In the scheduling of hard real-time systems on multicore platforms, significant unpredictability arises from interference caused by shared hardware resources. The objective of this paper is to offer a schedulability analysis for such systems by assuming a general model that introduces interference as a time parameter for each task. The analysis assumes constrained deadlines and is provided for fixed priorities. It is based on worst-case response time analysis, which exists in the literature for monocore systems. We demonstrate that the worst-case response time is an upper bound, and we evaluate our proposal with synthetic loads and execution on a real platform.