Restricted randomization: Difference between revisions

Revision as of 18:40, 18 March 2012

Revision as of 04:17, 25 March 2012

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Consider a batch process that uses 7 monitor wafers in each run. The plan further calls for measuring a [[response variable]] on each wafer at each of 9 sites. The organization of the [[sampling plan]] has a hierarchical or nested structure: the batch run is the topmost level, the second level is an individual wafer, and the third level is the site on the wafer.

The total amount of data generated per batch run will be 7 *  e· 9  =  63 observations. One approach to analyzing these data would be to compute the [[mean]] of all these points as well as their [[standard deviation]] and use those results as responses for each run.

Analyzing the data as suggested above is not absolutely incorrect, but doing so loses information that one might otherwise obtain. For example, site 1 on wafer 1 is physically different from site 1 on wafer 2 or on any other wafer. The same is true for any of the sites on any of the wafers. Similarly, wafer 1 in run 1 is physically different from wafer 1 in run 2, and so on. To describe this situation one says that sites are nested within wafers while wafers are nested within runs.