Optimal sample size for composite sampling with subsampling, when estimating the proportion of pecky rice grains in a field

摘要

The proportion of pecky rice grains has been estimated empirically using composite sampling with subsampling. The procedure can be summarized as follows: (1) A fixed number of rice plants, n 1, are drawn at random in the paddy field; (2) all of the rice grains in the collected rice plants are mixed well to form a composite; (3) a portion of the grains, n 2, is drawn at random from the composite; and (4) the collected grains are examined by eye to estimate the proportion of pecky rice grains. We propose a method for determining the optimal sample size in estimating the proportion of defective items by this type of composite sampling with subsampling. Spatial heterogeneity in the proportion of defective items is included in the estimation. We use Taylor’s power law to describe the density-dependent change of spatial heterogeneity. In controlling the precision of the estimate, we use the relative precision, D, which is defined by the coefficient of variation of the estimated proportion. We propose a rejection procedure in which the product is rejected if the estimate of proportion with D=0.25 is larger than a predetermined tolerable threshold of proportion. We also consider another control criterion in which the consumer’s risk, , is controlled by a zero-tolerance method. Finally, we examine the relationship between the two control criteria.