreliable server. Server’s working time is described by means of a D-spectrum. A failure of the server during the service of a claim implies a loss of the latter. After the servicing (successful one or not) ends, the server does not receive new claims for service during some time interval, i.e. it is blocked. Formulas are derived for such indices of service efficiency as probability of claim loss, load coefficient, mean waiting time for a claim, etc. A numerical example shows how these indices depend on initial data.