Adaptive sampling procedure is a method of selecting samples where the selection of sampling units depend on the values of the variable of interest observed during the survey. Adaptive sampling differs from the conventional sampling in the sense that in conventional sampling the procedure for selecting the sample does not depend on any values of the variable of interest and the entire sample is selected prior to the survey. Adaptive cluster sampling is a form of adaptive sampling where an initial sample is selected by some probability rule. Then if any initially selected unit satisfies a fixed condition, then its neighboring units are added to the sample. Again if any added unit meets the condition its neighboring units are added to the sample. The procedure continues until the whole cluster of units comes to the sample. It is a powerful method for estimating unknown characteristics of a population when the population is highly clumped with clumps widely separated. For example, to study a rare kind of tree in a forest, to investigate a rare contagious disease in an area, to survey the pollution level in a certain region, to assess the abundance of a rare animal species are the common situations. Adaptive cluster sampling procedures are designed to best possible for the above situations. Adaptive cluster sampling designs are the natural extension of conventional designs. Many real sampling situations where the whole population is unevenly distributed leads to the adaptive sampling strategy. For a given sampling effort, adaptive cluster sampling procedure gives the precise estimates for the above situations in comparison with conventional designs such as SRS, Systematic etc. In Adaptive cluster sampling designs, the procedure of adding neighboring units increases the yield of the sample so that more elements can be observed.

Although there are a lots of advantages, some difficulties may occur for designing such procedures. In Adaptive cluster sampling, the final sample size is random and therefore unknown. For this and other reasons, the appropriate theory has not been developed yet for using a pilot survey to establish a sampling experiment with a given precision of estimation. And if an inappropriate criterion C for adding neighborhoods is used, then there may be a large or a very few number of sampling units. If too many units are being added at each initially selected unit, we end up sampling with too many units. On the other hand, we might not get enough units. Therefore, the experiment may be very costly or a very low precision may be achieved. In many real life situations such as in ecological, environmental or epidemiological survey, the high values and low values of the variable of interest tend to be associated with neighboring high and low values respectively through such factors as spatial pattern or social connections. The usual adaptive cluster sampling methods may produce networks with a large number of units; consequently we may end up sampling with a large number of units.

In this study, using order statistics three approaches have been proposed to overcome the above difficulties in a optimal manner. The approaches though different can be used in different practical situations. For each approach the estimator of the population mean is proposed and the variances of the estimators are derived. The unbiased estimation and the estimated variances are also demonstrated. To understand the necessary calculations and computations, an example is illustrated for each case. Finally, conclusions are drawn for each approach.