<p>In this paper, we introduce a novel two-stage sampling scheme for the minimum risk point estimation (MRPE) of the mean exponential lifetime under interval censoring, addressing the limitations of existing risk-efficient sequential procedures that require continuous monitoring and real-time detection of failures and are often operationally inconvenient. Our proposed procedure involves a first-stage sample size determined by a lower bound of the optimal sample size, followed by a second-stage sample size based on data-driven adjustment. We establish the asymptotic efficiency and risk efficiency properties through theoretical proofs and extensive Monte Carlo simulations. To illustrate the practical applicability of the procedure, we analyze a real-world dataset on remission times for bladder cancer patients, demonstrating its ability to efficiently estimate the exponential mean with a reduced sample size.</p>