Methods and apparatus for hybrid outlier detection

Abstract

Methods and apparatus for data analysis according to various aspects of the present invention are configured to identify statistical outliers in test data for components, including hybrid outliers representing outliers within subsets of larger data populations.

1 . A test data analysis system for analyzing test data for multiple components fabricated on a wafer, comprising: 
 a memory configured to store the test data; and    a hybrid outlier system having access to the memory and configured to, for each of a plurality of test data for each of a plurality of selected components: 
 select a component as a central component;  
 identify a plurality of local components in a local area near the central component;  
 determine a derived value of the test data for the plurality of local components;  
 compare the test data for the central component to the derived value for the plurality of local components; and  
 identify whether the test data for the central component represents a hybrid outlier according to the comparison of the test data for the central component to the derived value for the plurality of local components.  
   
   
   
       2 . A test data analysis system according to  claim 1 , wherein hybrid outlier system is configured to normalize the test data for each component.  
   
   
       3 . A test data analysis system according to  claim 2 , wherein the hybrid outlier system is configured to compare the test data for the central component to the derived value for the plurality of test components by comparing the normalized test data for the central component to the derived value for the plurality of test components.  
   
   
       4 . A test data analysis system according to  claim 2 , wherein the test data comprises test data generated using multi-site testing, and wherein the hybrid outlier system is configured to normalize the test data for each component to counter an inconsistency induced by the multi-site testing.  
   
   
       5 . A test data analysis system according to  claim 1 , further comprising an outlier identification system configured to remove a global outlier from the test data before identifying whether the test data for the central component represents the hybrid outlier.  
   
   
       6 . A test data analysis system according to  claim 1 , wherein the derived value comprises an average value for the plurality of local components.  
   
   
       7 . A test data analysis system according to  claim 1 , wherein the hybrid outlier system is configured to identify the components in the plurality of local components according to a pattern, and wherein the hybrid outlier system is configured to automatically increase a size of the pattern until a minimum number of components satisfying a selected criterion are within the pattern.  
   
   
       8 . A computer-implemented method for analyzing test data for multiple components fabricated on a wafer, comprising: 
 selecting a component as a central component;    identifying a plurality of local components in a local area near the central component;    determining a derived value of the test data for the plurality of local components;    comparing the test data for the central component to the derived value for the plurality of local components; and    identifying whether the test data for the central component represents a hybrid outlier according to the comparison of the test data for the central component to the derived value for the plurality of local components.    
   
   
       9 . A computer-implemented method for analyzing test data according to  claim 8 , further comprising normalizing the test data for each component on the wafer.  
   
   
       10 . A computer-implemented method for analyzing test data according to  claim 9 , wherein comparing the test data for the central component to the derived value for the plurality of test components comprises comparing the normalized test data for the central component to the derived value for the plurality of test components.  
   
   
       11 . A computer-implemented method for analyzing test data according to  claim 9 , wherein: 
 the test data comprises test data generated using multi-site testing; and    normalizing the test data for each component comprises normalizing the test data to counter an inconsistency induced by the multi-site testing.    
   
   
       12 . A computer-implemented method for analyzing test data according to  claim 8 , wherein the derived value comprises an average value for the plurality of local components.  
   
   
       13 . A computer-implemented method for analyzing test data according to  claim 8 , further comprising removing a global outlier from the test data before identifying whether the test data for the central component represents the hybrid outlier.  
   
   
       14 . A computer-implemented method for analyzing test data according to  claim 8 , wherein identifying the components in the plurality of local components comprises identifying the components in the plurality of local components according to a pattern, and further comprising automatically increasing a size of the pattern until a minimum number of components satisfying a selected criterion are within the pattern.  
   
   
       15 . A computer program configured to cause a computer to analyze test data for components on a wafer, wherein the program causes the computer to: 
 select a component as a central component;    identify a plurality of local components in a local area near the central component;    determine a derived value of the test data for the plurality of local components;    compare the test data for the central component to the derived value for the plurality of local components; and    identify whether the test data for the central component represents a hybrid outlier according to the comparison of the test data for the central component to the derived value for the plurality of local components.    
   
   
       16 . A computer program according to  claim 15 , wherein the program causes the computer to normalize the test data for each component on the wafer.  
   
   
       17 . A computer program according to  claim 16 , wherein the program causes the computer to compare the test data for the central component to the derived value for the plurality of test components by comparing the normalized test data for the central component to the derived value for the plurality of test components.  
   
   
       18 . A computer program according to  claim 16 , wherein the test data comprises test data generated using multi-site testing, and wherein the hybrid outlier system is configured to normalize the test data for each component to counter an inconsistency induced by the multi-site testing  
   
   
       19 . A computer program according to  claim 15 , wherein the derived value comprises an average value for the plurality of local components.  
   
   
       20 . A computer program according to  claim 15 , wherein the program causes the computer to remove a global outlier from the test data before identifying whether the test data for the central component represents the hybrid outlier  
   
   
       21 . A computer program according to  claim 15 , wherein the components in the plurality of local components are selected according to a pattern, and wherein the program causes the computer to automatically increase a size of the pattern until a minimum number of components satisfying a selected criterion are within the pattern.