As companies run their business (e.g., sales, procurement), they conduct a set of business processes that include activities and flows connecting them. There exist an enormous number of patterns of business processes, or process-patterns. This industrial paper proposes a new technique, RP2A (Rare Process-Pattern Analysis), to examine process-patterns for finding operational problems such as compliance violations. The technique analyzes system execution data (= event log and user information) stored in the system related to the processes. By a combination of process-pattern search and activity search, RP2A discovers potential problem process-patterns in terms of execution frequency. We also report an industrial case study carried out using the technique. By analyzing the system execution data corrected from the 6-month system operation, we identified all 373 process-patterns, and 31 potential problem process-patterns out of them. Then, 4 domain experts in the industry verified the 31 process-patterns and found that 18 process-patterns, namely more than half of them (58% (= 18/31)) contain actual problems. Almost problems are violations of internal policies which even the domain experts did not recognize. The technique succeeded in finding a kind of unknown problems in the business processes.