In this paper, we propose an approach to estimate the Worst Case Response Time (WCRT) of tasks in a preemptive multi-tasking single-processor real-time system with a set associative cache. The approach focuses on analyzing the cache reload overhead caused by preemptions. We combine inter-task cache eviction behavior analysis and path analysis of the preempted task to reduce, in our analysis, the estimate of the number of cache lines that can possibly be evicted by the preempting task (thus requiring a reload by the preempted task). A mobile robot application which contains three tasks is used to test our approach. The experimental results show that our approach can tighten the WCRT estimate by up to 73% over prior state-of-the-art.