1-General Purpose Graphical Processing Units (GPGPUs) are increasingly used in safety critical applications such as the automotive ones. Hence, techniques are required to test them during the operational phase with respect to possible permanent faults arising when the device is already deployed in the field. Functional tests adopting Software-based Self-test (SBST) are an effective solution since they provide benefits in terms of intrusiveness, flexibility and test duration. While the development of the functional test code addressing the several computational cores composing a GPGPU can be done resorting to known methods developed for CPUs, for other modules which are typical of a GPGPU we still miss effective solutions. This paper focuses on one of the most relevant module consists on the scheduler core which is in charge of managing different scalar computational cores and the different executed threads. At first, we propose a method for evaluating the fault coverage that can be achieved using an application program. Then, we provide some guidelines for improving the achieved fault coverage. Experimental results are provided on an open-source VHDL model of a GPGPU.