In the context of lifetesting, an asymptotically risk-efficient procedure for the estimation of the exponential mean lifetime is considered when the survival times of the units are subject to random censorship. The loss function is the sum of squared error due to estimation, cost of recruitment of the units, and cost of total time on test. Asymptotic properties of the sequential estimator and stopping time are described as the per unit cost of total time on test decreases to zero.
"Time Sequential Estimation of the Exponential Mean Under Random Withdrawals." Ann. Statist. 14 (2) 607 - 618, June, 1986. https://doi.org/10.1214/aos/1176349941