This article concerns a profit model in a repair limit replacement problem with imperfect repair. If a system fails, we should decide whether we repair the failed system (repair option) or replace it by new one (replacement option with a lead time). We assume that repair times are random variables and can be estimated before repair with estimation error. If the estimated repair time is less than the specified limit (repair time limit), the failed unit is repaired but the unit after repair is different from the new one (imperfect repair). Otherwise, we order a new unit to replace the failed unit. The long run average profit (expected profit rate) is used as an optimization criterion and the optimal repair time limit maximizes the expected profit rate. Some special cases are derived.