To make modern communication systems superior in performance and reliability to the previous generation sys- tems they can be supplied with heterogeneous communication links. Such links can dier in availability, link data throughputs, power consumption and reliability characteristics. To model the dynamic behaviour of the links with dierent properties a queueing system with non-reliable heterogeneous servers can be used. While the rst steps in the performance analysis of controllable heterogeneous queueing systems have already been developed for completely reliable servers, a missing link to an applicability of these models is reliability analysis of such queues with servers subject to failures. In this paper we use a matrix transform based method to evaluate reliability measures such as reliability function and mean time to the rst failure for each server separately and for the total service facility under the xed threshold allocation control policy. The reliability functions are obtained in terms of the Laplace transform and numerical inversion algorithm is used to get the time dependent functions. Additionally a new discrete reliability metric which can be treated as a discrete counterpart to the distribution of the time to failure is introduced.