asymptotic properties of the sample mean in adaptive sequential sampling with multiple selection criteria

‎we extend the method of adaptive two-stage sequential sampling to‎‎include designs where there is more than one criteria is used in‎‎deciding on the allocation of additional sampling effort‎. ‎these‎‎criteria‎, ‎or conditions‎, ‎can be a measure of the target‎‎population‎, ‎or a measure of some related population‎. ‎we develop‎‎murthy estimator for the design that is unbiased estimators for‎‎the population mean‎, ‎and propose another‎, ‎more efficient‎,‎estimator‎. ‎we investigate asymptotic properties of this estimator‎.‎we use a simulation study to investigate design properties of the‎‎multi-criteria adaptive sequential sampling scheme and also some‎‎estimator properties under the design‎.