Restricted randomization: Difference between revisions

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Many [[process (engineering)|processes]] have more than one source of [[statistical dispersion|variation]] in them. In order to [[variance reduction|reduce variation]] in processes, these multiple sources must be understood, and that often leads to the concept of nested or hierarchical data structures. For example, in the semiconductor industry, a [[batch production|batch process]] may operate on several [[wafer (electronics)|wafers]] at a time (wafers are said to be '''nested''' within batch). Understanding the input variables that control variation among those wafers, as well as understanding the variation across each wafer in a run, is an important part of the strategy for minimizing the total variation in the system.

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As a consequence of this nesting, there are restrictions on the randomization that can occur in the experiment. This kind of restricted randomization always produces nested sources of variation. Examples of nested variation or restricted randomization discussed on this page are '''split-plot''' and '''strip-plot''' [[experimental design|designs]].

The objective of an experiment with this type of sampling plan is generally to reduce the variability due to sites on the wafers and wafers within runs (or batches) in the process. The sites on the wafers and the wafers within a batch become sources of unwanted variation and an investigator seeks to [[robustification|make the system robust]] to those sources -- insources—in other words, one could treat wafers and sites as noise factors in such an experiment.

Because the wafers and the sites represent unwanted sources of variation and because one of the objectives is to reduce the [[process sensitivity]] to these sources of variation, treating wafers and sites as [[random effect]]s in the analysis of the data is a reasonable approach. In other words, nested variation is often another way of saying nested random effects or nested sources of noise. If the factors "wafers" and "sites" are treated as random effects, then it is possible to estimate a [[variance component]] due to each source of variation through [[analysis of variance]] techniques. Once estimates of the variance components have been obtained, an investigator is then able to determine the largest source of variation in the process under experimentation, and also determine the magnitudes of the other sources of variation in relation to the largest source.