High utility pattern mining is an interesting yet challenging problem. The intrinsic computational cost of the problem will impose further challenges if efficiency in addition to the efficacy of a solution is sought. Recently, this problem was studied on interval-based event sequences with a constraint on the length and size of the patterns. However, the proposed solution lacks adequate efficiency. To address this issue, we propose a projected upper bound on the utility of the patterns discovered from sequences of interval-based events. To show its effectiveness, the upper bound is utilized by a pruning strategy employed by the HUIPMiner algorithm. Experimental results show that the new upper bound improves HUIPMiner performance in terms of both execution time and memory usage.