Assigning a value to any property of the material in a container or in a lot, consignment, or delivery involves a measurement process that includes both sampling and testing procedures. The correctness of the value assigned depends upon the variability due to testing. Even when the variability due to testing is minimized by carefully developed procedures, correct and consistent estimates of the true value of the property are possible only when the sampling procedure avoids systematic bias, minimizes variations due to sampling, and provides a laboratory sample of adequate size.

Practice D2258 may not give the most efficient sampling plan that might be devised in special situations but does present a general procedure that gives satisfactory precision with an economical amount of sampling and one which does not require elaborate statistical computation based on previous knowledge of the amount of variation between primary sampling units (such as cases, beams or fabric packages), between units of the laboratory sample taken from the primary sampling units of the lot sample (such as yarn packages taken from a case) and between specimens taken from units of the laboratory sample (such as lengths of yarn taken from a yarn package or a fabric swatch taken from a roll or piece). Many plans that include stratified sampling can be found in textbooks.

The smallest number of specimens required for a given variability in the average result will usually be obtained by (1) maximizing the number of shipping containers in the lot sample, (2) taking a single package end per shipping container in the laboratory sample, and (3) taking only one specimen per package. Unfortunately, this is rarely the most economical way to test a product because it normally costs most to take a shipping container as part of the lot sample, costs an intermediate amount to take a package from a shipping container as part of a laboratory sample, and costs least to take and test a specimen from a package or yarn.

To minimize the cost of sampling a lot of material, it is necessary to agree on the required variance for the reported average for a lot of material:

Estimate the variance due to lot samples, the variance due to laboratory samples, and the variance due to testing specimens.

Calculate the total variance for average test results for several combinations of the number of lot samples, the number of laboratory samples per lot sample, and the number of specimens per laboratory sample.

Calculate the cost of performing each of the sampling schemes considered in 5.4.2.

Select the sampling scheme that ( 1) has the required precision and (2) is most economical to perform.