Ch. 21. Subsampling designs in industry: Statistical inference for variance components

Abstract

Publisher Summary In many industrial problems, variability among the units can be attributed to various sources that are hierarchical in their occurrences. As the sources of variability are hierarchical in nature, the estimation of corresponding variance components would also require successive subsampling. This successive subsampling results in a “hierarchical” or “nested” design. In such designs, the sources of variability or factors are nested and this nesting is determined by the sampling design. As unit-to-unit variability, the lowest in hierarchy, is always assumed to be present, it is usually termed as the “random error.” Apart from random error, there are three other factors, and such a design is often termed as a “three-stage nested design.” A p-stage nested design is defined similarly. Factors can be fixed or random. However, by the very nature of subsampling, once a factor is assumed random, all factors that are lower in hierarchy are also deemed random. Because nested designs are often employed with the objective of estimating various sources of variability, all the factors are usually chosen as random. This chapter discusses nested designs in the random effects framework, as this is the most common situation in industrial problems.